https://osf.io/tj2sx/files/osfstorage/68f3de3e3c15ecd6a0c3fec6
https://chatgpt.com/share/68f3e129-a2e8-8010-b19c-2127413c0d6b

Observer-Centric Neurocybernetics: Unifying Closed-Loop Control, Language-Game Semantics, and Hinge Hyperpriors for Brain Science

0. Executive Overview — Diagrams Pack

Figure 0-A. The Observer Loop (Measure → Write → Act)

Diagram (captioned flow):
World state x_t → Measure M → outcome label ℓ_t → Write W (append to Trace T_t) → Act Π (policy reads T_t) → World updates to x_{t+1}.

One-line mechanics (paste under the figure):
Trace update: T_t = T_{t−1} ⊕ e_t. (0.1)
Latching (fixedness): E[e_t ∣ T_t] = e_t and Pr(e_t ∣ T_t) = 1. (0.2)
Policy reads the record: u_t = Π(T_t); branch diverges if the write differs. x_{t+1} = F(x_t, u_t, T_t). (0.3)

Rigour anchor. Latching is “conditional-expectation fixedness” of past events in the observer’s filtration; policy-read causes branch-dependent futures.

Figure 0-B. Thermostat-with-a-Notebook Analogy

Diagram (captioned flow):
Read room → if cold, write “heat_on” in notebook → heater turns on because controller reads the notebook → tomorrow is warmer → the note can’t be “unwritten” for the controller’s next step.

Minimal math under the picture:
Notebook write: e_t = “heat_on”; T_t = T_{t−1} ⊕ e_t. (0.4)
Delta-certainty of your own note: Pr(e_t = “heat_on” ∣ T_t) = 1. (0.5)
Why tomorrow changes: u_t = Π(T_t), so F(x_t, Π(…⊕“heat_on”), T_t) ≠ F(x_t, Π(…⊕“off”), T′_t). (0.6)

Figure 0-C. “Agreement You Can Trust” Panels

Layout (four tiles):

CSA@3 trend (top strip).
ε heatmap (critic-pair order sensitivity).
Redundancy index (fragments per claim in Trace).
CWA lamp (green/red “Averaging is legal?”).

One-line definitions under the panel:
Commutation on item d: A∘B(d) = B∘A(d). (0.7)
Order-sensitivity: ε_AB := Pr[A∘B ≠ B∘A]. (0.8)
CSA majority (k=3 critics): CSA@3 = mean_d[ majority label unchanged by any order ]. (0.9)
CWA pass rule: CWA_OK ⇔ [ CSA@3 ≥ 0.67 ] ∧ [ p̂ ≥ α ] ∧ [ max ε_AB ≤ 0.05 ], α=0.05. (0.10)

Operational note. These panels are the “go/no-go” for pooling across participants or sessions; if CWA fails, report per-case (SRA) only.

Figure 0-D. The Trace Ledger (Immutability at a Glance)

Diagram (captioned flow):
Append-only Trace with hash chain inside each session; daily Merkle root; dataset root for exports.

One-line formulas under the figure:
Hash chain: h₀ := 0; h_t := H(h_{t−1} ∥ canonical_json(e_t)). (0.11)
Verify trace: VerifyTrace(T) = 1 iff recomputed h_T equals stored h_T. (0.12)

Why it matters. Hash-chained writes make latching operational (tamper-evident past), so conditioning on your own record is well-defined for the controller Π.

Figure 0-E. System Planes (Where Each Step Runs)

Diagram (captioned boxes):
Data Plane — measurement hot-path, Trace writes, CWA-gated pooling.
Control Plane — Ô policy, tick cadence, safety gates.
Audit Plane — immutable ledger, certificate logs, exports.

Invariants under the figure:
Irreversible writes at tick τ_k; pooling only if CWA.score ≥ θ; slot conservation on buffers/tools. (0.13)

Figure 0-F. One-Minute CWA Certificate Checklist

Diagram (checkbox list beside the CWA lamp):

□ Three independent, non-mutating critics (units/invariants, contradiction vs Given, trace-referencer). (0.14)
□ Order test: all ε_AB ≤ 0.05 (swap critic order on a held-out batch). (0.15)
□ Permutation p-value: p̂ ≥ 0.05 under order+phase shuffles. (0.16)
□ CSA threshold: CSA@3 ≥ 0.67 (majority label stable). (0.17)
□ Redundant traces: ≥2 fragments/claim (e.g., tool log + hash). (0.18)
→ If all boxes ticked, CWA_OK = green; else SRA only (no group averages). (0.19)

Sources behind the figures (for readers without our library)

Latching & filtration (Figures 0-A, 0-B): fixedness via conditional expectation; policy-read branching.
Commutation, CSA, CWA (Figures 0-C, 0-F): order tests, thresholds, and the certificate recipe.
Ledger & planes (Figures 0-D, 0-E): hash-chain trace, auditability, and three-plane ops.

1. Minimal Math, Human Words: The Observer Triplet

1.1 First principles (plain words → one-liners)

What is an observer?
Think “a lab team with three moves”: Measure the world, Write the result into a record, then Act using that record. We’ll call the trio ℴ = (M, W, Π). The running record is a Trace of timestamped events. This is enough to build experiments, dashboards, and controllers.

Single-line definitions (Blogger-ready).
Observer triplet: ℴ = (M, W, Π). (1.1)
Trace as an append-only list: T_t = [e₁,…,e_t] = T_{t−1} ⊕ e_t. (1.2)
Event schema (concept): e_t = (τ, channel, ℓ_t, meta). (1.3)

Analogy (you’ll reuse it): your lab log. You measure, you write, and next steps are planned from what’s written. You can debate why later, but you can’t unhappen an entry once it’s in your own log.

1.2 Latching = “conditioning on your own record”

Once you write today’s outcome ℓ_t into T_t, any probability “from your point of view” is now conditioned on T_t. That makes the just-written event a fixed point: inside your frame, it’s certain; and because the policy reads the trace, tomorrow branches based on what you wrote. This is the operational face of “collapse-as-conditioning.”

One-liners.
Delta-certainty of the written label: Pr(ℓ_t = a ∣ T_t) = 1 if a = ℓ_t, else 0. (1.4)
Fixed-point form: E[1{ℓ_t = a} ∣ T_t] = 1{a = ℓ_t}. (1.5)
Policy reads the record: u_t = Π(T_t). (1.6)
Next step is label-selected: x_{t+1} = F_{∣ℓ_t}(x_t, u_t, ξ_t). (1.7)

Everyday picture. “Write ‘exposure_ready’ in the note → the scheduler runs the exposure branch next session. If you had written ‘not_ready’, the future would route differently.”

1.3 Commutation = “checks that don’t interfere”

Two checks A and B commute on an item when order doesn’t matter; then majority labels are stable under order-swap, and cross-observer agreement (CSA) rises. In practice, you test order-sensitivity ε_AB and require it to be small before you average anything (the CWA rule).

One-liners.
Commutation on x: A ∘ B(x) = B ∘ A(x). (1.8)
Order-sensitivity (held-out set D): ε_AB := Pr_{d∼D}[ A∘B(d) ≠ B∘A(d) ]. (1.9)
CSA (3 critics, order-invariant majority): CSA@3 = mean_d[ majority label unchanged by any order ]. (1.10)
CWA pass (pooling is legal): CWA_OK ⇔ [CSA@3 ≥ 0.67] ∧ [p̂ ≥ 0.05] ∧ [max ε_{AB} ≤ 0.05]. (1.11)

Everyday picture. Three “thermometers” that don’t affect each other (commute) + multiple receipts (redundant traces) → the reading is stable enough to average; if they do affect each other, don’t average.

1.4 Implementation (copy-paste friendly)

A) 10-line templates for M, W, Π (pseudo-code).

# Measure
def M(x_t, T_prev):
    ℓ_t = detect_label(x_t, T_prev)        # pure readout; no edits
    return ℓ_t

# Write (append-only)
def W(T_prev, τ, channel, ℓ_t, meta):
    e_t = { "tau": τ, "channel": channel, "label": ℓ_t, "meta": meta }
    return T_prev + [e_t]                  # no overwrites; hash-chain in storage

# Policy (controller reads trace)
def Π(T_t):
    return choose_action_from_rules(T_t)   # e.g., route to branch if last two labels match

These mirror the “Hello-Observer” blueprint: tick increments on append; branch logic reads the written outcome; the storage layer enforces immutability with a hash chain.

B) Event JSON (minimal, extensible).

{
  "tau": 17,
  "channel": "task/lexical",
  "label": "exposure_ready",
  "meta": {
    "confidence": 0.82,
    "rater": "O3_trace",
    "timestamp": "2025-10-18T14:03:22Z",
    "hash_prev": "h_t-1",
    "hash_self": "h_t"
  }
}

Use a hash-chain (h_t := H(h_{t−1} ∥ canonical_json(e_t))) to make retro-edits tamper-evident; verify by recomputing the chain. (1.12)

C) 10-line ε/CSA smoke test (order-swap).

def eps_AB(A,B,D):
    return mean([ A(B(d)) != B(A(d)) for d in D ])

def CSA3(o1,o2,o3,D):
    from itertools import permutations
    def maj(lbls): 
        return max(set(lbls), key=lbls.count)
    stable = 0
    for d in D:
        labs = set()
        for order in permutations([o1,o2,o3]):
            y = d
            for o in order: y = o(y)
            labs.add(maj([o1(d),o2(d),o3(d)]))
        stable += (len(labs)==1)
    return stable/len(D)

Gate pooling by CWA_OK; otherwise report per-case only.

1.5 Why this is rigorous (quick anchors)

Latching is just conditional expectation on your own trace: once written, the event is delta-certain in-frame; tomorrow’s action depends on it. Proof sketches and operator-algebra pointers are provided in the cited kit.
Agreement follows when effects commute and writes are redundant; our CSA/ε/CWA are practical proxies with thresholds you can run today.

Neuro note (how it maps later): channels map to tasks/areas; ticks to trial epochs/cycles; Π to top-down (e.g., PFC) policy reading the trace—exactly the observer/observed hierarchy your readers expect.

Remember: You can’t unhappen what you just wrote in your lab log. That single rule powers the math and the implementation.

2. Agreement You Can Trust: CSA & the CWA Certificate

2.1 Why this section exists (objectivity before averaging)

Before you pool participants/sessions, you need evidence that different graders/tools agree without stepping on each other and that order/phase shuffles don’t move your averages. This section gives you two computable gates:

CSA@3 — cross-system agreement from three independent, non-mutating critics.
CWA — a pass/fail certificate that says when simple averaging is legal.

Analogy. Three thermometers that don’t interfere, plus multiple receipts in the cabinet. If swapping the reading order doesn’t change the verdict and random shuffles don’t budge the average, your number is “objective enough” to pool.

2.2 Single-line, Blogger-ready definitions (copy next to your figures)

CSA from order-insensitive majority (three critics, N items):
CSA@3 := (1/N) · Σⱼ 1{ majority label for item j unchanged under all grader orderings }. (2.1)

Pairwise order-sensitivity (held-out set D):
ε_AB := Pr_{d∼D}[ A∘B(d) ≠ B∘A(d) ]. (2.2)

Order/phase permutation statistic for a scalar outcome s (e.g., session score):
T_obs := | mean(s) − mean_π(s) |. (2.3)
p̂ := (1/B) · Σ_{b=1}^B 1{ | mean(s) − mean_{π_b}(s) | ≥ T_obs }. (2.4)

CWA pass rule (defaults):
CWA_OK ⇔ [ CSA@3 ≥ 0.67 ] ∧ [ max ε_AB ≤ 0.05 ] ∧ [ p̂ ≥ 0.05 ]. (2.5)

Redundancy hint (receipts per claim):
Redundancy ≥ 2 fragments/claim ⇒ error shrinks by majority over fragments. (2.6)

Why this is principled. In the observer-with-trace framework, past writes are delta-certain in-frame; agreement emerges when effects commute and outcomes are redundantly recorded. CSA, ε, and CWA implement these guarantees in practice.

2.3 Implementation — minimal recipes you can run today

2.3.1 Build three pure critics (no mutations)

Start with:

O₁ Units/constraints (bounds, invariants),
O₂ NLI/contradiction (claim vs Given),
O₃ Trace auditor (each quantitative claim has ≥2 trace fragments).
Design rule: critics only evaluate, never rewrite inputs; this makes commutation testable.

2.3.2 Compute ε (order-sensitivity) and CSA (order-invariant majority)

def eps_AB(A,B,D): 
    return sum( A(B(d)) != B(A(d)) for d in D ) / len(D)

from itertools import permutations

def CSA3(O1,O2,O3,D):
    stable = 0
    for d in D:
        maj = lambda ys: max(set(ys), key=ys.count)
        base = maj([O1(d),O2(d),O3(d)])
        ok = True
        for order in permutations([O1,O2,O3]):
            y = [o(d) for o in order]
            if maj(y) != base: ok = False; break
        stable += ok
    return stable/len(D)

Targets: max ε_AB ≤ 0.05, CSA@3 ≥ 0.67 (2-of-3 stable under all orders).

2.3.3 Permutation test (order + phase)

Order: randomly permute critic order per item.
Phase: circular-shift within-session segments to ensure timing/phase does not bias the mean.
Compute T_obs and p̂ as in (2.3)–(2.4). Use B = 1000 permutations as a default.

2.3.4 Decide pooling

If CWA_OK by (2.5), you can average across cases; otherwise report per-case (SRA) and fix the pipeline (separate critic inputs, add trace redundancy, or split monolithic critics).

2.4 Dashboard spec (one screen your team will actually use)

Top strip — CSA@3 trend. 7-run EMA; target ≥ 0.67.
Middle left — ε heatmap. Cells alert > 0.05; quarantine a noisy critic if a cell spikes.
Middle right — Redundancy index. Mean fragments/claim (goal ≥ 2.0).
Bottom — CWA lamp. Green if (2.5) holds; red → “SRA only; add redundancy; refactor critics.”

Ops notes: log CSA, ε-matrix, redundancy; when CSA EMA < 0.67, cool interventions and re-verify; treat δ-max > 0.05 as an incident (order interference).

2.5 Troubleshooting & good habits

ε hot cell (> 0.05): critics share inputs or one mutates text. Fix: make critics pure; ensure NLI reads only the [Given]/Trace, not post-repair drafts; or split one big critic into two narrow ones.
CSA low (< 0.67): tighten definitions; improve critic separation; add trace redundancy to reduce ambiguity.
Permutation p̂ low: order/phase bias exists; stabilize timing (phase) or decouple graders; do not average.
Remember the principle: objectivity = commuting effects + redundant records; that’s the operational mirror of the formal agreement theorems.

Where the math lives (optional reading): proof sketches for latching and agreement (delta-certainty; AB-fixedness) and the invariance view (Collapse-Lorentz) that keeps agreement meaningful under frame remaps.

Deliverables you now possess: ① precise CSA/ε/CWA definitions (2.1–2.5), ② a 20-line implementation you can paste into your analysis notebook, ③ a dashboard layout with thresholds and ops rules. This is enough to gate pooling in EEG/MEG/fMRI/ECoG/TMS pipelines on day one.

3. Mapping to Brain Experiments (EEG/MEG/fMRI/ECoG/TMS)

3.1 One-page crosswalk (what maps to what)

Channels θ = task contexts / receptive fields; sensor-specific features are simple readouts of a latent neural state.
Single-line: y_modality(t) = Φ_modality[x(t)] with modality ∈ {EEG, MEG, fMRI, ECoG}. (3.1)

Ticks τ = trial epochs / cycles (e.g., cue→stimulus→response); writes happen at epoch boundaries.
Frame maps = area-to-area remaps (retinotopic→object-centric; parcel A→parcel B) used to compare observers across regions. Meta-observer logic lives in PFC (policy/frames); binder role is plausibly claustral.

PFC as meta-observer (top-down policy gain).
g_neuro := strength(PFC → target) via DCM/Granger or TMS-evoked transfer. (3.2)

Claustrum as binder (integration hub).
Binding cascade index: CI := coh(V1↔IT) · coh(IT↔PFC) (lag-ordered). (3.3)
Claustral synchrony: CL_sync := mean_coh(claustrum ↔ cortex) during integrated states − baseline. (3.4)

Stability dial (neural mirror).
Δ_neuro := g_neuro · β_neuro − γ_neuro. (3.5)
β_neuro := network switch rate (EEG microstates/HMM); γ_neuro := 1 ÷ τ_recover(neural). (3.6)

Objectivity gates for pooling.
Cross-modality agreement: CSA_neuro := fraction of items where {EEG, MEG, fMRI critics} agree under order-swap. (3.7)
Pooling is legal iff CWA_neuro = [CSA_neuro high] ∧ [permutation p̂ ≥ α]. (3.8)

Why these mappings: they are the neural mirrors of the observer-with-trace calculus (latching, commuting effects, redundancy) and align with independent PFC/claustrum predictions in the attached brain-science paper.

3.2 Protocol blocks you can run this week

(A) Order-swap rater pipeline (build ε and CSA first)

Critics (pure, no mutation):
• EEG critic: microstate/HMM labeler on sensor or parcel series.
• MEG critic: phase-locking / coherence-cascade scorer.
• fMRI critic: ROI pattern-match / directed-gain readout (for g_neuro).
Compute ε_AB := Pr[A∘B ≠ B∘A], target max ε_AB ≤ 0.05; then CSA@3 ≥ 0.67. (3.9)

Permutation test (order + phase): circular-shift session segments; shuffle critic order; require p̂ ≥ 0.05 before averaging across participants. (3.10)

Dashboard: top CSA@3 trend; middle ε heatmap; bottom CWA lamp; quarantine a noisy critic if a cell > 0.05. (3.11)

Analogy. Three thermometers that don’t jostle each other, plus a shuffle test to prove the average won’t move when you re-order the readings.

(B) Redundant trace fragments (text + time-locked sensor)

Every reported neural claim gets ≥ 2 fragments: (i) time-locked sensor feature (e.g., bandpower window ID), (ii) textual event (trial note / button log).
Hash-chain for tamper-evidence: h₀ := 0; h_t := H(h_{t−1} ∥ canonical_json(e_t)). (3.12)
Pooling only with CWA_neuro = green; else per-case (SRA) reporting. (3.13)

Analogy. Keep both the pharmacy receipt and the credit-card slip; the hash makes back-dating obvious.

(C) Pre-registered endpoints (clear dials + falsifiers)

Δ-dial perturbation (causal).
Design: single-pulse dlPFC TMS to modulate g_neuro; paced breathing to raise γ_neuro; free-association task to raise β_neuro.
Endpoint: Δ_neuro falls when g_neuro↓ or γ_neuro↑; hitting-time (CUSUM) shifts right. Fail = no change → revise mapping. (3.14)
Binding cascade with claustral check.
Design: narrative-integration task with MEG (CI) + fMRI/SEEG (CL_sync); optional tFUS/SEEG claustral perturbation where ethical/available.
Endpoint: CI↑ during integration; brief claustral disruption drops CI and CSA_neuro across modalities. Fail = no CI change → revise hub model. (3.15)
Transference direction field (A_θ) bias.
Design: evoke past-template vs present-cue; compute κ̂_neuro := bias(PFC→template) − bias(PFC→present).
Endpoint: labeling/time-indexing reduces κ̂_neuro and Δ_neuro. Fail = κ̂_neuro stays high at low TI with high CSA → bridge incomplete. (3.16)

Pedagogy rule: “one dial, one number, one test.” (g, β, γ, Δ, CI, CL_sync, CSA, CWA). (3.17)

3.3 Modality cheat-sheet (how to compute each dial)

EEG (β_neuro, γ_neuro, CSA role).
• β_neuro: fit K-state microstates/HMM; β_neuro = transitions/min. (3.18)
• γ_neuro: present probe (aversive image or single-pulse TMS); γ_neuro = 1 ÷ τ_recover in alpha/DMN signal. (3.19)
• Critic: microstate labeler for CSA trio.

MEG (CI, CSA role).
• CI: compute coh(V1↔IT) and coh(IT↔PFC) with lag (sensory→assoc→PFC); multiply. (3.20)
• Critic: phase-locking / coherence-cascade scorer.

fMRI (g_neuro, CL_sync, CSA role).
• g_neuro: DCM/Granger, or TMS-evoked ROI transfer from PFC. (3.21)
• CL_sync: average claustrum↔cortex synchrony in integrated vs baseline windows. (3.22)
• Critic: ROI pattern-match / directed-gain readout.

ECoG (all of the above where available).
• High-SNR confirmation of CI and CL_sync; optional intra-operative claustral mapping in rare cases. (3.23)

TMS/tFUS (perturbation handles).
• dlPFC TMS for g_neuro; tFUS SEEG-guided claustral ping for CL_sync (where ethical). Report with CSA/CWA gates. (3.24)

Independent alignment (reader-friendly): PFC as meta-observer and claustrum as binder are also argued independently in the attached theory paper, yielding testable predictions (TMS to PFC should alter reported experience; claustral changes should affect binding). (3.25)

3.4 Safety, governance, and reporting (the boring bits that save you)

CWA discipline. Never average unless CWA_neuro is green; otherwise publish per-case (SRA). Include CSA@3, max ε_AB, p̂, and fragments/claim in every report footer. (3.26)

Auditability. Export the dataset root hash + session hash tail; keep consent proof and role-based access logs. (3.27)

Runbook thresholds. Accept CSA@3 ≥ 0.67, max ε_AB ≤ 0.05; if CSA EMA dips, cool g_neuro interventions and re-verify before resuming pooling. (3.28)

3.5 Plain-speech recap (why this is practical)

You treat PFC as the policy knob (g_neuro), claustrum as the binder (CL_sync), and CI as the staircase that climbs from sensation to integration.
You prove objectivity with CSA/ε/p̂ before you average anything.
You write everything to an immutable trace so “you can’t unhappen what you just wrote,” and your next-step policy depends on that write.
Each dial is one line to compute and one test to pass, with falsifiers pre-registered—no PhD math required.

Where deeper theory lives (optional): the observer-with-trace invariants (latching; AB-fixedness under commuting effects; certificate-gated pooling) and their operationalization in ObserverOps/ESI.

Analogy. It’s a kitchen: PFC is your head chef (policy), claustrum is the expo station (binder), CSA is your blind taste-test agreement, and CWA is the rule “don’t publish the menu average until three tasters agree and the order of tasting doesn’t change the verdict.”

4. Closed-Loop Control for Neuroscience

4.1 Treat Π as a controller (the loop we actually run)

Closed loop = read signals, write to trace, choose an action, world updates.
State update: x_{t+1} = F(x_t, u_t, T_t) + η_t. (4.1)
Readout: y_t = H(x_t) + ε_t. (4.2)
Controller (policy): u_t = Π(T_t, y_t, c_t) with context c_t (task, safety, consent). (4.3)

Why trace matters. Writes make the just-observed event delta-certain in-frame, so Π must condition on T_t; that is latching as conditional expectation in the formal observer model.

4.2 The stability dial (push × echo − buffer)

We run control with one explainable dial; compute it from behavior/physio and show it live.
Stability discriminant: Δ := ĝ · β̂ − γ̂. (4.4)
Guidance slope: ĝ := cov(r_t, s_t) ÷ var(r_t) (reframe strength → stance shift). (4.5)
Amplification rate: β̂ := (1 ÷ T) · Σ_t [ jumps_t ÷ minutes_t ]. (4.6)
Damping buffer: γ̂ := 1 ÷ τ_recover (time to baseline after a spike/perturbation). (4.7)

Neuro mirrors. ĝ ↔ PFC→target gain (DCM/Granger or TMS-evoked transfer); β̂ ↔ microstate/assembly switch rate; γ̂ ↔ recovery constant of bandpower/DMN metrics.

4.3 Safe actuation: only when evidence says “OK”

CWA certificate gate (pooling/actuation legality):
CWA_OK ⇔ [ CSA@3 ≥ 0.67 ] ∧ [ max ε_AB ≤ 0.05 ] ∧ [ p̂ ≥ 0.05 ]. (4.8)
Action arming: u_t := u_t if CWA_OK else u_hold. (4.9)

Redundant receipts. Require ≥ 2 independent fragments per claim (e.g., sensor window + text tag) in T_t; hash-chain all writes.
Hash chain: h₀ := 0; h_t := H(h_{t−1} ∥ canonical_json(e_t)). (4.10)

4.4 Controller baselines you can deploy this week

(A) PID (robust, model-light)

Error to a target dial Δ*: e_t = Δ* − Δ_t. (4.11)
PID law (discrete): z_t = z_{t−1} + e_t · Δt; u^{raw}t = K_p e_t + K_i z_t + K_d (e_t − e{t−1}) ÷ Δt. (4.12)
Safeguards: u_t = sat_U( rate_limit( u^{raw}_t ) ). (4.13)

Defaults. Start tiny: K_p small, K_i off (0) until CSA is stable, K_d for overshoot control; anti-windup: freeze z_t while u_t saturates. Gate execution by (4.9).

(B) LQR (when you can identify a local model)

Local ID (rolling window): x_{t+1} ≈ A x_t + B u_t by ridge regression on recent pairs. (4.14)
LQR objective: min Σ_t [ x_tᵀ Q x_t + u_tᵀ R u_t ]. (4.15)
Policy: u_t = −K x_t, with K = dlqr(A,B,Q,R) (discrete Riccati). (4.16)

Practice tip. Keep Q on Δ-related coordinates, make R large for invasive actuators (TMS/tFUS), and still arm by CWA_OK.

4.5 Safe action sets, rate limits, and consent

Hard bounds (per actuator): U_safe = { u : |u| ≤ u_max ∧ |u−u_{t−1}| ≤ ρ_max ∧ IPI ≥ τ_ref }. (4.17)
Consent gate: Allow(u, action, resource) = 1 iff role/consent policy passes; else u = 0. (4.18)

Guardrails to log: CWA light, CSA@3 EMA, ε-matrix, redundancy index, consent state, Δ trend; auto-cool g-moves when CSA EMA dips.

4.6 Implementation sketch (neurofeedback, TMS/tDCS/tFUS, task gating)

loop each epoch:
  y_t ← H(x_t)  # EEG/MEG/fMRI/ECoG features
  T_t ← append(e_t) with hash-chain                # redundant receipts
  CSA, ε, p̂ ← update_agreement_metrics(D_holdout) # cheap batch
  CWA_OK ← (CSA≥0.67 and max ε≤0.05 and p̂≥0.05)

  ĝ, β̂, γ̂ ← estimate_slopes_and_times(y_t, T_t)  # (4.5)-(4.7)
  Δ_t ← ĝ*β̂ - γ̂                                   # (4.4)

  u_cmd ← controller(Δ_t, Δ*)                      # PID or LQR
  u_t ← (CWA_OK ? clamp_to_U_safe(u_cmd) : u_hold) # (4.9), (4.17)

  actuate(u_t)  # neurofeedback gain, TMS intensity/timing, task route
  log(Δ_t, CSA, ε, p̂, u_t, hashes)

This is the ObserverOps + ESI sidecar pattern: a tiny control layer, CSA-gated, with reproducible hashes and incident playbooks.

4.7 Audio channel-strip analogy (for the whole team)

Steering (Π focus) sets what you try to move (Δ target). Drive (ĝ) pushes; if the room is echo-y (β̂) you’ll ring; the fence (γ̂, U_safe, consent) keeps you out of trouble; routing (CWA_OK) only lets signal pass when meters say the chain is behaving.

4.8 When to stop or switch strategies (failure modes → actions)

ε spike (> 0.05) ⇒ critics interfering; split inputs, refactor to pure effects, retest; hold actuation.
CSA EMA < 0.67 ⇒ cool guidance (ĝ↓), add redundancy, re-arm later.
p̂ < 0.05 under order/phase permutations ⇒ phase/order bias; stabilize timing or per-case SRA only.

Bottom line. A simple Δ-dial with PID/LQR, armed by a CWA certificate and fenced by consent/limits, turns “observer-with-trace” into a safe, reproducible control loop for neurofeedback and perturbation studies—no heavy math required, but with rigorous anchors when you need them.

5. Language-Game Semantics in the Lab (Wittgenstein, Operationalized)

5.1 What we measure (plain words → one-liners)

Picture → world fit. A statement “fits” when its internal structure can be mapped into a scene-graph of the world without breaking relations; with noise, we score approximate fits.
Truth-as-correspondence (feasibility): ∃ map h: V → D such that every pictured tuple (v₁,…,v_m) in Qⱼ lands in a world tuple (h(v₁),…,h(v_m)) in Rⱼ. (5.1)
Empirical fit (with partial observability): Fit(h) := (1/|Obs|) · Σ_{o∈Obs} 1{ h respects o’s constraints }. (5.2)

Meaning = use (as policy). “What a word means” is the policy component that makes cooperative interaction go well; we estimate it from logs (inverse RL) and keep it stable with trust-region steps.
Meaning-as-policy: π*(a ∣ x,u) := argmax_π E[ Σ_t γ^t · u(x_t,a_t) ∣ π ]. (5.3)
IRL objective (max-ent form): θ̂ := argmax_θ [ E_{data}[φ] − log Z(θ) ], π_θ(a∣x) ∝ exp(θ·φ(x,a)). (5.4)
Trust-region update: KL(π_{new} ∥ π_{old}) ≤ δ, θ_{new} = θ_{old} + η·ĝ with KL-penalty. (5.5)

Hinge certainty (hyperpriors + switching costs). Background certainties (“hinges”) change only when evidence is overwhelming.
BF stream & stop rule: Λ_t := Σ_{k≤t} log BF_k; switch hinge iff Λ_t ≥ λ (cost-of-change). (5.6)

Why this is rigorous here. These restatements (CSP homomorphism; equilibrium/IRL; Bayes-factor stopping) are the core program of Wittgenstein, Operationalized, designed for estimation and falsification.

Analogy. Your statement is a subway map; the world is the city. A good map “fits” when station-to-station relations line up with streets and lines. “Meaning = use” is how commuters actually ride. Hinges are those non-negotiable landmarks you only revise when dozens of photos and GPS tracks prove the map is wrong.

5.2 Picture→world fits you can compute (CSP/ILP templates)

Objects. World 𝓦 = (D; R₁,…,R_k), Picture 𝓟 = (V; Q₁,…,Q_k), candidate map h: V→D.
Homomorphism constraint: (v₁,…,v_m)∈Qⱼ ⇒ (h(v₁),…,h(v_m))∈Rⱼ. (5.7)

Encoding (CSP). Variables = picture nodes; domains = candidate entities; constraints = relation arcs; solve by AC-3/AC-4; escalate to ILP/MaxSAT with slacks when noisy.
Noisy ILP (sketch): maximize Σ w_e z_e subject to: relation-preservation with slack s_e; z_e∈{0,1}; s_e ≥ 0; budget Σ s_e ≤ ϵ. (5.8)
Complexity note. Worst case NP; practical with bounded treewidth & small arities; keep pictures sparse.

Outputs to log: Fit@top-1, #violations, nDCG over candidate h, and ECE (calibration) for Fit confidence.

5.3 Meaning-as-use via IRL (trust-region loop you can run)

Data. Interaction log D = {(x_t, u_t, a_t, r_t)} with context u_t (task, norms), actions a_t, outcomes r_t.
Estimator. Max-ent IRL for θ over features φ; policy π_θ(a∣x) ∝ exp(θ·φ(x,a)). (5.9)
Stability. Use a KL trust region: maximize J(θ) − β·KL(π_θ ∥ π_{θ_old}), giving monotone surrogate decrease. (5.10)

One-screen loop (pseudocode).

repeat:
  θ ← θ + η * grad_IRL(D, θ)           # doubly robust off-policy eval
  enforce KL(πθ || πθ_old) ≤ δ         # trust region (clip or penalty)
  calibrate πθ with temperature τ*      # see 5.4 (ECE)
  log AUC@use, ΔU vs. baseline, κ/α, ECE, BF(hinges)
until ΔU, ΔExclusivity plateau

What you publish. ΔU (utility lift), out-of-context robustness, κ/α (inter-rater agreement), and calibration (ECE↓). Implementation/runtime notes are spelled out in the paper’s Appendix B.5.

5.4 Calibration & evaluation harness (ECE, κ/α, BF)

ECE (expected calibration error, b bins).
ECE := Σ_{b=1}^B (|S_b|/N) · | acc(S_b) − conf(S_b) |. (5.11)

Cohen’s κ (two raters).
κ := (p_o − p_e) ÷ (1 − p_e), p_o = observed agreement, p_e = chance agreement. (5.12)

Krippendorff’s α (K raters, any scale).
α := 1 − (D_o ÷ D_e), D_o = observed disagreement, D_e = expected by chance. (5.13)

Bayes-factor trajectory for hinges.
Λ_t := Σ_{k≤t} log( p(data_k ∣ H₁) ÷ p(data_k ∣ H₀) ); switch if Λ_t ≥ λ. (5.14)

CWA gate before reporting pooled scores.
CWA_OK ⇔ [ CSA@3 ≥ 0.67 ] ∧ [ max ε_AB ≤ 0.05 ] ∧ [ p̂ ≥ 0.05 ]. (5.15)

5.5 End-to-end implementation (drop-in blocks)

(A) Picture fit (CSP→ILP).

Build scene-graph (entities/relations). 2) Encode variables/domains/constraints. 3) AC-3 prune; if infeasible, run ILP/MaxSAT with slack budget ϵ. 4) Return Fit, ĥ, violations.

(B) Meaning (IRL).

Extract φ from usage (turn-level features). 2) Train π_θ with doubly-robust off-policy eval. 3) Apply trust-region (δ ≈ 0.01–0.1). 4) Calibrate with temperature/Platt, report ECE.

(C) Hinges (BF streams).

Declare hinge variables (what cannot drift without evidence). 2) Maintain Λ_t per (5.14). 3) Revise only if Λ_t ≥ λ (e.g., λ ≈ 3–5 nats). 4) Log switch decisions with evidence windows.

(D) Agreement & safety.
Run CSA@3, ε_AB, permutation p̂ each batch; only publish pooled metrics or actuate policies when CWA_OK. (5.15)

(E) Repro & governance.
Release tool cards, seeds, and exact CSP/IRL configs; attach data-minimization, privacy, and misuse mitigations (rate limits, audit logs, kill switch).

5.6 Subway-map analogy (why teams “get it” fast)

Picture fit = lining up the map with the city (station links ≙ relation constraints).
Meaning = use = how riders actually choose routes (policy learned from commuting logs).
Hinges = landmarks you only move after overwhelming photo/GPS evidence (BF threshold).
CWA certificate = “three surveyors agree; order of checks doesn’t change the verdict; shuffles don’t move the average” → you may publish the citywide average.

Where to look if readers want proofs or deeper scaffolding

Picture/Use/Hinges formalism + code notes: Wittgenstein, Operationalized §§2–6, §9, App. B.5 (CSP/ILP encoding, IRL trust-region runtime, metrics pack).
CSA/ε/CWA gate & dashboards: ESI §8; Freud→Control §8 + App. E (production thresholds, one-figure board).
Observer foundations (why latching/commutation matter): Self-Referential Observers Ch. 6 (conditional-expectation fixedness; commuting effects).

Bottom line. With these blocks, a lab can fit pictures, learn use-policies, guard hinges, and publish calibrated, agreement-vetted results—all with single-line equations and drop-in templates.

6. Psychoanalytic Knobs as Safe Operators (Clinically Intuitive, Mathematically Clean)

6.1 Operator dictionary (one-liners + what they do)

Repression = tighten the fence (Ŝ_tight).
Ŝ_tight[x] := Ŝ[x] + Λ · χ_taboo(x), with Λ ≥ 0 (mask χ_taboo penalizes forbidden regions). (6.1)
Δ effect. Damping γ̂↑ (less spill), but hidden pressure may re-route unless you also redirect V (risk of delayed β̂ rebound). Micro-vignette and mixing-board analogy appear below.

Isolation = channel decoupling (U_⊥).
C_iso := U_⊥(C) = diag(C) (drop cross-talk; keep only self-couplings). C is a coupling matrix among narratives/symptoms. (6.2)
Δ effect. Cuts amplification β̂↓ (fewer runaways); overused, integration stalls (Δ → 0).

Projection = frame rotation (R_θ).
x′ = R_θ · x (choose θ to re-aim “self ↔ other” axes for the active affect). (6.3)
Δ effect. Can mis-aim guidance ĝ; rotate slowly with γ̂↑ pacing to prevent overshoot.

Sublimation = path redirection (edit V into a safe basin).
V_id^→(x) := V_id(x) + μ · B_safe(x), μ>0; force becomes −∇V_id^→ = −∇V_id − μ∇B_safe. (6.4)
Δ effect. Pulls energy into a safe trench (effective ĝ↓ on risky routes, γ̂↑ via structured outlets).

Analogy (mixing board). Gate = repression; Mute/bus split = isolation; Pan = projection; Send-to-reverb/aux = sublimation. (Card repeated in §6.6.)

6.2 How they combine in one closed-loop step (the “plug-in chain”)

Edited update with defenses active:
x_{t+1} = F(x_t, Ω̂_self(x_t), 𝕋_t) − ∇V_id^→(x_t) − Ŝ_tight[x_t], with couplings replaced by C_iso = U_⊥(C). (6.5)
Read left→right like a channel strip: steering (Ω̂_self) → drive pull (−∇V) → fence (Ŝ) → routing (C_iso).

Why this is principled. The observer-with-trace model makes the write e_t delta-certain in-frame (latching), so changing Ω̂_self or the operator schedule genuinely changes the next-step map F (collapse-as-conditioning). Agreement and gating rely on commuting effects and redundant records.

6.3 Scheduling & safety (what you actually run)

Operator schedule (piecewise, tick-based):
σ(t) := { λ_S(t), λ_⊥(t), θ(t), μ(t) } controls Ŝ_tight, U_⊥, R_θ, V_id^→. (6.6)
Arming rule: Apply σ(t) only if CWA_OK ⇔ [CSA@3 ≥ 0.67] ∧ [max ε_AB ≤ 0.05] ∧ [p̂ ≥ 0.05]. (6.7)
Safe set: U_safe = {σ: |Δσ| ≤ ρ_max ∧ bounds(g,β,γ) respected}. (6.8)

Runtime heuristics (drop-in):
• Start with μ (sublimation) and small Λ (Ŝ_tight); schedule U_⊥ briefly; apply R_θ as micro-rotations.
• Never hard-gate (Λ big) if your CSA is low or ε hot; stabilize critics first, then escalate.

6.4 30-second micro-cases (before/after)

Case A — “Topic clips, then leaks elsewhere” (Repression).
Before: “When dad visits I… (breaks off).” After Ŝ_tight↑: “It’s nothing.” (Topic suppressed; later shows as insomnia.) Δ: γ̂↑, risk β̂ rebound—pair with V_id^→ (exercise/art trench). (6.9)

Case B — “Thought→body spiral” (Isolation).
Before: “Thinking about mom tightens my chest; I cancel plans.” After U_⊥: “I can think about mom without the chest stuff.” Δ: β̂↓; schedule re-coupling once γ̂ improves. (6.10)

Case C — “Blame flips outward” (Projection).
Before: “I’m furious at myself.” After R_θ: “My team keeps sabotaging me.” Then slowly rotate back toward the true source while pacing (γ̂↑). (6.11)

Case D — “Doom-scroll → morning sprint” (Sublimation).
Before: “When tense I doom-scroll.” After V_id^→: “When tense I walk and voice-note my short story.” Δ: ĝ↓ on risky path, γ̂↑ via structure. (6.12)

All together (one-week edit plan).
Ŝ_tight↑ on phone use after 23:00; U_⊥ between “critique→doom-scroll” for 2 weeks; R_θ to “anger at process, not self/others”; V_id^→ adds 07:30 writing trench. Observed: Δ = ĝ·β̂ − γ̂ falls (risk→safe). (6.13)

6.5 When not to use hard gates (and what to do instead)

Avoid hard Ŝ_tight or big R_θ when evidence is brittle. Use the CWA certificate first; if red, report per-case (SRA) and fix pipeline: make critics pure, reduce order-sensitivity ε, add redundant trace fragments. (6.14)
If ε hot (>0.05): critics are interacting—split inputs, re-run ε; only then re-arm σ(t). (6.15)
If CSA low (<0.67): defer averaging/hard gates; raise redundancy and tighten definitions; re-test. (6.16)

6.6 Pedagogy cards (paste alongside your plots)

One-liners to remember.
Repression: Ŝ_tight[x] := Ŝ[x] + Λ·χ_taboo(x). (6.1)
Isolation: C_iso := U_⊥(C) = diag(C). (6.2)
Projection: x′ = R_θ·x (re-aim affect vector). (6.3)
Sublimation: V_id^→ = V_id + μ·B_safe; −∇V_id^→ = −∇V_id − μ∇B_safe. (6.4)
Closed-loop with defenses: x_{t+1} = F(… ) − ∇V_id^→ − Ŝ_tight, with C→C_iso. (6.5)

Analogy card. Gate = repression; Mute/bus split = isolation; Pan = projection; Send-to-reverb/aux = sublimation.

6.7 Why this is rigorous (anchor in one breath)

Latching (delta-certainty). Once written to the trace, an event is a fixed point of conditional expectation; policies that read the trace make futures branch by what you just wrote. (Operator-algebra wording and proof sketch supplied.) (6.17)
Agreement (AB-fixedness). Commuting checks + redundant records produce order-invariant majorities (high CSA) and legal pooling (CWA). Your ε/CSA/CWA gates are the computable proxies. (6.18)
Production guardrails. Defaults, dashboards, and incident playbooks for CSA/ε/trace redundancy come from the deployment blueprints (ESI + clinical workflow). (6.19)

Bottom line. Treat defenses as scheduleable operators on V, Ŝ, Ω̂_self, C; compute Δ = ĝ·β̂ − γ̂; arm actions only when CWA_OK; and keep every decision tied to redundant, hashed trace fragments. That’s a clinically intuitive and mathematically clean way to use “psychoanalytic knobs” safely in a modern, closed-loop lab.

7. Data & Trace Engineering

7.1 Non-negotiables (design goals → one-liners)

Append-only trace. You never overwrite; you only append verifiable events.
T_t = T_{t−1} ⊕ e_t. (7.1)

Event shape (minimum viable).
e_t = (τ_t, label_t, meta_t). (7.2)

Time-lock within a session.
τ_t ≥ τ_{t−1} and iso_time_t strictly increasing. (7.3)

Hash-chain integrity (tamper-evident).
h₀ := 0; h_t := H(h_{t−1} ∥ canonical_json(e_t)). (7.4)

Merkle roll-ups for fast audit.
R_day := MerkleRoot({ h_t : e_t on that day }); R_dataset := MerkleRoot({ R_day }). (7.5)

Verifiability.
VerifyTrace(T) = 1 iff recomputed h_T equals stored h_T. (7.6)

Redundancy (receipts per claim).
fragments_per_claim ≥ 2 (e.g., sensor window ID + text note). (7.7)

RBAC + consent gate.
Allow(u, action, resource) = 1 iff [ role(u) ∈ policy[action,resource] ∧ consent(resource) ≥ level(action) ]. (7.8)

Publish/act only when evidence is stable.
PublishOK ⇔ CWA_OK ∧ VerifyTrace(T) ∧ consent ≥ metrics_only. (7.9)

Idempotent writes (retries are no-ops).
Append(T,e) does nothing if event_id(e) already exists with the same hash. (7.10)

Analogy. Lab EHR meets Git: every entry is a commit; daily and dataset Merkle roots are your release tags.

7.2 JSON schemas (paste-and-run)

(A) trace.jsonl — append-only ledger (one line = one event).

{
  "session_id": "S001",
  "event_id": "S001_e07",
  "iso_time": "2025-10-18T15:02:11Z",
  "label": "exposure_completed_tiny",
  "meta": { "SUDS_drop": 3, "rater_id": "r_lin", "device_id": "eeg_04" },
  "prev_hash": "0000000000",
  "hash": "8f7a...3b"        // H(prev_hash ∥ canonical_json(e_t))
}

Fields and hash recipe match the governance appendix; do not overwrite—append a correction_of when needed.

(B) segments.jsonl — time-locked features (EEG/MEG/etc.).

{
  "session_id": "S001",
  "segment_id": "S001_seg03",
  "start_sec": 720.0,
  "end_sec": 900.0,
  "rater_id": "r_kim",
  "device_id": "meg_02",
  "features": { "r_strength": 2, "stance_shift": 1, "assoc_jumps": 6, "minutes": 3.0 }
}

Keep rater/device IDs explicit for audit and bias checks.

(C) graders_O*.jsonl — pure critics (for CSA/ε/CWA).

{
  "item_id": "S001_seg03::avoidance_high",
  "order": ["O1","O2","O3"],
  "vote": 1,
  "confidence": 0.82,
  "rater_id": "o1_unitizer",
  "notes": "Units consistent; boundaries OK."
}

Critics are pure evaluators with disjoint inputs so order swaps don’t change votes (ε small).

7.3 ID & hashing conventions (cut-sheet)

Event IDs. event_id := session_id ++ “_e” ++ k, k = 2-digit counter. (7.11)
Device IDs. device_id := modality ++ “_” ++ index (e.g., eeg_04, tms_01). (7.12)
Rater IDs. rater_id ∈ {human initials, critic name}; store mapping in Ops vault. (7.13)
Hashing. hash := H(prev_hash ∥ canonical_json(e_t)); canonical JSON means stable key order + UTF-8; record prev_hash on every line. (7.14)
Daily/Master roots. Write R_day and R_dataset to meta.json after batch jobs. (7.15)

7.4 Minimal APIs (append, query, certify)

Append (idempotent).
Append(T,e) → return h_new; if event_id(e) exists with same hash, return existing h (no-op). (7.16)

Query (by time/range/label).
Query(T; t0,t1, labels, device_id, rater_id) → stream of events; includes prev_hash/hash. (7.17)

Certify (export gate).
Certify(range) returns { VerifyTrace=0|1, R_day[], R_dataset, CWA_OK }. (7.18)

RBAC wrapper.
Serve(action, resource) only if Allow(u, action, resource)=1; otherwise deny + audit log. (7.19)

One-line publish rule.
Export allowed iff PublishOK in (7.9); include dataset_root_hash in the report footer. (7.20)

7.5 Ops runbook (daily/weekly you can actually do)

Per session (≈ 20 min). Ingest → segment → compute ĝ, β̂, γ̂, Δ̄ → run CSA/ε/p̂ → set CWA lamp → Trace ▸ Append single-line event → export one-page Δ-report (hash tail + consent proof). (7.21)

End of day. Recompute CSA/CWA, write R_day, archive trace.jsonl and audit.jsonl. (7.22)

Weekly audit. Verify ℓ-chain for audit logs and h-chain for trace; scan anomalies (out-of-role access, mass export); sign review. (7.23)

Incident ladder. S1 identifiers, S2 integrity, S3 availability; T_detect ≤ 24 h; T_contain ≤ 48 h; T_notify (S1) ≤ 72 h; rotate keys; re-verify chains; post-mortem. (7.24)

Retention windows. TTL_A ≤ 6 mo (IDs); TTL_B ≤ 24 mo (content); TTL_C ≤ 36 mo (derived); TTL_D ≥ 36 mo (governance). (7.25)

De-redaction policy. Clinician/Auditor only; all de-redactions emit audited entries. (7.26)

CWA discipline. If CSA < 0.67 or max ε_AB > 0.05 or p̂ < 0.05, flip banner to SRA only; no averaging, no actuation; add redundancy and refactor critics. (7.27)

7.6 “Show me” examples (ready to paste)

Two-fragment claim (redundancy).
Text note: “S001_seg03 avoidance_high” + Sensor receipt: “bandpower window bp_720-900”. fragments_per_claim = 2 → vote=1 in O₃. (7.28)

Footer of export.
dataset_root_hash=af21…, session_hash_tail=…3b, consent=metrics_only@2025-10-18, CWA_OK=true. (7.29)

7.7 Why this works (and how it maps to the math)

Latching is guaranteed by the append-only + hash-chain ledger: once written, the event is fixed for the observer’s future policy (delta-certainty). (7.30)
Agreement becomes computable via CSA/ε with redundant fragments; CWA certifies when pooling is legal. (7.31)
Governance (RBAC/consent/audit) turns those math guarantees into clinic-grade operations you can defend. (7.32)

Analogy (to remember). Your trace is a lab EHR where every entry is a Git commit; critics are your CI tests (CSA/ε), the CWA lamp is the “build passing” badge, and Merkle roots are your signed releases.

8. Tooling Stack & Reproducibility

8.1 The Repro Contract (what every run must record)

Environment snapshot, frozen randomness, and a small set of metrics make your results portable and auditable. We standardize this as a one-screen contract.

One-line requirements.
Environment tuple: Env := (OS, CUDA/Driver, BLAS, Python, libs, commit). (8.1)
Seed vector: s⃗ := (s_py, s_np, s_torch, s_solver). (8.2)
Budget tuple: Bud := (wall, GPU·h, CPU·h, Wh). (8.3)
Energy check: Wh ≈ P̄ · wall, measured by sampler or meter. (8.4)
Reproduce flag: Reproduce(D, s⃗, Env) = 1 iff |Metric′ − Metric| ≤ tol for all registered metrics. (8.5)

Registered metrics (defaults). CSA@3, max ε_AB, CWA p̂, ĝ, β̂, γ̂, Δ̄, ECE, κ/α, BF-curve. (8.6)

8.2 Container spec (drop-in)

Base. Ubuntu 22.04 + Python 3.11; MKL/BLAS pinned; CUDA if needed.
Locked components. CSP/ILP solver, IRL/optimizer, plotting libs; write a lockfile and export tool cards (versions + hyperparams).

One-liners to write into the image.
Container label: io.repro.env = hash(Env). (8.7)
Seed entrypoint: on_start → set s⃗; export $RUN_SEED_JSON. (8.8)
Budget logger: log(Bud) per stage; attach to report footer. (8.9)

Why containers. Same bits → same hashes → same CSA/ε/CWA and Δ-dials when the data are identical. The append-only trace + Merkle roots keep provenance intact.

8.3 Project scaffold (paste this tree)

/data/          # raw & derived (read-only in jobs)
/trace/         # trace.jsonl, graders_*.jsonl, meta.json (hashes)
/pipelines/     # csa_eps_cwa.py, delta_dials.py, picture_fit.py, irl_loop.py
/dashboards/    # panels/, report_templates/, export.py
/configs/       # *.yaml (seeds, thresholds, paths)
/tests/         # unit_*.py (idempotency, hashes, metrics)
/container/     # Dockerfile, lockfile.txt, tool_cards.json

Scaffold aligns with the SOP/appendix quickstarts; the same layout reproduces figures and reports with synthetic or real data.

8.4 CLI: CSA/ε/CWA + core dials (four commands)

We ship a tiny CLI so labs can compute the gates and dials without opening notebooks. Thresholds match the CWA certificate defaults.

(A) CSA — cross-system agreement.
obs csa --graders /trace/graders_O.jsonl --out /dashboards/csa.json* (8.10)
Returns CSA@3 with 7-run EMA. Target: CSA@3 ≥ 0.67.

(B) ε — order-sensitivity matrix.
obs epsilon --graders … --heldout /data/heldout.jsonl --out ε.json (8.11)
Check max ε_AB ≤ 0.05 or refactor critics (pure effects, disjoint inputs).

(C) CWA — permutation test (order + phase).
obs cwa --scores /data/session_scores.json --B 1000 --out cwa.json (8.12)
Computes T_obs and p̂; pass if p̂ ≥ 0.05.

(D) Δ-dials — ĝ, β̂, γ̂, Δ̄, CUSUM.
obs delta --segments /data/segments.jsonl --out delta.json (8.13)
Reports ĝ, β̂, γ̂, Δ̄, CUSUM S_t with alarm thresholds.

Publish rule. CWA_OK ⇔ [CSA≥0.67] ∧ [max ε≤0.05] ∧ [p̂≥0.05]; otherwise “SRA only”. (8.14)

8.5 Minimal unit tests (must pass before publish)

Idempotent append. Re-appending the same event does not change h_t. (8.15)
Hash-chain integrity. Recompute h_t; must equal stored. (8.16)
CSA invariance. Shuffling grader order leaves CSA@3 unchanged on a stable batch. (8.17)
ε sanity. A synthetic non-commuting pair yields ε>0, commuting pair ε≈0. (8.18)
CWA permutation. For IID synthetic scores, p̂≈0.5 on average; for order-coupled scores, p̂→0. (8.19)
Seeds are real. Running obs delta twice with identical s⃗ reproduces Δ̄ to within tol. (8.20)

8.6 Metric harness scripts (calibration, agreement, evidence)

We include callable scripts so every paper can re-run the same evaluations with one command.

Harness outputs (single lines).
Calibration: ECE := Σ_b (|S_b|/N)·|acc(S_b)−conf(S_b)|. (8.21)
Agreement: κ := (p_o−p_e) ÷ (1−p_e), α := 1 − (D_o ÷ D_e). (8.22)
Evidence stream: Λ_T := Σ_{t≤T} log BF_t; switch if Λ_T ≥ λ. (8.23)

CLI examples.
obs calib --probs probs.json --labels y.json --out ece.json
obs agree --labels graders.json --out kappa_alpha.json
obs bf --liks H1.json H0.json --out bf_curve.json (8.24)

8.7 Compute budget reporting (fair, apples-to-apples)

You will publish the cost of your results alongside the numbers. The harness collects budget telemetry and prints a footer block that journals can copy.

Footer fields (auto-filled).
wall = Σ stages wall_i; GPU·h = Σ g_i·t_i; CPU·h = Σ c_i·t_i; Wh = P̄·wall; seeds = s⃗; env_hash = hash(Env). (8.25)

Policy. Release code, configs, lockfile, and evaluation harness; include dataset_root_hash and Merkle day roots so third parties can verify end-to-end. (8.26)

8.8 One-command reproduction (Quickstart)

obs repro --config /configs/paper.yaml --export /dashboards/report.pdf (8.27)
Runs CSA/ε/CWA, Δ-dials, calibration, evidence, and emits a one-page report (numbers aligned to the compact reporting block).

What appears in the footer.
env_hash=… seeds=… CSA@3=… max ε=… p̂=… ĝ/β̂/γ̂=… Δ̄=… ECE=… κ/α=… Λ_T=… wall/GPU·h/Wh=… dataset_root_hash=… (8.28)

8.9 Why this stack works (and maps to our math)

Append-only + hashes make writes latch (delta-certain in-frame) and keep provenance verifiable. (8.29)
CSA/ε/CWA implement the agreement proxy (commuting critics + redundancy + permutation guard). (8.30)
Seeds + container + harness satisfy the reproducibility checklist (same inputs → same outputs → same decisions). (8.31)
Budget disclosure keeps results comparable and responsible across labs. (8.32)

Mental model. Your stack is a flight recorder (trace + hashes) running inside a sealed cockpit (container) with three gauges front and center (CSA bar, ε heatmap, CWA lamp). If those are green and seeds/env are locked, anyone can fly the same route tomorrow and land on the same numbers.

9. ESI “Smoothness” for Cognitive Pipelines (Optional but Handy)

9.1 What “smoothness” means here (one breath)

We borrow ESI’s emulsion metaphor to keep multi-tool neuro pipelines from “curdling” (loops, contradictions, brittle order effects). Smoothness lives in a phase region controlled by tiny structure (starch S), gentle heat schedules (decoding/decision temperature T), and task load (capacity–diversity K), and it’s verified by cross-observer agreement (CSA) and a clump order parameter χ.

Axes (single lines).
Phase axes: T := temperature ⊕ nucleus-mass (top-p), S := % structural scaffold, K := capacity ÷ diversity. (9.1)
Smoothness proxy: Smooth ⇔ [ χ ≤ χ* ] ∧ [ CSA@3 ≥ 0.67 ]. (9.2)

9.2 The clump order parameter χ (what you actually compute)

ESI defines χ as a compact, unit-free score that rises when outputs clump (loops, premature collapse, contradictions). Use it as an early warning alongside CSA/ε.

Definition (one line).
χ := w_H·ΔH↓ + w_L·L_loop + w_C·C_contra, with w_H+w_L+w_C=1. (9.3)
Here ΔH↓ = normalized entropy drop between outline→draft, L_loop = loop rate (repeats/min), C_contra = contradiction rate vs Given/Trace. Defaults: w_H=0.4, w_L=0.3, w_C=0.3. (9.4)

Alarm & action.
Alarm ⇔ χ ≥ χ* (default χ*=0.6). → Cool T, raise S to next tier, re-run CSA/ε. (9.5)

9.3 Starch budget (tiny structure that prevents curdling)

ESI shows that 1–3% structural tokens (or protocol scaffolds) are enough to stabilize phase without biasing content. In neuro pipelines, this is protocol scaffolding, not “prompting”: concise slots that make checks addressable and critics commute.

Budget rule (one line).
S := {1% if v≤0.25; 2% if 0.25<v≤0.6; 3% if v>0.6}, v = task-volatility score. (9.6)

Scaffold grammar (≤120 tokens @ 4k ctx, adapt to your forms):
[Given] task & IDs • [Plan] goals→steps→tools • [Compute] succinct • [Checks] units/constraints/contradictions • [Trace] cite fragment IDs • [Answer] single final. (9.7)

Why S works (free-energy view, plain). Bounded structure slightly raises early conditional entropy (prevents premature collapse) while keeping macro-shape addressable; this reduces loop attractors. Result: χ↓, CSA↑. (Proof sketch in ESI §6.)

9.4 Sous-vide schedules (gentle heat across passes)

Run cool → warm → cool decoding/decision passes so the system explores, commits, then verifies—mirroring outline→draft→check. Works for LLM toolcalls and for analysis/label-fusion passes in your lab stack.

Schedule (one line).
T_pass := { T₁=cool (temp 0.3–0.5 / top-p 0.8–0.9), T₂=warm (0.6–0.8 / 0.9–0.98), T₃=cool (0.2–0.4 / 0.7–0.9) }. (9.8)

Operational rule.
If χ↑ or ε hot (>0.05), drop to T₁ and raise S tier; re-test CSA/ε before committing labels. (9.9)

9.5 How ESI plugs into CSA/CWA (the verification link)

ESI equates “smoothness” with agreement: commuting critics + redundant traces → order-insensitive majorities. Keep the CWA certificate as the legal gate for pooling/actuation; use χ as a stability meter that tells you when to cool/structure before you even get to CWA.

Gate (recall).
CWA_OK ⇔ [ CSA@3 ≥ 0.67 ] ∧ [ max ε_AB ≤ 0.05 ] ∧ [ p̂ ≥ 0.05 ]. (9.10)

Two-light rule.
Publish/act only if (CWA_OK = green) ∧ (χ ≤ χ*). (9.11)

9.6 Neuro-pipeline translation (drop-in settings)

Where “S” lives. Protocol cards and analysis templates, not free text:
[TaskSpec], [Windows], [Units], [Invariants], [TraceIDs], [Answer]. (9.12)

Where “T” lives. Multi-pass analysis:
Pass-1 (explore features, cool), Pass-2 (fit/segment calls, warm), Pass-3 (verify/CSA, cool). (9.13)

Where “χ/CSA” live. χ panel from draft logits/labels + loop/contra rates; CSA/ε from your three pure critics (Units • NLI-vs-Given • Trace-referencer). (9.14)

9.7 Minimal recipes (paste-and-run)

(A) Volatility → starch tier.
v := α_len·v_len + α_sym·v_sym + α_amb·v_amb + α_hist·v_hist; pick S by (9.6). (9.15)

(B) χ monitor (per batch).
χ_t := 0.4·ΔH↓_t + 0.3·L_loop,t + 0.3·C_contra,t; Alarm if χ̄ ≥ 0.6. (9.16)

(C) Heat controller.
if χ̄≥χ* or max ε>0.05 → T:=T₁; S:=next tier; else keep T:=T₂ then T₃ for verify. (9.17)

(D) Commit rule.
Commit labels ⇔ CWA_OK ∧ χ≤χ*. Else: SRA only; add redundancy; retry. (9.18)

9.8 Defaults & dashboards (one screen)

Defaults. S ∈ {1,2,3}%, χ*=0.6, T_pass as (9.8), CSA/ε thresholds per §2, CWA α=0.05. (9.19)

Dashboard rows.
Top: CSA@3 trend; Mid-L: ε heatmap; Mid-R: χ sparkline + alarm; Bottom: CWA lamp + action coach (“Cool T / Raise S / Add redundancy / SRA only”). (9.20)

9.9 Why this is principled (not just vibes)

ESI’s “starch + sous-vide” maps exactly to the observer math: bounded scaffolds make the policy measurable and critics approximately commute; redundant trace fragments meet the SBS condition; CSA/CWA certify objectivity. The free-energy sketch explains why small S lowers loop channels (χ↓). That’s why the same settings that make LLM tool use creamy also stabilize EEG/MEG/fMRI/ECoG/TMS analysis stacks.

Analogy. Keep your sauce from curdling: add a pinch of starch (S), warm it slowly (T), don’t overload the pot (K), and taste-test with three tasters who agree no matter the order (CSA). If the sauce starts to clump (χ↑), cool it, add a touch more starch, and only plate when the CWA light is green.

10. Metrics & Dashboards (What to Look At Every Day)

10.1 Core KPIs (single-line, Blogger-ready)

Cross-system agreement (three independent, non-mutating critics):
CSA@3 := (1/N) · Σⱼ 1{ majority label for item j unchanged under all grader orderings }. (10.1)

Order-sensitivity (held-out set D):
ε_AB := Pr_{d∼D}[ A∘B(d) ≠ B∘A(d) ]. (10.2)

Redundancy (receipts per claim):
ρ := (total fragments logged) ÷ (total claims). (10.3)

Stability dial (segment-level; see §4):
Δ_t := ĝ_t · β̂_t − γ̂_t, Δ̄ := EMA_W(Δ_t). (10.4)

CWA certificate (pooling legality):
CWA_OK ⇔ [ CSA@3 ≥ 0.67 ] ∧ [ max ε_AB ≤ 0.05 ] ∧ [ p̂ ≥ 0.05 ]. (10.5)

Why these five? They’re the computable proxies of the observer-with-trace guarantees: latching (delta-certainty), commuting effects, and redundant records → objectivity. The dashboard bundles them into one glance.

10.2 Threshold bands (defaults you can ship)

CSA@3: green ≥ 0.67, amber 0.50–0.67, red < 0.50. (10.6)
ε_AB (each pair): green ≤ 0.05, amber 0.05–0.08, red > 0.08. (10.7)
ρ (redundancy): green ≥ 2.0, amber 1.5–2.0, red < 1.5. (10.8)
Δ̄ (needle): green ≤ −0.2, amber −0.2…+0.2, red ≥ +0.2. (10.9)
CWA light: green iff (10.5); else red → SRA only. (10.10)

10.3 Screen layout (copy this arrangement)

Top-left: Δ̄ big needle.
Top-right: CUSUM S_t with alarm line h.
Middle-left: ĝ, β̂, γ̂ mini-gauges (arrows vs. previous session).
Middle-right: CSA@3 bar + ε heatmap + ρ.
Bottom: CWA light and Action Coach (if Δ̄ red: suggest “reduce g / chunk β / add γ”; if CWA red: “SRA only; add redundancy; refactor critics”).

Analogy. Think cockpit: the Δ needle is your horizon, the CSA bar + ε map are your instrument cross-checks, and the CWA lamp is the “clear to land” light.

10.4 Ready-to-paste plotting calls (minimal stubs)

CSA trend (with band):
plot_line(csa_series, y_ref=0.67, title="CSA@3 (goal ≥ 0.67)") (10.11)

ε heatmap (flag hot cells):
plot_heatmap(epsilon_matrix, vmax=0.10, annotate_hot>0.05) (10.12)

Redundancy bar:
plot_hbar({"fragments/claim": rho}, bands=[1.5, 2.0]) (10.13)

Δ needle + CUSUM:
plot_gauge(delta_bar, bands=[-0.2, 0.2]); plot_line(S_t, y_ref=h) (10.14)

CWA lamp:
lamp = "green" if (csa≥0.67 and max_eps≤0.05 and p_hat≥0.05) else "red" (10.15)

These stubs match the CLI from §8 (obs csa, obs epsilon, obs cwa, obs delta) so you can wire them without notebooks.

10.5 Alert rules (paste into your ops playbook)

A1. Quarantine noisy critic.
If ε_AB spikes above 0.05 for any pair → quarantine that critic, split inputs (make it pure), and re-run ε/CSA before publishing. (10.16)

A2. Cool guidance on CSA dip.
If CSA@3 EMA < 0.67 → cool ĝ (reduce reframe rate), raise redundancy ρ, and hold pooling (CWA=red). (10.17)

A3. Permutation fail.
If p̂ < 0.05 (order/phase) → SRA only; stabilize timing; do not average or actuate. (10.18)

A4. Δ̄ in red.
If Δ̄ ≥ +0.2 → Action Coach suggests (g↓ / β↓ / γ↑), then re-check CSA/ε before committing new labels to Trace. (10.19)

A5. Verify before export.
Publish only if VerifyTrace=1 and CWA_OK=green; attach dataset_root_hash in footer. (10.20)

10.6 Daily loop (10 minutes, every session)

Compute ĝ, β̂, γ̂, Δ̄, S_t; 2) Run CSA/ε; 3) Run CWA p̂; 4) Render the five-line board; 5) Append event to Trace (hash-chained); 6) Export one-page report (numbers aligned in footer). (10.21)

Footer block (auto).
CSA@3=… max ε=… ρ=… p̂=… ĝ/β̂/γ̂=… Δ̄=… S_max/h=… CWA=… dataset_root_hash=… (10.22)

10.7 Why this dashboard is defensible

Math-to-ops link. Latching (fixedness) + commuting effects + redundancy ⇒ objectivity; your CSA/ε/CWA panels are the operational mirrors. (10.23)
Clinically legible. One dial (Δ̄), one lamp (CWA), one cross-check (CSA + ε + ρ)—the same recipe used in our closed-loop control and Freud→Control bridges. (10.24)
Reproducible. The ObserverOps blueprint ships the SDK, dashboards, and config playbooks so another lab can rerun your exact board. (10.25)

Bottom line. If the Δ needle settles, the CSA bar stays high, the ε map stays cool, redundancy ρ ≥ 2, and the CWA light is green—you can trust your averages and (if applicable) arm interventions. If any lamp flips red, drop to SRA only, fix the culprit, and try again.

11. Failure Modes & Falsification

11.1 Quick map of what can break (tests you can run)

Non-measurable policy (Π not a function of the written past).
Measurability pass: Meas_OK ⇔ Var[ Π(T_t, y_t, c_t) ∣ T_t fixed ] ≤ θ_m. (11.1)
Replay the same T_t (and context y_t,c_t) through Π; if actions vary, Π is peeking at hidden/unstated state → stop pooling/actuation. This violates the “policy is ℱ_t-measurable” premise behind latching.

Non-commuting checks (order changes the verdict).
Commutation pass: Commute_OK ⇔ max ε_AB ≤ 0.05, where ε_AB := Pr[ A∘B ≠ B∘A ]. (11.2)
If any ε cell is hot, critics interact; fix inputs or split effects before averaging.

Missing redundancy (no receipts).
Redundancy pass: ρ := fragments/claim ≥ 2.0 (text + time-locked sensor). (11.3)
Without SBS-style redundancy, agreement cannot “stick.”

Frame mis-alignment (bad remaps across areas/modalities).
Alignment pass (estimate f̂ by Procrustes/CCA): E_align := ∥ f̂(X_A) − X_B ∥_F ÷ ∥X_B∥_F ≤ 0.2. (11.4)
High E_align means compare/average within frame only (SRA).

Pooling legality (recap).
CWA_OK ⇔ [ CSA@3 ≥ 0.67 ] ∧ [ max ε_AB ≤ 0.05 ] ∧ [ p̂ ≥ 0.05 ]. (11.5)
If false → SRA only, fix the cause, and re-run checks.

Analogy. If your thermometers fight each other (ε hot) or you lost the receipts (ρ low), don’t average them; read each thermometer separately (SRA).

11.2 Falsification, not just “error-bars” (how to disprove us fairly)

(F1) Latching-in-practice test.
We predict: writing e_t changes action distributions because Π reads T_t.
Test: Δ_u := d_TV[ u ∣ (T⊕e) , u ∣ (T⊕e′) ] over matched sessions; expect Δ_u > θ_l. (11.6)
If Δ_u ≈ 0 after verifying Meas_OK, implementation contradicts “collapse-as-conditioning” at the policy layer—report as a falsifier.

(F2) AB-fixedness test under stated premises.
Premises satisfied: Commute_OK ∧ ρ ≥ 2 on a held-out set. Prediction: order-invariant agreement.
Falsifier: ∃d : A∘B(d) = B∘A(d) ∧ redundant writes, yet majority label flips under order. (11.7)
If observed, this violates the AB-fixedness guarantee (not just low power). Publish as a counterexample.

(F3) Permutation invariance after CWA pass.
Premise satisfied: CWA_OK = green. Prediction: p̂ ≈ uniform ≥ 0.05 under order/phase shuffles.
Falsifier: p̂ ≪ 0.05 repeatedly with green gates → hidden coupling or frame leak; if audits clear, the CWA recipe is insufficient—document and amend thresholds. (11.8)

(F4) Hinge switching without evidence.
Prediction (hinges): no switch unless log-BF crosses λ.
Falsifier: Λ_T < λ yet hinge flipped across raters/tools passing CSA → hyperprior spec invalid. (11.9)

11.3 Stress tests (break it on purpose before it breaks you)

ST-1: Non-measurable Π. Replay identical T_t but hide a private cache Π was using; flag Meas_OK if actions now differ. Expect (11.1) to fail; fix by making inputs explicit in T.

ST-2: Non-commuting critics. Let O₂ read a post-edited draft from O₁; ε spikes by design; verify (11.2) catches it; refactor to pure critics with disjoint inputs.

ST-3: Missing redundancy. Drop sensor receipts (ρ→1); CSA becomes brittle; CWA flips red. Restore dual fragments to pass (11.3), (11.5).

ST-4: Frame scramble. Insert a random orthogonal map between ROI sets; E_align↑, CSA falls across frames; verify (11.4) forces per-frame SRA.

ST-5: Hinge jitter. Force frequent hinge flips below λ; BF stream alarms (11.9) should fire; if not, calibrate λ or BF estimators.

11.4 Counterexample library (template)

{
  "id": "CE_ST2_noncommute_v1",
  "purpose": "Show ε hot when critics interact",
  "setup": {
    "O1": "units/invariants",
    "O2": "NLI reading O1-mutated text (bad)",
    "O3": "trace referencer"
  },
  "expected": {
    "max_epsilon": ">0.05",
    "CSA@3": "<0.67",
    "CWA_OK": false
  },
  "fix": "Make O2 read Given/Trace only; split O2 if needed"
}

Ship a dozen such JSON cases (non-measurable Π, missing ρ, frame scramble, hinge jitter) and keep them in /tests/counterexamples/.

11.5 When to revert to per-case (SRA) immediately

SRA_NOW ⇔ [¬Meas_OK] ∨ [max ε_AB > 0.05] ∨ [ρ < 2] ∨ [E_align > 0.2] ∨ [p̂ < 0.05]. (11.10)
Turn off pooling and actuation; append an incident note; fix, re-verify, then restore CWA flow.

11.6 Ops glue (tiny scripts you’ll actually run)

Policy measurability probe.
δΠ := mean_t 1{ Π(T_t,y_t,c_t) ≠ Π(T_t,y_t,c_t) on exact replay }. (11.11)
Pass ⇔ δΠ ≤ θ_m (e.g., 1%).

Alignment probe (per batch).
E_align := ∥ f̂(X_A) − X_B ∥_F ÷ ∥X_B∥_F; Pass ⇔ E_align ≤ 0.2. (11.12)

Falsifier logger.
Append { test_id, premise_checks, metric_values, verdict } to trace.jsonl; hash-chain as usual so falsifiers are auditable facts, not opinions. (11.13)

11.7 Why this is the right kind of “hard to fake”

Latching & measurability. If Π ignores T, replay exposes it (11.1); the algebraic fixed-point view explains why this matters.
Agreement from commuting + redundancy. ε and ρ are the computable guards for AB-fixedness; our CWA gate formalizes pooling legality.
Hinges with evidence. Bayes-factor streams make “certainty” falsifiable by design.
Governance spine. Hash-chained traces, RBAC/consent, and incident runbooks make failures visible and recoverable.

Plain recap. If your “thermometers” (critics) interfere, or you lack receipts, or you’re comparing apples in one frame to oranges in another, don’t average. Use these tests to catch each failure fast, publish per-case when needed, and—crucially—keep a small library of counterexamples so you can prove your gates actually work. That’s falsifiable science, not vibes.

12. Case Studies & Starter Protocols

12.1 EEG microstate labeling — order-swap critics + redundant traces

Goal. Label EEG segments with microstates, prove objectivity (CSA/ε), and only pool sessions when the CWA gate is green.

Neural proxy dials. β_neuro := state-switch rate (HMM/microstates) per minute; γ_neuro := 1 ÷ τ_recover; Δ_neuro := g_neuro·β_neuro − γ_neuro. (12.1)

Critics (pure, non-mutating).
O₁=Units/constraints (windowing, SNR, artifact bounds); O₂=Microstate/HMM labeler; O₃=Trace-referencer (verifies ≥2 receipts/claim). CSA_neuro := fraction stable under all orderings; ε_AB := Pr[A∘B ≠ B∘A]. (12.2)

Redundancy rule. Every claim = text note + time-locked sensor fragment (≥2 receipts) in an append-only trace with hash-chain: h₀:=0; h_t:=H(h_{t−1} ∥ canonical_json(e_t)). (12.3)

CWA gate (pooling legality). CWA_neuro ⇔ [CSA@3 ≥ 0.67] ∧ [max ε_AB ≤ 0.05] ∧ [p̂ ≥ 0.05] (order/phase permutations). (12.4)

Pre-registered endpoints.
Primary: CSA@3, max ε_AB, p̂; Secondary: β_neuro, γ_neuro, Δ̄_neuro (EMA). Pass ⇔ CWA_neuro=green. (12.5)

SOP (copy-paste).

Segment EEG → compute features; 2) Run O₁/O₂/O₃; 3) Compute ε, CSA@3; 4) Permute order + circular phase for p̂; 5) If CWA=green, average; else SRA only; 6) Append one event to trace.jsonl with prev_hash/hash. (12.6)

One-liners to report.
β_neuro = transitions/min; γ_neuro = 1 ÷ τ_recover; Δ̄_neuro = EMA(ĝ·β̂−γ̂). (12.7)

Why it’s defensible. Order-insensitive majors + redundant receipts realize the agreement theorem; the hash-chain makes latching operational.

12.2 fMRI/TMS: PFC-as-meta-observer perturbation (CWA-gated)

Goal. Causally test the g_neuro handle by perturbing dlPFC and observing Δ_neuro.

Neural handles. g_neuro := strength(PFC→target) (DCM/Granger or TMS-evoked transfer); Δ_neuro := g_neuro·β_neuro − γ_neuro. (12.8)

Design (Battery A). Single-pulse dlPFC TMS blocks interleaved with baseline; measure evoked transfer + ROI patterns; parallel EEG/MEG for β_neuro, probes for γ_neuro. Prediction: lowering g_neuro (TMS) → Δ_neuro↓, hitting-time (CUSUM) shifts right. (12.9)

Objectivity checks (before pooling). Run CSA_neuro across {EEG critic, MEG critic, fMRI critic}; compute ε and permutation p̂; require CWA_neuro=green. (12.10)

Pre-registered endpoints.
Primary: Δ_neuro change (pre vs post TMS), CUSUM S_t shift; Secondary: g_neuro gain drop, CI (optional binding cascade). Fail if Δ_neuro unchanged with verified g_neuro↓. (12.11)

SOP (copy-paste).

Acquire fMRI (or SEEG where available) + TMS timing logs; 2) Estimate g_neuro; 3) Run EEG/MEG microstates for β_neuro, probes for γ_neuro; 4) Compute Δ̄_neuro, S_t; 5) Gate pooling by CWA; 6) Append hashed events; 7) Export one-page report with dataset root hash. (12.12)

Why it’s defensible. “Meta-observer PFC” is tested via directed gain; Δ-dial gives a one-number causal readout; CWA avoids order/phase illusions.

12.3 ECoG language-game task — hinge switching metrics

Goal. Operationalize “meaning = use” and hinge certainty in an intracranial language-game, reporting calibration and BF trajectories.

Meaning-as-use (policy). Estimate π_θ(a∣x) ∝ exp(θ·φ(x,a)) from interaction/choice logs; report ΔU versus baseline and ECE for calibration. (12.13)

Hinges (slow hyperpriors, BF stop). Maintain Λ_T := Σ_{t≤T} log BF_t; switch hinge iff Λ_T ≥ λ (cost-of-change). (12.14)

Agreement & publicness. Report κ/α across raters; pre-commit CWA gate before any across-trial pooling. (12.15)

Pre-registered endpoints.
Primary: Fit AUC (picture→world CSP), ΔU (policy lift), ECE (↓ better), κ/α (↑ better), BF trajectory Λ_T (hinge switch events). (12.16)

SOP (copy-paste).

Build scene-graphs (CSP) for “picture fit”; 2) Run max-ent IRL for π_θ; 3) Compute ECE, κ/α; 4) Maintain BF streams for hinges; 5) Gate pooled metrics by CWA; 6) Append hashed trace events with tool cards/versions. (12.17)

Why it’s defensible. Wittgenstein-operationalized gives CSP/IRL/BF instruments + reporting standards (prereg, artifacts, thresholds).

12.4 Pre-registration mini-template (fill & paste)

Hypotheses. H₁: TMS lowers g_neuro and thus Δ_neuro; H₂: microstate β_neuro predicts Δ̄; H₃: hinge switches occur only when Λ_T ≥ λ. (12.18)
Primary endpoints. CSA@3, max ε_AB, p̂; Δ̄_neuro; Fit AUC, ΔU, ECE, κ/α, Λ_T. (12.19)
Stopping rules. CWA=red ⇒ SRA only; hinge switch at τ* = inf{T : Λ_T > λ}. (12.20)
Artifacts. Code, configs, seeds, container lockfile, dataset/Merkle roots, tool cards. (12.21)

12.5 Copy-paste SOP blocks (per case)

EEG microstates (CSA/ε/CWA).
Compute: β_neuro, γ_neuro, Δ̄_neuro, CSA, ε, p̂. Publish: only if CWA=green; else SRA. Trace: append JSONL event with prev_hash/hash. (12.22)

fMRI/TMS (Δ perturbation).
Estimate: g_neuro (DCM/evoked transfer); recompute Δ̄_neuro; CUSUM S_t shift. Gate: CWA. Fail: Δ unchanged with g drop. (12.23)

ECoG language-game (hinges).
Run: CSP fit → IRL policy → ECE/κ/α → BF stream. Switch: only when Λ_T ≥ λ. Gate pooled AUC/ΔU by CWA. (12.24)

12.6 Compact reporting footer (paste under each figure)

CSA@3=… max ε=… p̂=… ρ=… β_neuro=… γ_neuro=… Δ̄_neuro=… g_neuro=… S_max/h=… FitAUC=… ΔU=… ECE=… κ/α=… Λ_T=… env_hash=… seeds=… dataset_root_hash=… (12.25)

12.7 Why these three are “starter-ready”

Same math, three modalities. y=Ω̂[x], g/β/γ→Δ, CSA/ε/CWA, and hashed traces are shared scaffolds; only the sensors change. (12.26)
Causal + calibrated. PFC perturbation tests g_neuro; microstates probe β_neuro; ECoG games quantify meaning and hinges with BF and calibration (ECE). (12.27)
Repro-first. Prereg, seeds, containers, and Merkle roots make results portable; the CWA gate keeps averages honest. (12.28)

Analogy (to brief the team). Three different kitchens, same line check: do the tasters agree regardless of order (CSA/ε)? Is the house special stable (Δ needle)? Are receipts in the drawer (redundancy + hashes)? If yes, serve the average; if not, plate per case.

13. Ethics, Safety, and Governance

13.1 What we enforce (one screen, one-liners)

De-identification (default-on).
Redaction rule: redact(text) := Redact(text; rules R, token set Σ). (13.1)
Salted tokenization (no plaintext IDs): map[token] := H_salt(identifier). (13.2)
Retention windows: TTL_A≤6 mo, TTL_B≤24 mo, TTL_C≤36 mo, TTL_D≥36 mo. (13.3)

Consent & cognitive liberty.
Consent machine-state: consent(u,scope) ∈ {none, minimal, metrics_only, full_sharing}. (13.4)
Off-switch: if consent < metrics_only ⇒ stop metrics & exports. (13.5)

Auditability (tamper-evident).
Trace hash-chain: h₀:=0; h_t:=H(h_{t−1} ∥ canonical_json(e_t)). (13.6)
Verify trace: VerifyTrace(T)=1 ⇔ recompute(h_T)=stored(h_T). (13.7)
Admin/audit log chain: ℓ₀:=0; ℓ_t:=H(ℓ_{t−1} ∥ canonical_json(log_t)). (13.8)

Role-based access (RBAC).
Allow rule: Allow(u, a, r)=1 ⇔ [ role(u)∈policy[a,r] ∧ consent(r)≥level(a) ]. (13.9)

“Do-not-average” locks (CWA gate).
Publish/act only if: CWA_OK ⇔ [CSA@3≥0.67] ∧ [max ε_AB≤0.05] ∧ [p̂≥0.05]. (13.10)
UI lock: DoNotAverage = 1{¬CWA_OK}. (13.11)

Sharing guardrail.
PublishOK ⇔ [CWA_OK] ∧ [k-anonymity k≥5] ∧ [no Class-A fields]. (13.12)

Incident clock (S1/S2/S3).
T_detect≤24 h; T_contain≤48 h; T_notify(S1)≤72 h. (13.13)

Drift & fairness monitors.
Drift: D_t:=PSI(P_t,P_ref) (or KL); alert if D_t≥δ. (13.14)
Parity: gap_CSA := max_group(CSA) − min_group(CSA); flag if gap_CSA>0.15. (13.15)

Human-in-the-loop.
“Dashboard is assistive; clinician decides. No covert collection. Pooling legal only with CWA_OK; else SRA (per-case).”

Why these are principled. Latching and agreement are made operational by append-only hashes and CWA gating; RBAC/consent enforces cognitive liberty; all of this ties back to the formal observer calculus (delta-certainty; commuting effects).

Analogy. Seatbelts and a black box: you always wear the seatbelt (redaction/RBAC), the cockpit recorder is immutable (hash-chains), and you don’t take off unless the tower’s green light (CWA) is on.

13.2 Copy-paste policy blocks (minimal, production-ready)

A) Access & consent (RBAC).

{
  "rbac": {
    "roles": ["patient","clinician","annotator","supervisor","ops","researcher","auditor"],
    "allow": "Allow(u,a,r)= (role(u)∈policy[a,r]) && (consent(r)≥level(a))",
    "reviews": {"cadence_days":30, "revoke_inactive_days":60}
  },
  "consent_states": ["none","minimal","metrics_only","full_sharing"],
  "off_switch": "if consent<metrics_only: stop_metrics=true; stop_exports=true"
}

(Ready-to-use mappings and consent semantics per Appendix F.)

B) Exports & residency.

exports:
  allowlist_targets: ["grc-vault","soc-binder"]
  format: "jsonl+sig"
  dlp: { enabled: true, block_on_match: ["P3","auth_token"] }
  residency: { eu: ["eu-grc-vault"], us: ["us-grc-vault"] }
  rate_limits: { max_bytes_s: 2000000, max_records_min: 5000 }

(Ship signed manifests; block non-allowlisted sinks; enforce DLP and residency.)

C) Do-not-average lock (UI).

{
  "cwa_gate": "CWA_OK = (CSA>=0.67) && (max_eps<=0.05) && (p_hat>=0.05)",
  "ui": { "avg_button_enabled": "CWA_OK", "banner_if_false": "SRA only" }
}

(Prevents pooled reports/actions when evidence is unstable.)

D) Audit log schema (hash-chained).

{
  "log_id":"L000123",
  "iso_time":"2025-10-18T16:03:22Z",
  "actor_id":"u_451","actor_role":"Clinician",
  "action":"READ","resource":"segments.jsonl","resource_id":"S001_seg03",
  "details":{"fields":["r_strength","stance_shift"]},
  "ip":"203.0.113.45","sig":"ed25519:...=="
}

Audit chain: ℓ_t = H(ℓ_{t−1} ∥ canonical_json(log_t)); verify with VerifyAudit(L)=1. (13.16)

13.3 De-identification SOP (default-on)

Classify fields into A (identifiers), B (content), C (derived), D (governance); redact A; tokenize references in B; keep C/D separate.
Token map stored in Ops-only vault; de-redaction allowed only for Clinician/Auditor, always audit-logged.
Right-to-erasure via crypto-erase (rotate keys; rebuild de-ID view) while preserving minimal anchored hashes for integrity.

13.4 Human oversight & ethical use

Humans decide. The board is advisory; sensitive interventions require clinician approval; researchers receive de-ID aggregates only with CWA_OK.
Hinge transparency. Declare hinge priors, Bayes-factor thresholds, and who set them (Hinge Card); publish subgroup calibration and agreement.
Risk limits. Cap framing intensity/frequency; cool-off windows; full debrief for any deception-style task; pre-checks for harm content.

13.5 Security & compliance quicksheet

Crypto. AES-256 at rest; mTLS in transit; keys in KMS/HSM; split-role approvals for key export.
Privacy dashboards. PII detections, encryption coverage, export DLP blocks, RBAC drift, residency violations, trace integrity.
SOC/ISO mapping. RBAC reviews, signed admin logs, export allowlists, privacy-lint in CI; include policy hash and ledger head hash in every export.

13.6 Failure response (who does what, when)

Severity ladder: S1 identifiers, S2 integrity, S3 availability. Clock in plain text: detect ≤24 h; contain ≤48 h; notify (S1) ≤72 h. (13.17)
Recipe: isolate → rotate keys → VerifyTrace & VerifyAudit → notify → root-cause → harden → post-mortem (hash the report).

13.7 Why this governance maps to the math (one breath)

Latching ⇒ immutability: Append-only, hash-chained traces make “you can’t unhappen a write” operational (delta-certainty).
Agreement ⇒ CWA gate: Commuting critics + redundancy + permutation guard yields a computable legality test for averaging (CWA_OK).
Cognitive liberty ⇒ RBAC/consent: The person controls scope; researchers get aggregates only under PublishOK.
Falsifiable ops: All accesses and exports are signed and chain-verified; drift/fairness meters expose bias over time.

Bottom line. Treat privacy, consent, and audit as first-class invariants. Keep the CWA lamp wired to a do-not-average lock. If evidence or consent drops, the system falls back to SRA automatically. That’s how rigorous math (latching, agreement) becomes everyday clinical safety you can defend—to patients, IRBs, and auditors alike.

14. Appendices — A. Notation & One-Line Identities (Blogger-ready Unicode)

Paste as-is. All equations are single-line Unicode with (14.n) tags; symbols match Sections 0–13.

A1. Core objects & symbols

Observer triplet (measure, write, policy): ℴ := (M, W, Π). (14.1)
Append-only trace: T_t = T_{t−1} ⊕ e_t. (14.2)
Event schema (minimal): e_t := (τ_t, channel_t, label_t, meta_t). (14.3)
Hash chain (tamper-evident): h₀ := 0; h_t := H(h_{t−1} ∥ canonical_json(e_t)). (14.4)
Trace verification: VerifyTrace(T)=1 ⇔ recompute(h_T)=stored(h_T). (14.5)

Policy call (controller reads record): u_t = Π(T_t, y_t, c_t). (14.6)
World + readout (no model commit): x_{t+1} = F(x_t, u_t, T_t) + η_t; y_t = H(x_t) + ε_t. (14.7)

Latching (delta-certainty of own write): Pr(e_t ∣ T_t)=1; E[1{e_t=a} ∣ T_t]=1{a=e_t}. (14.8)
Commutation (order-insensitive check): A∘B(d)=B∘A(d). (14.9)

CSA (3 critics, order-invariant majority): CSA@3 := (1/N)·Σ_j 1{majority label unchanged under all orderings}. (14.10)
Order-sensitivity (held-out D): ε_AB := Pr_{d∼D}[A∘B(d) ≠ B∘A(d)]. (14.11)
Permutation p-value (order+phase): p̂ := (1/B)·Σ_{b=1}^B 1{|mean(s)−mean_{π_b}(s)| ≥ |mean(s)−mean_π(s)|}. (14.12)
CWA gate (pooling legality): CWA_OK ⇔ [CSA@3 ≥ 0.67] ∧ [max ε_AB ≤ 0.05] ∧ [p̂ ≥ 0.05]. (14.13)

Stability dial (behavior/physio): Δ := ĝ·β̂ − γ̂. (14.14)
Guidance slope: ĝ := cov(r,s) ÷ var(r). (14.15)
Amplification rate: β̂ := (1/T)·Σ_t (jumps_t ÷ minutes_t). (14.16)
Damping buffer: γ̂ := 1 ÷ τ_recover. (14.17)

Neuro mirrors: Δ_neuro := g_neuro·β_neuro − γ_neuro; β_neuro := transitions/min; γ_neuro := 1 ÷ τ_recover(neural). (14.18)
Directed gain (meta-observer PFC): g_neuro := strength(PFC→target) (DCM/Granger/evoked). (14.19)
Binding cascade: CI := coh(V1↔IT)·coh(IT↔PFC) (lag-ordered). (14.20)
Claustral synchrony: CL_sync := mean_coh(claustrum↔cortex)_{integrated} − baseline. (14.21)

Picture→world fit (CSP homomorphism): ∃h:V→D s.t. (v₁,…,v_m)∈Q_j ⇒ (h(v₁),…,h(v_m))∈R_j. (14.22)
Meaning = use (max-ent policy): π_θ(a∣x) ∝ exp(θ·φ(x,a)). (14.23)
Calibration (ECE, b bins): ECE := Σ_{b=1}^B (|S_b|/N)·|acc(S_b)−conf(S_b)|. (14.24)
Agreement (κ, α): κ := (p_o−p_e)÷(1−p_e); α := 1 − (D_o ÷ D_e). (14.25)

Hinges (Bayes-factor stream): Λ_T := Σ_{t≤T} log BF_t; switch hinge iff Λ_T ≥ λ. (14.26)

Frame map & alignment error: E_align := ∥f̂(X_A)−X_B∥_F ÷ ∥X_B∥_F. (14.27)

ESI phase knobs: S := starch %; T := decoding/decision temperature; χ := clump order parameter. (14.28)
Clump score (default weights): χ := 0.4·ΔH↓ + 0.3·L_loop + 0.3·C_contra. (14.29)

Psychoanalytic operators (scheduleable):
Repression: Ŝ_tight[x] := Ŝ[x] + Λ·χ_taboo(x). (14.30)
Isolation: U_⊥(C) := diag(C). (14.31)
Projection: x′ := R_θ·x. (14.32)
Sublimation: V_id^→ := V_id + μ·B_safe; −∇V_id^→ = −∇V_id − μ∇B_safe. (14.33)

PID (discrete): e_t=Δ−Δ_t; z_t=z_{t−1}+e_t·Δt; u_t=K_p e_t + K_i z_t + K_d (e_t−e_{t−1})/Δt.* (14.34)
LQR (local, discrete): u_t=−Kx_t; K=dlqr(A,B,Q,R) with x_{t+1}≈Ax_t+Bu_t. (14.35)

A2. Identities, passes, and “red→green” fixes

Policy measurability pass: Meas_OK ⇔ Var[Π(T_t,y_t,c_t) ∣ T_t,y_t,c_t fixed] ≤ θ_m. (14.36)
Commutation pass: Commute_OK ⇔ max ε_AB ≤ 0.05. (14.37)
Redundancy pass: ρ := fragments/claim ≥ 2.0. (14.38)
Alignment pass: Align_OK ⇔ E_align ≤ 0.2. (14.39)

Publish/act rule: PublishOK ⇔ CWA_OK ∧ VerifyTrace(T)=1 ∧ consent ≥ metrics_only. (14.40)
SRA trigger (no pooling): SRA_NOW ⇔ [¬Meas_OK] ∨ [max ε_AB>0.05] ∨ [ρ<2] ∨ [E_align>0.2] ∨ [p̂<0.05]. (14.41)

Idempotent append: Append(T,e) is a no-op if event_id(e) exists with identical hash. (14.42)
Daily roll-ups: R_day := MerkleRoot({h_t for day}); R_dataset := MerkleRoot({R_day}). (14.43)

AB-fixedness (operational rule-of-thumb): Commute_OK ∧ ρ≥2 ⇒ order-invariant majority on held-out (CSA@3 high). (14.44)

Δ needle colors (defaults): green if Δ̄ ≤ −0.2; amber if −0.2<Δ̄<0.2; red if Δ̄ ≥ 0.2. (14.45)

ESI two-light rule: Commit ⇔ (CWA_OK = green) ∧ (χ ≤ χ), with χ≈0.6.** (14.46)

A3. Thresholds & defaults (copy block)

CSA@3 ≥ 0.67; max ε_AB ≤ 0.05; p̂ ≥ 0.05; ρ ≥ 2.0; E_align ≤ 0.2; χ = 0.6; Δ̄ bands = (−0.2, +0.2).* (14.47)

Starch budget S: 1% (low volatility), 2% (medium), 3% (high). (14.48)
Sous-vide passes: T₁ cool (0.3–0.5), T₂ warm (0.6–0.8), T₃ cool (0.2–0.4). (14.49)

PID safe start: K_p small; K_i = 0 until CSA stable; K_d for overshoot; rate-limit + saturate; gate by CWA_OK. (14.50)
LQR guard: large R for invasive actuators (TMS/tFUS); always gate by CWA_OK. (14.51)

Pre-reg endpoints (common): CSA@3, max ε_AB, p̂, ρ, Δ̄ (with ĝ,β̂,γ̂), ECE, κ/α, Λ_T, VerifyTrace, dataset_root_hash. (14.52)

A4. Report footers (uniform fields)

CSA@3=… max ε=… p̂=… ρ=… ĝ/β̂/γ̂=… Δ̄=… S_max/h=… FitAUC=… ΔU=… ECE=… κ/α=… Λ_T=… g_neuro=… CI=… CL_sync=… env_hash=… seeds=… dataset_root_hash=… (14.53)

A5. One-line reminders (to brief the team)

“You can’t unhappen your own write” → use (14.2), (14.4), (14.5), (14.8). (14.54)
“Don’t average fighting thermometers” → require (14.10)–(14.13). (14.55)
“One dial, one lamp” → watch Δ̄ and CWA_OK (14.14, 14.13). (14.56)
“If χ clumps or ε spikes, cool/structure then retry” → (14.29), (14.37), (14.46), (14.49). (14.57)

End Appendix A.

14. Appendices — B. 10-Line Recipes (CSA/ε/CWA, Δ Estimators, Controllers)

Paste as-is. Each block is exactly 10 lines, Blogger-ready Unicode with (14.Bx.n) tags. Thresholds match the CWA certificate.

B1. CSA/ε/CWA in 10 lines (order-swap agreement, interference, legality to average)

Build three pure, non-mutating critics O₁,O₂,O₃ with disjoint inputs (units • NLI-vs-Given • trace-referencer). (14.B1.1)
For each item d, compute 2-of-3 majorities under all 6 orders; CSA@3 := (1/N)·Σ 1{majority unchanged}. (14.B1.2)
On a held-out set D, for each pair (A,B) estimate ε_AB := Pr_{d∼D}[A∘B(d) ≠ B∘A(d)]. (14.B1.3)
Compute a scalar per case (score sⱼ); define T_obs := | mean(s) − mean_π(s) | where π shuffles grader order & phase. (14.B1.4)
p̂ := (1/B)·Σ_{b=1}^B 1{ | mean(s) − mean_{π_b}(s) | ≥ T_obs }. (14.B1.5)
Track redundancy ρ := fragments/claim (text + time-locked sensor); require ρ ≥ 2. (14.B1.6)
CWA_OK ⇔ [ CSA@3 ≥ 0.67 ] ∧ [ max ε_AB ≤ 0.05 ] ∧ [ p̂ ≥ 0.05 ]. (14.B1.7)
If ¬CWA_OK ⇒ SRA only (per-case reporting; no pooling/actuation). (14.B1.8)
Append one ledger event: h_t := H(h_{t−1} ∥ canonical_json(e_t)) (tamper-evident). (14.B1.9)
Report footer: CSA@3, max ε, p̂, ρ, CWA_OK, seeds, env_hash, dataset_root_hash. (14.B1.10)

B2. Δ estimators in 10 lines (push × echo − buffer, with CUSUM)

Prepare per-segment signals: r_t (guidance/“push”), s_t (stance shift), jumps_t/minutes_t, τ_recover. (14.B2.1)
ĝ := cov(r,s) ÷ var(r) (guidance slope; robust to scale). (14.B2.2)
β̂ := (1/T)·Σ_t (jumps_t ÷ minutes_t) (amplification rate). (14.B2.3)
γ̂ := 1 ÷ τ_recover (damping/buffer). (14.B2.4)
Δ_t := ĝ_t·β̂_t − γ̂_t; Δ̄ := EMA_W(Δ_t). (14.B2.5)
CUSUM: S_t := max(0, S_{t−1} + Δ_t − τ); alarm if S_t ≥ h. (14.B2.6)
Bands: green if Δ̄ ≤ −0.2; amber if −0.2<Δ̄<0.2; red if Δ̄ ≥ +0.2. (14.B2.7)
Defaults: α=0.05 (CWA), window W=3, log 95% CIs for ĝ,β̂,γ̂. (14.B2.8)
Act only if CWA_OK; else cool guidance or add redundancy, then recompute. (14.B2.9)
Append Δ event to Trace (hash-chain); include Δ̄, S_max, τ,h in footer. (14.B2.10)

B3. Controller stubs (CWA-gated)

B3-A. PID in 10 lines (model-light, safe by default)

If ¬CWA_OK ⇒ u_t := u_hold; return. (14.B3A.1)
Target dial: Δ* (e.g., −0.2); error e_t := Δ* − Δ_t. (14.B3A.2)
Integrator: z_t := clamp(z_{t−1} + e_t·Δt, z_min, z_max) (anti-windup). (14.B3A.3)
Derivative: d_t := (e_t − e_{t−1}) ÷ Δt. (14.B3A.4)
Raw control: u_raw := K_p e_t + K_i z_t + K_d d_t. (14.B3A.5)
Safety: u_lim := rate_limit(u_raw; ρ_max); u_t := sat_U(u_lim) (bounds, IPIs). (14.B3A.6)
Defaults: K_p small; K_i=0 until CSA stable; K_d to tame overshoot. (14.B3A.7)
Log Δ̄, u_t, guard states; if CSA dips or ε spikes, arm u_hold. (14.B3A.8)
Append actuation event to Trace (hash-chain). (14.B3A.9)
Publish only with VerifyTrace=1 and CWA_OK=green in footer. (14.B3A.10)

B3-B. LQR in 10 lines (when a local model is available)

If ¬CWA_OK ⇒ u_t := u_hold; return. (14.B3B.1)
Identify local dynamics: x_{t+1} ≈ A x_t + B u_t (ridge on recent window). (14.B3B.2)
Choose costs: Q ≽ 0 (weight Δ/Δ-coords), R ≻ 0 (actuator penalty). (14.B3B.3)
Solve Riccati (discrete): K := dlqr(A,B,Q,R). (14.B3B.4)
Policy: u_raw := −K x_t. (14.B3B.5)
Safety: u_t := sat_U(rate_limit(u_raw)). (14.B3B.6)
Re-ID A,B on a rolling window; freeze K if CSA dips or ε warms. (14.B3B.7)
Prefer large R for invasive actuators (TMS/tFUS). (14.B3B.8)
Hash-append controller step to Trace; store Q,R,K,A,B in tool card. (14.B3B.9)
Publish only with CWA_OK=green and VerifyTrace=1. (14.B3B.10)

Why these work. The CSA/ε/CWA block is the operational mirror of the observer results (latching + commuting + redundancy), Δ compresses push/echo/buffer into one actionable dial, and the controller stubs are thin, CWA-gated policies that respect safety and provenance (append-only, hash-chained Trace).

14. Appendices — C. Repro Pack (Seeds, Configs, Metrics Harness)

Paste-as-is. Blogger-ready Unicode; single-line equations with (14.Cn) tags. Matches the SOPs and gates from §§8–13.

C1. Seeds & versions (what every run must record)

Seed vector (four knobs).
s⃗ := (s_global, s_split, s_solver, s_boot). (14.C1)

Environment tuple (hashable).
Env := (OS, CUDA/Driver, BLAS, Python, libs, commit). (14.C2)

Reproduce flag (metrics-tolerant).
Reproduce(D, s⃗, Env)=1 ⇔ ∀m∈M, |m′−m| ≤ tol_m, M={CSA@3, max ε, p̂, ĝ, β̂, γ̂, Δ̄, ECE, κ/α, Λ_T}. (14.C3)

meta.json (drop-in).

{
  "dataset_version": "v1.0.0",
  "dataset_root_hash": "af21…",
  "env_hash": "sha256:…",
  "global_seed": 314159,
  "split_seed": 271828,
  "solver_seed": 161803,
  "boot_seed": 141421
}

(Seeds & versions logged alongside the dataset root hash.)

C2. Config file (paths, thresholds, seeds, switches)

configs/paper.yaml (copy-paste).

paths:
  data:        "/data"
  trace:       "/trace/trace.jsonl"
  graders_glob:"/trace/graders_O*.jsonl"
  out_dir:     "/dashboards"
thresholds:
  csa_min: 0.67
  eps_max: 0.05
  alpha_cwa: 0.05
  delta_bands: [-0.2, 0.2]
repro:
  env_hash: "sha256:…"
  seeds: {global:314159, split:271828, solver:161803, boot:141421}
report:
  include: [CSA, epsilon, CWA, rho, ghat, bhat, ghat_buf, Dbar, ECE, kappa, alpha, BF]
  footer_hashes: true

(Thresholds = CWA certificate defaults; footer prints hashes/seeds.)

C3. Metrics harness (one-screen CLI)

CSA (order-invariant majority).
obs csa --graders /trace/graders_O*.jsonl --out /dashboards/csa.json (14.C4)

ε (order-sensitivity heatmap).
obs epsilon --graders /trace/graders_O*.jsonl --heldout /data/heldout.jsonl --out /dashboards/eps.json (14.C5)

CWA permutation test (order + phase).
obs cwa --scores /data/session_scores.json --B 1000 --out /dashboards/cwa.json (14.C6)

Δ-dials (ĝ, β̂, γ̂, Δ̄, CUSUM).
obs delta --segments /data/segments.jsonl --out /dashboards/delta.json (14.C7)

Calibration & agreement extras.
obs calib --probs probs.json --labels y.json --out ece.json • obs agree --labels graders.json --out kap_alpha.json • obs bf --liks H1.json H0.json --out bf.json (14.C8)

Green-light rule (auto).
CWA_OK ⇔ [CSA@3 ≥ 0.67] ∧ [max ε_AB ≤ 0.05] ∧ [p̂ ≥ 0.05]. (14.C9)

C4. Deterministic data generation (synthetic fixtures)

Poisson jumps (amplification proxy).
assoc_jumps ∼ Poisson(λ = topic_density × escalation_speed). (14.C10)

Affect AR(1) with scripted shocks (buffer proxy).
affect_t = μ + ϕ·affect_{t−1} + ε_t; recovery slope → γ̂ := 1 ÷ τ_recover. (14.C11)

Split recipe (stable splits).
train/dev/test = 70/15/15 with stratify by scenario × Δ-regime using split_seed. (14.C12)

C5. Δ estimators (the exact one-liners the harness uses)

Guidance slope: ĝ := cov(r,s) ÷ var(r). (14.C13)
Amplification rate: β̂ := (Σ_t jumps_t) ÷ (Σ_t minutes_t). (14.C14)
Buffer: γ̂ := 1 ÷ median_i(τ_recover,i). (14.C15)
Dial & EMA: Δ_t := ĝ_t·β̂_t − γ̂_t; Δ̄ := EMA_W(Δ_t). (14.C16)
CUSUM: S_t := max(0, S_{t−1} + Δ_t − τ); alarm if S_t ≥ h. (14.C17)

C6. Hashes & exports (tamper-evident by default)

Trace chain: h₀ := 0; h_t := H(h_{t−1} ∥ canonical_json(e_t)). (14.C18)
Merkle roll-ups: R_day := MerkleRoot({h_t}); R_dataset := MerkleRoot({R_day}). (14.C19)
Verify: VerifyTrace(T)=1 ⇔ recompute(h_T)=stored(h_T). (14.C20)
Export footer fields: env_hash, seeds, dataset_root_hash, CSA@3, max ε, p̂, ĝ/β̂/γ̂, Δ̄, ECE, κ/α, Λ_T. (14.C21)

C7. Unit tests that must pass (repro sanity)

Idempotent append: re-append same event → h_T unchanged. (14.C22)
CSA invariance: shuffling grader order leaves CSA@3 stable on a fixed batch. (14.C23)
ε sanity: construct an interaction (O₂ reads O₁ output) → ε_AB > 0. (14.C24)
Permutation fairness: IID scores → p̂ ≈ 0.5; order-coupled scores → p̂ → 0. (14.C25)
Seed reality: rerun obs delta with same s⃗ → identical Δ̄ (within tol). (14.C26)

C8. One-command run (quickstart)

obs repro --config /configs/paper.yaml --export /dashboards/report.pdf (14.C27)
(Computes CSA/ε/CWA, Δ-dials, calibration, agreement, BF; emits a one-page report with hashes & seeds.)

C9. What “pass” looks like (acceptance bands)

CSA@3 ≥ 0.67; max ε_AB ≤ 0.05; p̂ ≥ 0.05; Δ̄ in green (≤ −0.2); VerifyTrace=1; footer shows env_hash, seeds, dataset_root_hash. (14.C28)

C10. Notes & pointers (where each piece comes from)

Seeds/splits & synthetic fixtures: Appendix D (seeds, Poisson/AR(1), split recipe).
CSA/ε/CWA gates: Section 8 (definitions, permutation p̂).
Δ & CUSUM: Session-to-dashboard SOP (E.2–E.6).
Hashes/exports: Governance appendix (F.3–F.6) + Quickstart.

Bottom line. Lock s⃗ and Env, run the four CLI calls, check the CWA lamp, and export with hashes. Anyone with your meta.json and config can rerun your figures and land on the same numbers. That’s the whole point of this repro pack.

References

Core observer/measurement theory and ops

Self-Referential Observers in Quantum Dynamics: A Formal Theory of Internal Collapse and Cross-Observer Agreement. [SRO] — Formal filtration/latching (delta-certainty), commutation, and AB-fixedness; the math backbone.
https://osf.io/7cbsu/files/osfstorage/68c5961e10e31c4095d998f5
ObserverOps Technical Blueprint. [OBS] — Engineering playbook: trace ledger, CSA/ε/CWA gates, APIs, dashboards.
https://osf.io/yj5aw/files/osfstorage/68d30242dd3f77699b3c315f
Semantic Meme Field Theory (SMFT): Foundations, Projection, and Dynamics (Rev1). [SMFT] — Field layer linking continuous evolution with punctate collapse; frame invariance.
https://osf.io/ya8tx/files/osfstorage/68e77fa0cd19895405a0d243
Emulsion-Stabilized Inference (ESI): Phase-Controlled Decoding with Structural “Starch” and Observer-Aligned Verification. [ESI] — “Smoothness” (χ), starch budgets, sous-vide schedules; plugs into CSA/CWA.
https://osf.io/q8egv/files/osfstorage/68d58d6a5d44329625432c73
Semantic Collapse Geometry: A Unified Topological Model Linking Gödelian Logic, Attractor Dynamics, and Prime Number Gaps. [SCG] — Collapse topology; invariants and attractor structure.
https://osf.io/7jzpq
Proto-Eight Collapse Geometry—SMFT Applied to Growth, Memory, and Systems Built on Incubation Trigram (先天八卦). [P8] — Application of collapse geometry to growth/memory patterns.
https://osf.io/ya8tx/files/osfstorage/68b84641534f31b42fef989e

Control, action, and variational foundations

AGI by Surplus-Aware Control: A Closed-Loop Framework of Surplus Flows, Semantic Field Geometry, and Dissipative Decoding. [SAC] — Closed-loop surplus flows; links to Δ = ĝ·β̂−γ̂.
https://osf.io/2wmky/files/osfstorage/68bd728b0fd5cbd1040356a2
From Entropy-Minimizing Attractor Proofs to Dissipative Lagrangian Dynamics: A Rigorous Foundation for the HeTu–LuoShu Variational Framework. [HT-DL] — Variational/dissipative groundwork for the HeTu–LuoShu formalism.
https://osf.io/2wmky/files/osfstorage/68b4d262a233f0f2da96aecd
A Generalized Least Action Principle for Local and Dissipative Systems: Axioms, Proof, and Domain of Validity. [GLA] — Generalized action for non-conservative systems; domain where Δ-style control is valid.
https://osf.io/2wmky/files/osfstorage/68b32a5ff4b17ecb9dc62067
The Slot Interpretation of HeTu and LuoShu: A Rigorous Mathematical and Semantic Proof by Wolfram 4.1 GPTs
https://osf.io/692wg/files/osfstorage/68960924847e9ead456b0e6c
Δ5 Phase Opposition in HeTu: Pairwise Minimum-Dissipation Cycles and a D₁₀–Spectral Extension of the Slot Interpretation
https://osf.io/38pw7/files/osfstorage/68e578b1dbe76397706d350d
[HT-Slot] — Slot structure, phase opposition, spectral extensions for collapse scheduling.

Methods, coherence, and macro structure

CAFT + CWA + SRA: A Universal Additive Model of Macro Coherence (App A–F). [CAFT/CWA/SRA] — Coherence accounting; the “certificate to average” recipe and per-case reporting rules.
https://osf.io/7cbsu/files/osfstorage/68a3065155d1ad4d6c7e40d4
Industrializing Insight: A Reproducible Method to Empower （灌頂加持）LLMs via the E=G+M+D Decomposition. [E=G+M+D] — Practical instrumentation of guidance (ĝ), amplification (β̂), damping (γ̂).
https://osf.io/6mybg/files/osfstorage/68d7dce87b362f1ca4b8f825
v1_01-05 System Topology Knowledge Base (txt). [STKB] — Glossary/topology snippets used across sections.
https://osf.io/q8egv/files
Belt Holonomy Is Inevitable_ A Two-Boundary Worldsheet from Standard Quantum Geometry
https://osf.io/yaz5u/files/osfstorage/68cd926d1fd155818374e8f1
Belt Theory for AGI — A Mini-Textbook
https://osf.io/yaz5u/files/osfstorage/68cdecc75ecb719a6a413f46
Purpose-Flux Belt Theory (PFBT)
https://osf.io/yaz5u/files/osfstorage/68d01dd47195bb99223b7dfe
ONE Assumption 帶出宇宙⌈意圖⌋的必然性
https://gxstructure.blogspot.com/2025/09/one-assumption.html
— Macro-intent and purpose-flux notes (contextual background).

Consciousness/awareness geometry

The Geometry of Awareness: Designing Semantic Collapse in AI Systems
https://www.amazon.com/dp/B0F8NSFKKM
意識原本: 重構語義、模因與AI自我之源代碼 (Traditional Chinese Edition)
https://www.amazon.com/dp/B0F8D32ZJD
[GoA] — Emergence of Ô (observer) as a projection solution in nonlinear dynamics.
Trace之道：語義 AI 的設計哲學與未來教育場景重構
https://gxstructure.blogspot.com/2025/04/trace-ai.html
Ô Mirror：數位阿賴耶識與語義投胎系統設計白皮書
https://gxstructure.blogspot.com/2025/04/o-mirror.html
[Ālaya] — Applications of deep memory store constructs in observer terms.
Unified Field Theory of Everything - Ch1~22 Appendix A~D
https://osf.io/ya8tx/files/osfstorage/68ed687e6ca51f0161dc3c55
[UFTE] — Broad unification backdrop; used here only for notation/intuition.
Nested Uplifts Inevitability: A Sequential-Evidence and Small-Gain Theory of Regime Switching in Open Dissipative Systems
https://osf.io/ne89a/files/osfstorage/68effd340c8fad784bc40616
Nested Uplifts Inevitability (INU) Assumption 3.3 and the Riemann Hypothesis: Engineering Relaxations, Conceptual Bridges, and What Current Evidence Allows
https://osf.io/y98bc/files/osfstorage/68f0afbacaed018c3cc3fd9b
The Birth of Arithmetic Stability Theory: A Mathematical Bridge Rooted in Confucian Symmetry and Balance
https://fieldtheoryofeverything.blogspot.com/2025/10/the-birth-of-arithmetic-stability.html
從⌈黎曼猜想⌋到 - 觀察的本質就是「譜塌縮」
https://gxstructure.blogspot.com/2025/10/blog-post_17.html
[INU/RS] — Regime switching and spectral-collapse notes (used for stress-test design).

Bridging to brain science & humanities (the three on-topic companions)

The Observer And The Observed: A Unified Theory of Consciousness Across Biological Systems. [O&O] — PFC as meta-observer; claustrum as binder; proposed empirical batteries.
https://thegrandredesign.substack.com/api/v1/file/fd4ad912-ba1f-439b-a7e2-e472580c8851.pdf
From Psychoanalytic Constructs to Closed-Loop Control: A Rigorous Mathematical Recast of Freud via Observer-Centric Collapse. [Freud→Control] — Operators Ŝ_tight, U_⊥, R_θ, V^→; safe scheduling in Δ-space.
https://osf.io/w6be2/files/osfstorage/68f3d5d48a8dd1325519ff88
Wittgenstein, Operationalized: A Unified Mathematical Framework for Picture Theory, Language Games, and Hinge Certainty. [Witt-Ops] — CSP picture-fit, IRL “meaning = use,” BF hinge switching.
https://osf.io/tjf59/files/osfstorage/68f2c1745bd9c41be2f98369

Disclaimer

This book is the product of a collaboration between the author and OpenAI's GPT-5, Wolfram's GPTs language model. While every effort has been made to ensure accuracy, clarity, and insight, the content is generated with the assistance of artificial intelligence and may contain factual, interpretive, or mathematical errors. Readers are encouraged to approach the ideas with critical thinking and to consult primary scientific literature where appropriate.

This work is speculative, interdisciplinary, and exploratory in nature. It bridges metaphysics, physics, and organizational theory to propose a novel conceptual framework—not a definitive scientific theory. As such, it invites dialogue, challenge, and refinement.

I am merely a midwife of knowledge.

Saturday, October 18, 2025

Observer-Centric Neurocybernetics: Unifying Closed-Loop Control, Language-Game Semantics, and Hinge Hyperpriors for Brain Science

Observer-Centric Neurocybernetics: Unifying Closed-Loop Control, Language-Game Semantics, and Hinge Hyperpriors for Brain Science

0. Executive Overview — Diagrams Pack

Figure 0-A. The Observer Loop (Measure → Write → Act)

Figure 0-B. Thermostat-with-a-Notebook Analogy

Figure 0-C. “Agreement You Can Trust” Panels

Figure 0-D. The Trace Ledger (Immutability at a Glance)

Figure 0-E. System Planes (Where Each Step Runs)

Figure 0-F. One-Minute CWA Certificate Checklist

Sources behind the figures (for readers without our library)

1. Minimal Math, Human Words: The Observer Triplet

1.1 First principles (plain words → one-liners)

1.2 Latching = “conditioning on your own record”

1.3 Commutation = “checks that don’t interfere”

1.4 Implementation (copy-paste friendly)

1.5 Why this is rigorous (quick anchors)

2. Agreement You Can Trust: CSA & the CWA Certificate

2.1 Why this section exists (objectivity before averaging)

2.2 Single-line, Blogger-ready definitions (copy next to your figures)

2.3 Implementation — minimal recipes you can run today

2.3.1 Build three pure critics (no mutations)

2.3.2 Compute ε (order-sensitivity) and CSA (order-invariant majority)

2.3.3 Permutation test (order + phase)

2.3.4 Decide pooling

2.4 Dashboard spec (one screen your team will actually use)

2.5 Troubleshooting & good habits

3. Mapping to Brain Experiments (EEG/MEG/fMRI/ECoG/TMS)

3.1 One-page crosswalk (what maps to what)

3.2 Protocol blocks you can run this week

(A) Order-swap rater pipeline (build ε and CSA first)

(B) Redundant trace fragments (text + time-locked sensor)

(C) Pre-registered endpoints (clear dials + falsifiers)

3.3 Modality cheat-sheet (how to compute each dial)

3.4 Safety, governance, and reporting (the boring bits that save you)

3.5 Plain-speech recap (why this is practical)

4. Closed-Loop Control for Neuroscience

4.1 Treat Π as a controller (the loop we actually run)

4.2 The stability dial (push × echo − buffer)

4.3 Safe actuation: only when evidence says “OK”

4.4 Controller baselines you can deploy this week

(A) PID (robust, model-light)

(B) LQR (when you can identify a local model)

4.5 Safe action sets, rate limits, and consent

4.6 Implementation sketch (neurofeedback, TMS/tDCS/tFUS, task gating)

4.7 Audio channel-strip analogy (for the whole team)

4.8 When to stop or switch strategies (failure modes → actions)

5. Language-Game Semantics in the Lab (Wittgenstein, Operationalized)

5.1 What we measure (plain words → one-liners)

5.2 Picture→world fits you can compute (CSP/ILP templates)

5.3 Meaning-as-use via IRL (trust-region loop you can run)

5.4 Calibration & evaluation harness (ECE, κ/α, BF)

5.5 End-to-end implementation (drop-in blocks)

5.6 Subway-map analogy (why teams “get it” fast)

Where to look if readers want proofs or deeper scaffolding

6. Psychoanalytic Knobs as Safe Operators (Clinically Intuitive, Mathematically Clean)

6.1 Operator dictionary (one-liners + what they do)

6.2 How they combine in one closed-loop step (the “plug-in chain”)

6.3 Scheduling & safety (what you actually run)

6.4 30-second micro-cases (before/after)

6.5 When not to use hard gates (and what to do instead)

6.6 Pedagogy cards (paste alongside your plots)

6.7 Why this is rigorous (anchor in one breath)

7. Data & Trace Engineering

7.1 Non-negotiables (design goals → one-liners)

7.2 JSON schemas (paste-and-run)

7.3 ID & hashing conventions (cut-sheet)

7.4 Minimal APIs (append, query, certify)

7.5 Ops runbook (daily/weekly you can actually do)

7.6 “Show me” examples (ready to paste)

7.7 Why this works (and how it maps to the math)

8. Tooling Stack & Reproducibility

8.1 The Repro Contract (what every run must record)

8.2 Container spec (drop-in)

8.3 Project scaffold (paste this tree)

8.4 CLI: CSA/ε/CWA + core dials (four commands)

8.5 Minimal unit tests (must pass before publish)

8.6 Metric harness scripts (calibration, agreement, evidence)

8.7 Compute budget reporting (fair, apples-to-apples)

8.8 One-command reproduction (Quickstart)