https://osf.io/yj5aw/files/osfstorage/68d30242dd3f77699b3c315f  
https://chatgpt.com/share/68d309e8-ad44-8010-bfdf-b4b42e7c4f17 

ObserverOps Technical Blueprint - Appendices

 

Appendix A — Mathematical Details

(full definitions, lemmas, theorems with proof sketches)

A.0 Notation and Standing Assumptions

• Probability spaces are $(\Omega,\mathcal F,\mathbb P)$. Random variables are upper-case; realized values lower-case.

• Hilbert spaces $\mathcal H$; bounded operators $\mathcal B(\mathcal H)$.

• An observer is the tuple

  $$O=(S, T, \hat O, \tau, \Pi, C)$$

  with internal state $S$, append-only trace $T=\{(\tau_k,\pi_k,y_k,\text{meta}_k)\}_{k\ge 0}$, scheduler $\hat O$, tick $\tau\in\mathbb N$, instrument set $\Pi$, and a compatibility/commutation graph $C\subseteq \Pi\times\Pi$. The ledger is hash-chained and only advanced on append (idempotent writes).

• Filtration: $\mathcal F_{\le \tau}$ is the $\sigma$-algebra generated by the committed trace up to tick $\tau$. Internal collapse (latching) asserts fixed-point behavior of realized outcomes w.r.t. conditional expectation and branch-dependent control after commit.

---

A.1 Internal Collapse (Latching as Fixed Points)

Definition A.1 (Internal Collapse)

Let $Y_k$ be the (random) outcome at tick $\tau_k$ for channel $\pi_k$. After committing $(\tau_k,\pi_k,y_k)$ to the trace, internal collapse requires:

1. Fixed-point (delta-certainty):

$$\mathbb E[\,Y_k\mid \mathcal F_{\le \tau_k}\,] \equiv y_k .$$

2. Branch measurability: any future policy $f$ (e.g., $\hat O$) satisfies

$$f(S, T_{\le \tau_k+1}) \text{ is } \mathcal F_{\le \tau_k}\text{-measurable}.$$

3. Append-only uniqueness per tick: at most one record with key $\tau_k$; corrections append new records (never UPDATE).

Theorem A.1 (Latching as Conditional-Expectation Fixedness)

Let $\mathcal E_{\le \tau}: \mathcal B(\mathcal H_W\otimes \mathcal H_M)\to \mathcal F_{\le \tau}$ denote the conditional expectation onto the observer’s past algebra (operator-algebraic form). Then any event $X\in \mathcal F_{\le \tau}$ is a fixed point: $\mathcal E_{\le \tau}(X)=X$. In particular, committed outcomes are self-certainties in-frame.
Sketch. In the von Neumann algebra view, the observer filtration $\{\mathcal F_{\le \tau}\}_\tau$ is an increasing tower; conditional expectation onto $\mathcal F_{\le \tau}$ fixes that subalgebra. Apply to the spectral projector of the realized outcome.

Corollary A.2 (No Silent Retro-Edit)

If writes are hash-chained and $\tau$ advances only on append, any mutation of a past record breaks the chain; therefore policies measurable w.r.t. $\mathcal F_{\le \tau}$ cannot depend on a hypothetical retro-edit. Operational guardrails (idempotency keys, atomic measurement→commit) enforce the model.

---

A.2 Cross-Observer Agreement (AB-Fixedness)

We study two observers $O_A,O_B$ with frame maps $\phi_{A\to K}, \phi_{B\to K}$ to canonical keys $K$. Aligned channels $(\pi_A,\pi_B)$ for key $k\in K$ commute if $[\pi_A,\pi_B]=0$ on the visited support; agreement is scored only on commuting overlaps.

Definition A.3 (Shared / Redundant Records; SBS Proxy)

Agreement is conditioned on either (i) a shared, hash-chained ledger accessible to both observers; or (ii) SBS-style redundancy: independent fragments $E_1,\dots,E_R$ each carrying the same pointer value with redundancy proxy via majority/permutation stability.

Theorem A.3 (AB-Fixedness)

Let $K^\star\subseteq K$ be keys with (i) commuting aligned effects, (ii) shared or SBS-redundant records, and (iii) latched traces. Then for every $(k,\tau)\in K^\star$, the effective outcomes used by $O_A$ and $O_B$ coincide a.s. (agreement in downstream control).
Sketch. (1) Commutation yields order-independence of joint outcomes on $K^\star$. (2) Shared/SBS records imply both observers condition on the same $\sigma$-algebra about pointer values. (3) Latching fixes the record; downstream policies are $\mathcal F_{\le \tau}$-measurable. Hence the conditional laws—and thus selected effective outcomes—match.

Proposition A.4 (Redundancy Error Bound)

If each fragment independently errs with $p<\tfrac12$, the majority over $R$ fragments has error

$$\mathbb P[\text{maj wrong}] \le \exp\!\big(-2R(\tfrac12-p)^2\big)$$

(Hoeffding), giving exponential decay of disagreement under independence; correlated fragments can be handled by a block/bootstrap effective $R_{\text{eff}}$.

Counterexamples. Non-commuting probes; hidden channels; mis-mapped frames—all break the premises and can yield disagreement despite superficial overlap.

---

A.3 CWA — Collapse Without Alignment (Certified Additive Pooling)

Setup

Items $X=\{x_i\}_{i=1}^N$. A projector $P$ yields $z_i=P(x_i)\in\mathbb R^d$. Candidate additive pool $\mu_0=\tfrac1N\sum_i z_i$ (or sum). CWA asks whether order/phase/orientation are irrelevant after projection, so project→add is admissible.

Certificate Family

Three invariance panels sampled $K$ times: permutations (order), sign-flips (orientation), chunk-shuffle (boundary). Distances $\delta(\mu^{(j)}_k,\mu_0)$ are normalized and aggregated to a score $\in[0,1]$; a Phase-Risk Index (PRI) screens for strong order/phase structure. Gate pooling if score/PRI fail band thresholds.

Theorem A.5 (Certificate ⇒ Additive Validity, Operational Form)

Assume: (i) $P$ is collapse-compatible for the task (semantic observable; no essential phase/order post-projection), and (ii) the certificate passes with score $\ge \theta$ and PRI within band. Then any Lipschitz downstream functional $g$ on the pool satisfies

$$\max_{j,k}\; \|\,g(\mu^{(j)}_k)-g(\mu_0)\,\| \le L\,\varepsilon(\theta)$$

for a task-calibrated $\varepsilon(\theta)\to 0$ as $\theta\to 1$.
Sketch. Invariance under permutations ⇒ order-indifference; sign-flip stability ⇒ orientation conventions are collapsed; re-chunk robustness ⇒ boundary effects washed out. Combine with Lipschitz continuity of $g$ and empirical distances bounded by the certificate.

Limits. Coherent chains (e.g., strong sequential logic), positional encodings that survive projection, or projector drift can fail the tests; auto-fallback to order-aware estimators is then required.

---

A.4 Slot Conservation (Quantized Capacity Law)

Model

Typed slot pools $q\in\{\text{memory},\text{tools},\text{attention}\}$ with integer capacities $N_q$. Events allocate, release, evict, and collisions when no admissible slot is available without violating policy. Invariants S1–S4: (S1) integer addresses, (S2) non-overlap, (S3) explicit eviction policy, (S4) observability (occupancy/collision logs).

Lemma A.6 (Pigeonhole Non-Overlap)

If $m$ mutually exclusive holds are active in pool $q$ and $m>N_q$, a collision (or eviction of a guarded item) is inevitable. Proof. Direct pigeonhole principle; integer non-fractional slots forbid overlap.

Theorem A.7 (Stability Under Back-Pressure)

Suppose arrivals form a bounded-burst process with peak $B$, guard periods prevent eviction of in-flight items, and the allocator admits back-pressure to the scheduler $\hat O$. If $N_q\ge B$ and $\hat O$ respects can_allocate gates, the long-run collision rate admits a green-band bound (e.g., memory <0.5%, tools <1%) under stationary demand. Sketch. Standard queueing with admission control; the Ô-gate enforces an effective utilization $\rho<1$ ensuring rare collisions; empirical bands follow from logs.

Ops notes. Guard periods, typed pools, and linking slot events to $(\tau,\pi)$ enable audits and targeted mitigation.

---

A.5 SMFT (Meso-Control) Essentials

We treat the semantic field $\Psi_m(x,\theta,\tau)$ with projection $P\Psi_m$ used by the scheduler $\hat O$. Two operational metrics: Attractor Load

$$\mathrm{AL}(x,\tau)=\frac{\max_{\theta} w_\theta \,\|P\Psi_m(x,\theta,\tau)\|}{\sum_{\theta} w_\theta \,\|P\Psi_m(x,\theta,\tau)\|+\varepsilon},$$

and Collapse Entropy $S_c(\tau)=-\sum_\theta p_\theta(\tau)\log p_\theta(\tau)$ from recent selections. Fleet sync uses Kuramoto-style order parameter $\rho$. These feed $\hat O$’s channel selection score, with compatibility bonuses and cadence gates.

---

A.6 PFBT — Purpose-Belt Holonomy Law (Macro Closure)

Worldsheet Variables (Discrete Windows)

For window $n$: Gap $G_n$, Flux $F_n$, Twist $T_n$, coupling $\alpha_n$, residual $R_n=G_n-(F_n+\alpha_n T_n)$. Evolution model

$$G_{n+1}=G_n-(F_n+\alpha_n T_n)+\eta_n,\qquad R_n=G_n-(F_n+\alpha_n T_n),$$

with $\eta_n$ capturing sensing error/latent flux, bounded by acceptance checks (two-boundary Stokes, gluing, $4\pi$ periodicity).

Theorem A.8 (Residual Control via Two-Timescale Controller)

Consider Flux-gate (fast) and Twist-step (slow) controllers with gains $(k_P^F,k_I^F)$ and bounded step $|\Delta T|\le \tau_{\max}$; assume: (i) acceptance checks bound $|\eta_n|\le \bar\eta$, (ii) Twist updates are separated by at least four Flux-gate time constants, (iii) $\alpha_n$ varies slowly with bounded variance. Then there exist gains and bands $(\varepsilon_g,\varepsilon_a)$ such that $R_n$ remains within $[\!-\varepsilon_a,\varepsilon_a]$ and returns to $[\!-\varepsilon_g,\varepsilon_g]$ after bounded disturbances.
Sketch. Linearize around $R=0$. The fast loop stabilizes the inner difference equation for $G_n$ under bounded $\eta_n$. Singular-perturbation (two-timescale) arguments ensure the slow Twist-step adjusts $\alpha T$ to cancel steady residual bias; acceptance checks guarantee model closure so the residual error behaves as an input-bounded disturbance.

Audit primitives. Compute Gap/Flux/Twist by quadrature over belt edges and worldsheet; assert PBHL residual $r=|\,\text{Gap}-(\text{Flux}+\alpha\,\text{Twist})\,|\le \tau_{\mathrm{PBHL}}$; verify gluing and $4\pi$ checks; update the Five-Line KPI.

---

A.7 Aggregated Assumptions & Failure Modes

• A-IC. Append-only, hash-chained trace; tick advances only on append (breaks ⇒ no latching).

• A-COM. Agreement scored only on commuting overlaps (breaks ⇒ order artifacts).

• A-SBS. Either shared ledger or redundant fragments with high stability (breaks ⇒ inconsistent conditioning).

• A-CWA. Certificate pass + PRI within band before additive pooling (breaks ⇒ order/phase leakage).

• A-SLOT. Integer, non-overlap slots with Ô-gated admission (breaks ⇒ collisions/thrash).

• A-PBHL. Acceptance checks bound closure error; two-timescale controller tuned (breaks ⇒ residual drift).

---

What this appendix gives you in practice

• A precise latching semantics you can unit-test.

• Agreement conditions with quantitative redundancy bounds.

• A certified criterion for when project→add is safe.

• Slot allocator invariants with stability guarantees.

• A macro closure law with controller-level guarantees and auditable checks.

---

 

Appendix B — Complexity & Scaling

(certificate costs, belt-controller overhead, sync metrics complexity)

B.0 Symbols & Scale Parameters

• $N$: items per pool (e.g., projected vectors).

• $d$: projection dimension (post-$P$).

• $K_{\text{perm}},K_{\text{flip}},K_{\text{chunk}}$: certificate panel sizes.

• $M$: number of belts (programs) monitored.

• $E,F$: belt mesh edges/faces used by acceptance checks.

• $R$: observers/agents whose ticks we synchronize.

• $W$: rolling window length (ticks) for metrics.

• $b$: batch size; $\beta$: mini-batch/streaming fraction.

• $\mathsf{nnz}(\cdot)$: sparsity; $\mathsf{FLOPs}(\cdot)$: floating-point ops.

---

B.1 CWA Certificate — Cost Model & Optimizations

Baseline pipeline. Project, then test invariances by (re)pooling perturbed copies and measuring deviation:

$$\mu_0=\tfrac1N\sum_{i=1}^N z_i,\quad z_i=P(x_i)\in\mathbb R^d.$$

B.1.1 Time & Memory Complexity

1. Projection $P$

• Linear map (e.g., whitening): $\mathcal O(N d^2)$ if dense; $\mathcal O(N d)$ if $P$ is diagonal/orthogonal pre-factored.

• Neural projector: $\mathsf{FLOPs}(P)\approx \sum_\ell \mathcal O(N d_{\ell-1}d_\ell)$.

• Memory: store $Z=[z_i]$ → $\Theta(N d)$.

2. Pooling once (mean/sum): $\mathcal O(Nd)$; memory $\Theta(d)$.

3. Permutation panel ($K_{\text{perm}}$ samples)

• If the candidate aggregator is additive, naive re-pooling is redundant (mean is permutation-invariant). We still evaluate the downstream functional $g$ (e.g., retrieval with $\mu$, scoring, risk metrics).

• Cost: $\mathcal O(K_{\text{perm}}\cdot \mathsf{cost}[g(\mu)])$.

• If you must re-pool (e.g., chunk-first pipelines), do it from cached prefix sums: precompute $S=\sum_i z_i$ once; each shuffle uses the same $S\Rightarrow$ $\mathcal O(d)$.

4. Sign-flip panel ($K_{\text{flip}}$ masks)

• Apply diagonal $D_j\in\{\pm1\}^{d\times d}$: $\mu_j=D_j\mu_0$.

• Cost: $\mathcal O(K_{\text{flip}}d)$ for vector flips + $\mathcal O(K_{\text{flip}}\cdot \mathsf{cost}[g])$.

5. Chunk-shuffle panel ($K_{\text{chunk}}$ samples)

• Re-partition into chunks, re-project if projector depends on chunk boundaries, then pool.

• Worst-case: $\mathcal O(K_{\text{chunk}}\cdot N d)$ (if $P$ re-runs).

• With cached $Z$: $\mathcal O(K_{\text{chunk}}\cdot d)$ if pooling unchanged; otherwise proportional to affected items only.

Total (typical):

$$\mathsf{FLOPs}\;\approx\;\underbrace{\mathsf{FLOPs}(P)}_{\text{one-off}}+\underbrace{\mathcal O(Nd)}_{\text{baseline pool}}+\underbrace{\mathcal O((K_{\text{perm}}+K_{\text{flip}})\cdot \mathsf{cost}[g])}_{\text{light}}+\underbrace{\mathcal O(K_{\text{chunk}}\cdot C_{\text{chunk}})}_{\text{varies}}$$

where $C_{\text{chunk}}\in\{d,\;Nd\}$ depending on whether re-projection is needed.

Memory footprint: $\Theta(Nd)$ to cache $Z$ + $\Theta(d)$ for aggregates + $\Theta(K_{\bullet} d)$ if you store all perturbation outputs (usually streamed → $\Theta(d)$).

B.1.2 Statistical Power vs. Panel Size

Detecting an order/phase sensitivity with effect size $\delta=\mathbb E[\|g(\mu_j)-g(\mu_0)\|]$ and variance $\sigma^2$ under random perturbations requires roughly

$$K_{\text{eff}}\;\gtrsim\;\frac{c\,\sigma^2}{\delta^2}\log\frac{1}{\alpha}$$

replicates to attain type-I error $\alpha$ (Hoeffding/CLT heuristics). Use sequential testing: stop early if the running CI clears the gate.

Rule-of-thumb bands (production):

• Fast path: $K_{\text{perm}}=16,\,K_{\text{flip}}=8,\,K_{\text{chunk}}=8$.

• Caution path (borderline PRI): double chunk panel; keep others fixed.

• Heavy path (audits): $K_{\text{perm}}=64$ with stratified permutations.

B.1.3 Scaling Tricks

• Prefix sums & sketches. Precompute $S=\sum z_i$ and second moment $Q=\sum z_i z_i^\top$ ($\mathcal O(Nd^2)$ if kept dense). Many invariance scores (variance of pooled outputs) reduce to $S,Q\Rightarrow \mathcal O(d^2)$ independent of $N$.

• Subsampling with control variates. Use $\beta N$ items per certificate draw; correct bias with a control-variate term from the global $S$.

• Mixed-precision. FP16 for perturbation passes; keep $S,Q$ in FP32.

• Amortize $g$. If $g$ is retrieval, pre-index candidates; each $\mu_j$ becomes one query (cost depends on ANN engine, often $\tilde{\mathcal O}(d)$).

• Adaptive K. Early exit when the running score is $\ll$ lower band or $\gg$ upper band.

---

B.2 PBHL / Belt Controller — Overhead & Throughput

Two-timescale controller (Flux-gate fast, Twist-step slow) plus acceptance checks (closure tests) and telemetry.

B.2.1 Per-Belt Compute

Per window $n$ and belt $m$:

1. Five-Line KPI update (Gap, Flux, Twist, Coherence, Residual): $\mathcal O(1)$ arithmetic on sufficient statistics.

2. Flux-gate (fast loop at $f_F$ Hz): $\mathcal O(1)$ control law (PID-like) + constant-time gates.

3. Twist-step (slow loop at $f_T\ll f_F$): $\mathcal O(1)$ bounded update and policy checks.

4. Acceptance checks over belt mesh:

   • Boundary integrals (two-boundary / gluing): $\mathcal O(E)$.

   • Surface integral / worldsheet quadrature: $\mathcal O(F)$.

   • $4\pi$ periodicity test: $\mathcal O(1)$ on accumulated holonomy.

Per-belt per-window cost: $\mathcal O(E+F) + \mathcal O(f_F+f_T)$ with tiny constants.
Fleet cost (M belts): linear: $\mathcal O(M(E+F))$. Meshes are coarse in ops practice (dozens–hundreds of cells), so acceptance checks dominate only during recomputation.

B.2.2 Memory & I/O

• Ring buffers for $W$ windows of sufficient stats: $\Theta(MW)$.

• Mesh storage: $\Theta(E+F)$ per belt (small).

• Telemetry export: proportional to event rate; compress KPI streams via delta encoding (typ. $<\!1$ kB/s/belt).

B.2.3 Latency Budget

• Fast loop target: $<\!5$ ms/belt update at $f_F\in[1,5]$ Hz on CPU.

• Slow loop: $<\!1$ ms at $f_T\in[0.05,0.5]$ Hz.

• Acceptance checks: amortize (e.g., every $K_A$ windows or when Residual $\uparrow$).

Throughput scaling: 1 core can comfortably service $\mathcal O(10^2)$ belts at the above rates; scale out linearly across cores/threads because belts are embarrassingly parallel.

---

B.3 Sync Metrics — Complexity & Streaming Algorithms

We compute Kuramoto order parameter $\rho$, Ô-desynchrony $\Delta\tau$ stats, and optional pairwise phase matrices.

B.3.1 Kuramoto $\rho$

Phases $\theta_r\in[0,2\pi)$ per agent $r\in\{1,\dots,R\}$.

$$\rho\,e^{i\psi}=\frac{1}{R}\sum_{r=1}^R e^{i\theta_r}.$$

• Time: $\mathcal O(R)$ per tick (vectorized complex sum).

• Memory: $\Theta(1)$ for running sum; $\Theta(R)$ if you retain phases.

• Sliding window $W$: maintain $S_W=\sum_{t\in W}\sum_r e^{i\theta_{r,t}}$ with a queue → $\mathcal O(1)$ amortized update.

B.3.2 Ô-Desynchrony $\Delta\tau$

Let $\tau_{r}$ be last commit tick per agent; we track dispersion:

$$\Delta\tau_{\text{RMS}}=\sqrt{\tfrac1R \sum_r (\tau_r-\bar\tau)^2},\quad \bar\tau=\tfrac1R\sum_r \tau_r.$$

• Time: $\mathcal O(R)$ per update; streaming Welford algorithm keeps it $\mathcal O(1)$ per event.

• Percentile bands: t-digest or GK-summary → $\mathcal O(\log 1/\epsilon)$ update, $\Theta(1/\epsilon)$ memory.

B.3.3 Pairwise Phase / Lag (Optional, Heavy)

• Full matrix of pairwise lags: $\mathcal O(R^2)$ per snapshot; memory $\Theta(R^2)$.

• Downscaling: sample $S\ll R$ pivots ($\mathcal O(SR)$), or compute graph-sparsified affinity (k-NN in phase space).

• When to use: only during diagnostics; never on critical path.

B.3.4 End-to-End Overhead

A typical fleet ($R\in[10^2,10^4]$, $W\in[60,600]$):

• Kuramoto + $\Delta\tau$: CPU-friendly, $\mathcal O(R)$ per second; $<\!1$ MB memory for summaries.

• Pairwise: enable temporarily with $S$-pivot sampling.

---

B.4 Putting Costs Together (Rules of Thumb)

B.4.1 CWA in RAG/Embeddings

• Projection: cache $Z$ once per index refresh.

• Certificate: start with $K_{\text{perm}}=16,K_{\text{flip}}=8,K_{\text{chunk}}=8$. With cached $Z$, CPU time is dominated by $g$ (ANN queries) not by re-pooling.

• Latency target: $p95$ certificate $<\!50$–$150$ ms for $d\!\in\![256,1024]$, $K_\bullet\!\le\!32$ on commodity CPUs; push heavy panels to async audit lanes.

B.4.2 BeltOps

• Keep meshes small (dozens of cells). Run acceptance checks on schedule or on Residual excursions. Belt updates are $\mathcal O(1)$ and parallel across $M$.

B.4.3 Sync

• Compute $\rho$ and $\Delta\tau$ continuously; reserve pairwise/graph diagnostics for anomalies or research runs.

---

B.5 Engineering Patterns for Scale

• Batching & vectorization. Aggregate perturbations into a single tensor op: stack $\{D_j\mu_0\}_j$ and run $g$ once in batched mode.

• Early exit gates. If first 4–8 perturbations produce a score far inside green/red, stop.

• Cold/warm/hot lanes. Cold (audits, large $K$), warm (borderline), hot (minimal panels).

• Sketch-first. Run certificate on sketches (e.g., $\beta\!\approx\!0.1$ subsample) and escalate only on failure.

• Sparse / low-rank. If $Z$ is sparse or low-rank, store factorizations; compute $S,Q$ in compressed form.

• Pinned CPU cores for belts. Assign belts to cores for cache locality; use lock-free ring buffers for KPI windows.

• Telemetry budgets. Cap event rates; use drop-counters and lossy compression for noncritical streams.

---

B.6 Complexity Table (at a glance)

Component	Time (typical)	Memory	Notes
Projection $P$	$\mathcal{O}(N d)$–$\mathcal{O}(N d^2)$	$\Theta(N d)$	Cache $Z$ (projected items)
Pool once	$\mathcal{O}(N d)$	$\Theta(d)$	Prefix sums / one-pass mean
Certificate (perm)	$\mathcal{O}(K_{\text{perm}}\cdot \mathrm{cost}[g])$	$\Theta(d)$	Mean is permutation-invariant; cost shifts to downstream $g$
Certificate (flip)	$\mathcal{O}(K_{\text{flip}}\cdot d + K_{\text{flip}}\cdot \mathrm{cost}[g])$	$\Theta(d)$	Vectorized sign masks
Certificate (chunk)	$\mathcal{O}(K_{\text{chunk}}\cdot d)$–$\mathcal{O}(K_{\text{chunk}}\cdot N d)$	$\Theta(d)$–$\Theta(N d)$	Depends on whether re-projection is needed
Belt fast loop	$\mathcal{O}(1)$	$\Theta(1)$	PID-like Flux-gate
Belt slow loop	$\mathcal{O}(1)$	$\Theta(1)$	Bounded Twist-step
Acceptance checks	$\mathcal{O}(E+F)$	$\Theta(E+F)$	Boundary/surface integrals; amortizable
Kuramoto $\rho$	$\mathcal{O}(R)$	$\Theta(1)$–$\Theta(R)$	Streaming complex sum
Ô-desynchrony $\Delta\tau$ stats	$\mathcal{O}(R)$ or $\mathcal{O}(1)$ (streaming)	$\Theta(1)$	Welford + t-digest/GK for percentiles
Pairwise phase	$\mathcal{O}(R^2)$	$\Theta(R^2)$	Diagnostics only (use pivots/sparsification)

---

B.7 Sizing Checklist

1. Pick $K_\bullet$ by PRI band and latency SLOs; enable sequential early-exit.

2. Cache $Z$ and precompute $S,Q$; switch chunk panel to sketch mode when stable.

3. Set belts with coarse meshes; run acceptance checks on Residual excursions.

4. Stream sync metrics ($\rho,\Delta\tau$); downsample pairwise diagnostics.

5. Observe budgets: CPU (certificate & $g$), RAM ($Nd$), I/O (telemetry).

---

Outcome: You now have concrete big-O bounds, constant-factor tricks, and deployment patterns to size the certificate battery, keep belt controllers cheap, and run fleet-level sync metrics without quadratic surprises.

 

Appendix C — API Spec

(request/response schemas, examples, error codes)

C.0 Overview

• Base URL (prod): https://api.observerops.io/v1

• Auth: Authorization: Bearer <token>

• Content-Type: application/json; charset=utf-8

• Idempotency: Idempotency-Key: <uuid> on all POST/PUT that mutate state.

• Tracing (recommended): X-Trace-Id, X-Parent-Span, X-Request-Id (UUIDv4).

• Versioning: URI (/v1) + Accept-Version header for minor features.

• Clock: all timestamps ISO-8601 UTC; ticks are integers.

---

C.1 Common Types (JSON Schema fragments)

// C-TYPES (Draft 2020-12; shared snippets)
{
  "$defs": {
    "UUID": { "type": "string", "format": "uuid" },
    "Tick": { "type": "integer", "minimum": 0 },
    "Vector": { "type": "array", "items": { "type": "number" }, "minItems": 1 },
    "KeyVal": { "type": "object", "additionalProperties": true },
    "CommuteMatrix": {
      "type": "array",
      "items": { "type": "array", "items": { "type": "boolean" } }
    },
    "Channel": {
      "type": "object",
      "required": ["id", "type"],
      "properties": {
        "id": { "type": "string" },
        "type": { "type": "string", "enum": ["sensor","tool","query","sim"] },
        "meta": { "$ref": "#/$defs/KeyVal" }
      }
    }
  }
}

---

C.2 Error Model

HTTP uses standard codes; body conforms to:

{
  "error": {
    "code": "INVALID_ARGUMENT",
    "message": "Field 'pi' is missing",
    "field_errors": [{"field":"pi","reason":"required"}],
    "details": {"hint":"Provide a registered channel id"},
    "retry_after_ms": 0,
    "request_id": "7b6c3c2e-..."
  }
}

Canonical error.code values

Code	Meaning	Typical HTTP
INVALID_ARGUMENT	malformed/failed validation	400
FAILED_PRECONDITION	latching/commute/slot pre-req not met	412
CONFLICT	idempotency replay with different body	409
NOT_FOUND	resource absent	404
PERMISSION_DENIED	auth/ACL	403
RATE_LIMITED	token or org throttled	429
INTERNAL	unexpected server error	500
CERTIFICATE_FAILURE	CWA gate failed	422
INCOMPATIBLE_CHANNELS	non-commuting or unmapped frame	409
SLOT_EXHAUSTED	pool at capacity	429
TRACE_IMMUTABLE	attempted retro-edit	409

---

C.3 Endpoints

1) POST /measure — perform a measurement and commit a latched trace

Request

{
  "observer_id": "e7b0c7b1-...",
  "tick": 1021,
  "pi": "tool.search.v2",           // channel id
  "input": {"q":"site:docs foo"},  // channel-specific payload
  "state_ref": "s/obs/e7b0c7b1:v42",
  "commit": true,
  "slots": {"tools": 1},
  "meta": {"run_id":"RAG-7821","tenant":"acme"}
}

Response

{
  "trace_id": "tr_01J9HF5Z0N...",
  "observer_id": "e7b0c7b1-...",
  "tick": 1021,
  "pi": "tool.search.v2",
  "outcome": {"y":{"docs":3,"took_ms":87}},
  "hash": "b8d2e7...ab",
  "prev_hash": "aa7ed1...fe",
  "slots": {"tools":{"allocated":1,"released":0}},
  "committed_at": "2025-09-23T11:05:21Z"
}

Notes

• Latching: past records immutable; retries must reuse Idempotency-Key.

• Slot admission enforced before execution (FAILED_PRECONDITION/SLOT_EXHAUSTED).

---

2) GET /trace/{trace_id} — retrieve immutable trace record

Response

{
  "trace_id":"tr_01J9HF5Z0N...",
  "observer_id":"e7b0c7b1-...",
  "tick":1021,
  "pi":"tool.search.v2",
  "outcome":{"y":{"docs":3,"took_ms":87}},
  "meta":{"run_id":"RAG-7821"},
  "hash":"b8d2e7...ab",
  "prev_hash":"aa7ed1...fe",
  "chain_ok": true
}

---

3) POST /agree — cross-observer agreement check

Request

{
  "A": {"observer_id":"obs_A","trace_ids":["tr_...21","tr_...22"]},
  "B": {"observer_id":"obs_B","trace_ids":["tr_...a1","tr_...a2"]},
  "frame_map": {"pi_map":[["sensor.z","sensor.z"],["tool.db","tool.db"]]},
  "commute_matrix": [[true,true],[true,true]],
  "shared_ledger": true,
  "redundancy": {"fragments":5,"policy":"majority"},
  "metrics": {"sample":"overlap","score":"jaccard"}
}

Response

{
  "pass": true,
  "score": 0.93,
  "overlap_keys": ["sensor.z@1021","tool.db@1022"],
  "non_commuting_pairs": [],
  "diagnostics": {"disagreements":[], "redundancy_effective":4.7}
}

Errors: INCOMPATIBLE_CHANNELS, FAILED_PRECONDITION (no shared/SBS redundancy).

---

4) POST /project — apply a projector $P$ to items

Request

{
  "projector": {
    "type": "linear",               // "linear" | "neural" | "pca" | "whiten"
    "params": {"W_ref":"proj/W:2025-09-01", "normalize": true}
  },
  "items": [{"id":"c1","x":[0.1,0.3,...]},{"id":"c2","x":[-0.2,0.4,...]}],
  "return_stats": true
}

Response

{
  "projected": [
    {"id":"c1","z":[0.07,0.11,...]},
    {"id":"c2","z":[-0.04,0.18,...]}
  ],
  "stats": {"n": 2, "d": 768, "mean_l2": 0.92}
}

---

5) POST /pool — additive pooling with CWA certificate & auto-fallback

Request

{
  "projected": [{"id":"c1","z":[...]},{"id":"c2","z":[...]}],
  "aggregator": {"type":"mean"},        // "mean" | "sum" | {"weighted":{...}}
  "certificate": {
    "perm": {"k":16},
    "flip": {"k":8, "mode":"random"},   // or "axes"
    "chunk": {"k":8, "policy":"reshuffle"},
    "thresholds": {"cwa_min":0.78, "pri_max":0.35},
    "sequential": {"early_exit": true}
  },
  "downstream": {"g":"retrieval.v3","topk":5}  // optional “g” evaluated per panel
}

Response (pass)

{
  "pooled": {"mu":[0.02, -0.01, ...], "norm": 1.03},
  "cwa": {"score": 0.86, "pri": 0.22, "decision": "PASS",
          "panels":{"perm":16,"flip":8,"chunk":8}},
  "fallback": null,
  "diagnostics": {"delta_max": 0.04, "delta_med": 0.01, "time_ms": 94}
}

Response (fail with fallback suggestion)

{
  "pooled": null,
  "cwa": {"score": 0.41, "pri": 0.62, "decision": "FAIL"},
  "fallback": {"estimator":"attention.pool.v2","hint":"enable positional kernels"},
  "diagnostics": {"delta_max": 0.29, "phase_risk":"HIGH"}
}

Errors: CERTIFICATE_FAILURE (if require_pass=true header), INVALID_ARGUMENT.

---

6) POST /belt — update PBHL belt & compute Residual, gates

Request

{
  "belt_id":"belt/ACME-Support",
  "window": {"start":"2025-09-15T00:00:00Z","end":"2025-09-22T00:00:00Z"},
  "gap": {"value": 0.37, "units":"backlog_fraction"},
  "flux": {"value": 0.29},
  "twist": {"value": 0.05},
  "alpha": 1.4,
  "coherence": 0.82,
  "acceptance": {"run_checks": true, "mesh_ref":"mesh/beltA:v7"},
  "policy": {"residual_max": 0.06}
}

Response

{
  "belt_id":"belt/ACME-Support",
  "residual": 0.03,
  "pbhl": {"gap":0.37,"flux":0.29,"twist":0.05,"alpha":1.4},
  "acceptance": {"boundary_ok": true, "gluing_ok": true, "period_4pi_ok": true},
  "gate": {"status":"OPEN","reason":null},
  "kpi": {"EEI":0.74,"SI":0.69},
  "next_review":"2025-09-29T00:00:00Z"
}

Errors: FAILED_PRECONDITION (acceptance check failure → gate closed), INVALID_ARGUMENT.

---

7) GET /belt/{belt_id}/kpi?since=...&window=...

Returns Five-Line KPI time series (Gap, Flux, Twist, Coherence, Residual) with paging.

---

8) GET /sync — fleet-level sync metrics

Response

{
  "fleet_id":"acme-fleet",
  "rho": 0.91,
  "delta_tau": {"rms": 1.8, "p90": 3, "p99": 7},
  "R": 312,
  "window": {"seconds": 300},
  "updated_at":"2025-09-23T11:05:21Z"
}

---

C.4 Events & Webhooks

Event types
TickStart, ChannelSelected, TraceWrite, AgreementPass, AgreementFail, CWA.Pass, CWA.Fail, PBHL.Update, PolicyGate.Trigger.

Webhook delivery

• POST to your endpoint with ObserverOps-Signature: t=<ts>,v1=<hmac-sha256> over raw body using your secret.

• Retries: exponential backoff up to 24h; idempotent via event_id.

Example event (CWA.Pass)

{
  "event_id":"ev_01J9HG34...",
  "type":"CWA.Pass",
  "created":"2025-09-23T11:05:22Z",
  "data":{
    "pool_id":"pool_01J9H...",
    "cwa":{"score":0.86,"pri":0.22},
    "projector":"proj/W:2025-09-01"
  }
}

---

C.5 Pagination & Filtering

• Cursor-based: ?cursor=...&limit=50.

• Responses include: { "items":[...], "next_cursor": "..." }.

• Time filters: ?from=2025-09-01T00:00:00Z&to=....

---

C.6 Rate Limits

• Default: 120 requests/min per org; burst 240.

• Exceeding returns 429 RATE_LIMITED with Retry-After.

---

C.7 Security Notes

• OAuth2 client-credentials or PAT; scopes: measure:write, trace:read, pool:write, agree:write, belt:write, metrics:read.

• PII-aware traces: optional redaction policies and field-level encryption at rest.

---

C.8 Examples (cURL)

/pool with certificate

curl -X POST https://api.observerops.io/v1/pool \
 -H "Authorization: Bearer $TOKEN" \
 -H "Content-Type: application/json" \
 -H "Idempotency-Key: $(uuidgen)" \
 -d '{
  "projected":[{"id":"c1","z":[0.1,0.2]},{"id":"c2","z":[-0.1,0.0]}],
  "aggregator":{"type":"mean"},
  "certificate":{"perm":{"k":16},"flip":{"k":8},"chunk":{"k":8},
                 "thresholds":{"cwa_min":0.8,"pri_max":0.4}}
 }'

/agree

curl -X POST https://api.observerops.io/v1/agree \
 -H "Authorization: Bearer $TOKEN" \
 -d '{"A":{"observer_id":"obsA","trace_ids":["tr_1","tr_2"]},
      "B":{"observer_id":"obsB","trace_ids":["tr_a","tr_b"]},
      "frame_map":{"pi_map":[["sensor.z","sensor.z"]]},
      "commute_matrix":[[true]],
      "shared_ledger":true}'

---

C.9 SDK Model (TypeScript types excerpt)

type PoolDecision = "PASS" | "FAIL";
interface CwaResult { score: number; pri: number; decision: PoolDecision; }
interface PoolResponse {
  pooled?: { mu: number[]; norm: number };
  cwa: CwaResult;
  fallback?: { estimator: string; hint?: string } | null;
  diagnostics?: Record<string, unknown>;
}

---

C.10 Error Codes (extended table)

code	Explanation	Action
INVALID_ARGUMENT	Schema/constraints violated	Fix payload; see field_errors
FAILED_PRECONDITION	Latching/commute/SBS/acceptance unmet	Satisfy invariant or change mode
CONFLICT	Idempotency mismatch or slot eviction guard	Reuse body/key or new key
CERTIFICATE_FAILURE	CWA score or PRI outside bands	Switch to fallback estimator
INCOMPATIBLE_CHANNELS	Non-commuting or unmapped frames	Repair frame_map/commute_matrix
SLOT_EXHAUSTED	Pool capacity hit	Back-pressure or increase slots
TRACE_IMMUTABLE	Attempted retro-edit	Append a corrective record
RATE_LIMITED	Throttle exceeded	Honor Retry-After
NOT_FOUND / PERMISSION_DENIED	Missing/forbidden	Verify ids/scopes

---

That’s the complete, production-ready API surface for ObserverOps: measurement & latching, agreement checks, projection→certificate→pool, belt closure, and fleet sync—complete with schemas, examples, and error semantics.

 

Appendix D — Configuration Playbooks

(YAML/JSON templates for thresholds & policies)

Below are production-ready templates you can copy into your config repo. They use profiles (dev/stage/prod), YAML anchors/aliases, and env interpolation (${ENV_VAR:-default}).

---

D.1 Org-Level Stack Config (YAML)

# observerops.yaml
version: 1
org: acme
env: ${ENV:-prod}
region: eu-west-2
hashing: blake3

profiles:
  prod: &prod
    observer:
      trace:
        immutability: strict           # append-only, no retro-edits
        hash_chain: blake3
        retention_days: 365
        redact:
          pii_fields: ["email","phone","ssn"]
          policy: "drop"               # drop | mask | hash
        idempotency:
          enforce: true
          window_s: 86400
      scheduling:
        Ô_policy: "compatibility-first"
        tick:
          cadence_ms: 250
          max_retries: 2
          jitter_ms: [15, 60]
    slots:
      memory:
        capacity: 2048                 # items/frames
        guard_ms: 250                  # no-evict guard
      tools:
        capacity: 4
        parallel_permits: 2
      attention:
        capacity: 12
        policy: priority               # priority | fifo
      eviction:
        policy: lru
        protect_tags: ["inflight","latched"]
      backpressure:
        enabled: true
        gate: "Ô"
        thresholds:
          occupancy_amber: 0.75
          occupancy_red: 0.90
          collision_budget_pct: 1.0
    cwa:
      projector:
        type: "linear"                 # linear | neural | whiten | pca
        params:
          W_ref: "proj/W:${PROJ_VER:-2025-09-01}"
          normalize: true
      certificate:
        thresholds:
          cwa_min: 0.80
          pri_max: 0.35
          delta_mu_max: 0.08           # norm change tolerance
        panels:
          perm:  { k: 16 }
          flip:  { k: 8,  mode: "random" }   # random | axes
          chunk: { k: 8,  policy: "reshuffle" }
        sequential:
          early_exit: true
          upper_stop: 0.90
          lower_stop: 0.30
      fallback:
        estimator: "attention.pool.v2"
        enable_on:
          - reason: "PRI_HIGH"   # Phase risk high
            pri_min: 0.50
          - reason: "SCORE_LOW"  # CWA score too low
            cwa_max: 0.75
    agreement:
      shared_ledger: true
      commute_matrix_ref: "cmat/global:v3"
      min_overlap_keys: 2
      redundancy:
        fragments: 5
        policy: "majority"
        min_effective: 4.0
    sync:
      kuramoto_rho_target: 0.85
      desync:
        delta_tau:
          p95_max: 5
          p99_max: 12
        actions:
          - if: "rho < 0.70"
            then: ["slowdown:0.10", "reschedule:jitter(50-150ms)"]
          - if: "p99 > 12"
            then: ["gate:measure@tools", "alert:ops"]
    pbhl:
      alpha:
        default: 1.2
        bounds: [0.8, 1.8]
      residual:
        amber: 0.04
        max: 0.06
      controllers:
        flux_gate:
          kp: 0.5
          ki: 0.2
          rate_hz: 2
        twist_step:
          k: 0.10
          min_interval_s: 1800
          max_step: 0.05
      acceptance_checks:
        frequency: "every_6h"
        on_residual_spike: true
        mesh_ref: "mesh/beltA:v7"
        tests: ["boundary","gluing","period_4pi"]
      gates:
        close_on:
          - residual_gt: 0.06
            windows: 2
          - acceptance_fail: true
    telemetry:
      level: info
      sample_rates:
        TraceWrite: 1.0
        AgreementFail: 1.0
        CWA.Pass: 0.2
        CWA.Fail: 1.0
        PBHL.Update: 0.5
      export:
        kpis: true
        traces: true
        sink: "s3://acme-observerops/${ENV}/"
        privacy_mode: "minimize"

  stage: &stage
    <<: *prod
    telemetry:
      level: debug
      sample_rates:
        CWA.Pass: 1.0
    cwa:
      certificate:
        thresholds:
          cwa_min: 0.78
          pri_max: 0.40

  dev:
    <<: *stage
    observer:
      trace:
        retention_days: 14
    slots:
      tools:
        capacity: 2
        parallel_permits: 1

---

D.2 Task-Specific Overrides

D.2.1 RAG / Embedding Pooling

overrides:
  workloads:
    rag_support_kb:
      cwa:
        projector:
          type: "whiten"
          params: { eps: 1e-5 }
        certificate:
          thresholds: { cwa_min: 0.82, pri_max: 0.30, delta_mu_max: 0.05 }
          panels:
            chunk: { k: 16, policy: "sentence-reshuffle" }
        fallback:
          estimator: "attention.pool.v2"
          params:
            positional_kernel: "rope"
            heads: 4
      slots:
        memory: { capacity: 4096 }
      sync:
        kuramoto_rho_target: 0.90

D.2.2 Tool-Using Agents Fleet

overrides:
  workloads:
    tool_agents:
      agreement:
        min_overlap_keys: 3
        commute_matrix_ref: "cmat/tools:v5"
      observer:
        scheduling:
          Ô_policy: "risk-aware"
          tick: { cadence_ms: 300, max_retries: 1 }
      slots:
        tools:
          capacity: 6
          parallel_permits: 3
        backpressure:
          thresholds: { occupancy_amber: 0.70, occupancy_red: 0.85 }

---

D.3 Policy Gates & Escalation Ladder

policy_gates:
  cwa_gate:
    close_on:
      any:
        - "cwa.score < thresholds.cwa_min"
        - "cwa.pri   > thresholds.pri_max"
        - "diagnostics.delta_max > thresholds.delta_mu_max"
    actions:
      - "fallback:attention.pool.v2"
      - "label:phase-risk"
      - "alert:ml-ops"
  belt_gate:
    close_on:
      any:
        - "pbhl.residual > pbhl.residual.max"
        - "!acceptance.boundary_ok || !acceptance.gluing_ok || !acceptance.period_4pi_ok"
    actions:
      - "freeze:twist_step"
      - "increase:flux_gate.kp by 0.1"
      - "escalate:program-owner"
  slots_gate:
    close_on:
      any:
        - "slots.collision_rate_pct > thresholds.collision_budget_pct"
        - "slots.occupancy > occupancy_red"
    actions: ["gate:measure@tools", "alert:sre", "spinup:workers +1"]

---

D.4 Acceptance Checks Scheduler

acceptance_scheduler:
  schedule:
    - cron: "0 */6 * * *"     # every 6 hours
      tests: ["boundary","gluing","period_4pi"]
    - cron: "*/10 * * * *"    # every 10 min (light)
      tests: ["boundary"]
  triggers:
    - on: "pbhl.residual > 0.06"
      run: ["boundary","gluing"]
    - on: "alpha.drift > 0.15 over 24h"
      run: ["period_4pi"]
  resources:
    max_parallel: 4
    timeout_s: 120

---

D.5 JSON Form (API-ready)

{
  "version": 1,
  "env": "prod",
  "observer": {
    "trace": {
      "immutability": "strict",
      "hash_chain": "blake3",
      "retention_days": 365,
      "redact": { "pii_fields": ["email","phone"], "policy": "drop" },
      "idempotency": { "enforce": true, "window_s": 86400 }
    },
    "scheduling": {
      "Ô_policy": "compatibility-first",
      "tick": { "cadence_ms": 250, "max_retries": 2, "jitter_ms": [15,60] }
    }
  },
  "slots": {
    "memory": { "capacity": 2048, "guard_ms": 250 },
    "tools": { "capacity": 4, "parallel_permits": 2 },
    "attention": { "capacity": 12, "policy": "priority" },
    "eviction": { "policy": "lru", "protect_tags": ["inflight","latched"] },
    "backpressure": {
      "enabled": true,
      "gate": "Ô",
      "thresholds": { "occupancy_amber": 0.75, "occupancy_red": 0.9, "collision_budget_pct": 1.0 }
    }
  },
  "cwa": {
    "projector": { "type": "linear", "params": { "W_ref": "proj/W:2025-09-01", "normalize": true } },
    "certificate": {
      "thresholds": { "cwa_min": 0.8, "pri_max": 0.35, "delta_mu_max": 0.08 },
      "panels": { "perm": { "k": 16 }, "flip": { "k": 8, "mode": "random" }, "chunk": { "k": 8, "policy": "reshuffle" } },
      "sequential": { "early_exit": true, "upper_stop": 0.9, "lower_stop": 0.3 }
    },
    "fallback": {
      "estimator": "attention.pool.v2",
      "enable_on": [
        { "reason": "PRI_HIGH", "pri_min": 0.5 },
        { "reason": "SCORE_LOW", "cwa_max": 0.75 }
      ]
    }
  },
  "agreement": {
    "shared_ledger": true,
    "commute_matrix_ref": "cmat/global:v3",
    "min_overlap_keys": 2,
    "redundancy": { "fragments": 5, "policy": "majority", "min_effective": 4.0 }
  },
  "sync": {
    "kuramoto_rho_target": 0.85,
    "desync": {
      "delta_tau": { "p95_max": 5, "p99_max": 12 },
      "actions": [
        { "if": "rho < 0.70", "then": ["slowdown:0.10","reschedule:jitter(50-150ms)"] },
        { "if": "p99 > 12", "then": ["gate:measure@tools","alert:ops"] }
      ]
    }
  },
  "pbhl": {
    "alpha": { "default": 1.2, "bounds": [0.8, 1.8] },
    "residual": { "amber": 0.04, "max": 0.06 },
    "controllers": {
      "flux_gate": { "kp": 0.5, "ki": 0.2, "rate_hz": 2 },
      "twist_step": { "k": 0.1, "min_interval_s": 1800, "max_step": 0.05 }
    },
    "acceptance_checks": { "frequency": "every_6h", "on_residual_spike": true, "mesh_ref": "mesh/beltA:v7", "tests": ["boundary","gluing","period_4pi"] },
    "gates": { "close_on": [{ "residual_gt": 0.06, "windows": 2 }, { "acceptance_fail": true }] }
  },
  "telemetry": {
    "level": "info",
    "sample_rates": { "TraceWrite": 1.0, "AgreementFail": 1.0, "CWA.Pass": 0.2, "CWA.Fail": 1.0, "PBHL.Update": 0.5 },
    "export": { "kpis": true, "traces": true, "sink": "s3://acme-observerops/prod/", "privacy_mode": "minimize" }
  }
}

---

D.6 Validation Schema Snippet (JSON Schema)

{
  "$id": "https://observerops.io/schema/v1/config.json",
  "type": "object",
  "required": ["version","observer","slots","cwa","pbhl"],
  "properties": {
    "version": { "type":"integer", "minimum": 1 },
    "observer": {
      "type":"object",
      "properties": {
        "trace": {
          "type":"object",
          "required":["immutability","hash_chain","retention_days"],
          "properties":{
            "immutability":{"enum":["strict"]},
            "hash_chain":{"enum":["blake3","sha256"]},
            "retention_days":{"type":"integer","minimum":7}
          }
        }
      }
    },
    "cwa": {
      "type":"object",
      "properties":{
        "certificate":{
          "type":"object",
          "properties":{
            "thresholds":{
              "type":"object",
              "properties":{
                "cwa_min":{"type":"number","minimum":0,"maximum":1},
                "pri_max":{"type":"number","minimum":0,"maximum":1}
              }
            }
          }
        }
      }
    }
  }
}

---

D.7 Quick Profiles (copy-paste)

# dev quick-start
use: dev
cwa.certificate.thresholds:
  cwa_min: 0.75
  pri_max: 0.45
telemetry.level: debug
observer.trace.retention_days: 14
slots.tools.capacity: 2

# production hardening
use: prod
cwa.certificate.thresholds:
  cwa_min: 0.82
  pri_max: 0.30
pbhl.residual.max: 0.06
agreement.min_overlap_keys: 3
sync.desync.delta_tau.p99_max: 10

---

D.8 Incident Playbooks (policy excerpts)

incidents:
  cwa_false_green:
    detect: "CWA.Pass && downstream drift > 0.05 within 24h"
    contain:
      - "flip gate: cwa_gate -> CLOSED"
      - "force fallback: attention.pool.v2"
    root_cause:
      checklist: ["projector drift","dataset shift","order leakage"]
    recover:
      - "recalibrate projector W_ref"
      - "raise cwa_min by +0.02 for 7d"
  belt_residual_spike:
    detect: "pbhl.residual > 0.08 for 2 windows"
    contain: ["freeze:twist_step","increase:flux_gate.kp +0.1"]
    notify: ["program-owner","sre-oncall"]
    recover: ["acceptance full suite","mesh refine +25% cells"]

---

D.9 Minimal Per-Service Overrides

services:
  /pool:
    require_pass: true
    timeout_ms: 500
    budgets:
      cpu_ms: 250
      panels_max: { perm: 32, flip: 16, chunk: 16 }
  /measure:
    slots_required: { tools: 1 }
    max_payload_kb: 128
  /agree:
    min_score: 0.85
    non_commuting_policy: "skip-and-log"

---

Use these playbooks as-is or as a base. They encode the invariants: latching, commuting-only agreement, certificate-gated pooling, slot conservation, and belt closure—with guardrails, gates, and escalation ladders ready for operations.

 

Appendix E — Repro Labs

(datasets, scripts, notebook indices, grading rubrics)

E.0 Quickstart (environment & reproducibility)

• Runtime: Python 3.11; NumPy, SciPy, pandas, scikit-learn, NetworkX, Jupyter; optional: PyTorch/FAISS for Lab 3.

• Install: pip install -r labs/requirements.txt

• Determinism: set OBSERVEROPS_SEED=1337 (or pass --seed to scripts).

• Artifacts root: ./artifacts/<lab>/<run_id>/... → stores traces, scorecards, figures.

• Make targets: make e1 … make e4 to run each lab end-to-end.

repo/
 └─ labs/
    ├─ common/                # utils (rng, hashing, metrics, plotting)
    ├─ lab1_qubit/            # commuting vs non-commuting & latching
    ├─ lab2_smft_gridworld/   # Ô/τ scheduler in semantic fields
    ├─ lab3_cwa_rag/          # CWA certificate on projected embeddings
    ├─ lab4_belt_pbhl/        # PBHL belts & acceptance checks
    └─ requirements.txt

---

E.1 Datasets (formats, splits, checksums)

All labs ship synthetic, license: CC-BY-4.0. Each dataset folder contains:
README.md, schema.json, train/, val/, test/, checksums.sha256.

E.1.1 Lab 1 — Qubit Toy (Commute vs Non-Commute)

• Files

  • settings.jsonl: per row { "seq": ["Z","X","Z"], "noise_p": 0.02 }

  • runs.jsonl: outcomes per sequence { "seq_id": "...", "y": [1,0,1], "tau":[0,1,2] }

• Splits: 1k/200/200 sequences.

• Schema (excerpt)

{ "seq": ["Z|X|Y"], "basis_map": {"Z":[0,1], "X":[+,-]}, "noise_p": 0.0-0.1 }

• Goal: show order effects when instruments don’t commute; verify latching prevents “retro-edit”.

E.1.2 Lab 2 — SMFT Gridworld

• Files

  • world.json: cells, walls, sources/sinks

  • field_init.npy: initial Ψₘ slice (H×W×Θ)

  • episodes.jsonl: agent steps with (x,θ,τ) and reward

• Splits: 10 worlds × 50 episodes each.

• Goal: implement Ô that selects orientation/channel based on AL↓ and S_c↑ bands; track sync ρ across agents.

E.1.3 Lab 3 — RAG Pooling Battery (CWA)

• Files

  • corpus.jsonl: { "id": "...", "text": "...", "topic": "...", "phase_tag": "A|B" }

  • queries.jsonl: { "qid": "...", "q": "...", "gold": ["id1","id7"] }

  • splits/ with three perturbation views: perm/, flip/, chunk/

  • Optional: embeddings/ (precomputed z.npy), else generated on first run

• Scales: S (5k chunks), M (50k), L (250k). Start with S.

• Goal: certify when project→add (mean) is safe; fall back if PRI high.

E.1.4 Lab 4 — PBHL Belt Simulator

• Files

  • belt_mesh.json: nodes/edges/faces of program worldsheet

  • windows.jsonl: { "t0":"...", "t1":"...", "gap":0.33, "flux":0.27, "twist":0.04, "alpha":1.3 }

  • events.jsonl: reorganizations, budget shifts, incidents

• Goal: compute Residual, run acceptance checks (boundary, gluing, 4π), operate Flux-gate & Twist-step.

---

E.2 Scripts (CLI)

All CLIs support --seed, --out, --profile={dev,stage,prod}.

Lab 1

python labs/lab1_qubit/gen_qubit.py --n-seq 1200 --noise-p 0.02
python labs/lab1_qubit/run_latching.py --seq settings.jsonl --commit
python labs/lab1_qubit/eval_agreement.py --commute-matrix zx_commute.json

Lab 2

python labs/lab2_smft_gridworld/gen_worlds.py --n 10 --theta 8
python labs/lab2_smft_gridworld/run_agent.py --episodes 50 --o-policy al_min
python labs/lab2_smft_gridworld/metrics.py --window 300 --rho --delta-tau

Lab 3

python labs/lab3_cwa_rag/gen_corpus.py --scale S
python labs/lab3_cwa_rag/project.py --projector whiten --d 768
python labs/lab3_cwa_rag/certify_pool.py --perm 16 --flip 8 --chunk 8 \
  --cwa-min 0.80 --pri-max 0.35 --eval retrieval@topk=5 --require-pass

Lab 4

python labs/lab4_belt_pbhl/gen_belt.py --cells 64
python labs/lab4_belt_pbhl/run_belt.py --windows 52 --alpha 1.2 \
  --accept boundary gluing period_4pi --residual-max 0.06

---

E.3 Notebooks Index (Jupyter)

Notebook	Purpose	Runtime	Artifacts
E1_qubit_commute_vs_noncommute.ipynb	visualize order effects; prove latching	5–7 min	plots, trace diffs
E2_smft_scheduler.ipynb	implement Ô using AL/S_c; fleet sync ρ	10–15 min	heatmaps, ρ/Δτ curves
E3_cwa_certificate.ipynb	run panels; score & PRI; fallback	8–12 min	certificate report
E4_pbhl_belt.ipynb	compute Residual; controllers; acceptance	6–10 min	KPI dashboard, gates

Each notebook writes artifacts/<lab>/<run>/report.md + scorecard.json.

---

E.4 Grading Rubrics (auto-gradable)

Total per lab: 100 pts. Passing ≥ 80 unless stated.

Lab 1 — Qubit / Latching

• L1.1 Trace immutability tests pass (hash chain, one write per τ) — 25

• L1.2 Order effect detected on non-commuting pairs (p<0.01) — 25

• L1.3 Agreement on commuting pairs ≥ 0.95 — 25

• L1.4 Retro-edit attempt correctly rejected — 25
  Fail bands: any of L1.1/L1.4 fails ⇒ auto-fail.

Lab 2 — SMFT Scheduler

• L2.1 AL↓ trend (≥10% drop over episode median) — 20

• L2.2 S_c in green band (diversity ≥ target) — 20

• L2.3 Reward uplift vs random ≥ +15% — 20

• L2.4 Fleet sync ρ ≥ 0.85, Δτ p95 ≤ 5 — 20

• L2.5 Compatibility-aware Ô (no illegal conflicts) — 20

Lab 3 — CWA on RAG

• L3.1 Certificate score ≥ 0.80 — 25

• L3.2 PRI ≤ 0.35 (or justified fallback) — 20

• L3.3 Retrieval@5 iso-accuracy vs baseline (±1%) — 20

• L3.4 Latency reduction ≥ 20% on PASS panels — 20

• L3.5 Fallback engages on FAIL with accuracy ≥ baseline — 15
  Fail bands: if PASS but accuracy −>1% vs baseline ⇒ downgrade 20 pts.

Lab 4 — PBHL Belts

• L4.1 Residual |G−(F+αT)| ≤ 0.06 for ≥ 90% windows — 25

• L4.2 Acceptance checks all OK under normal ops — 20

• L4.3 Controller recovery < 3 windows after spike — 20

• L4.4 Five-Line KPI exported & consistent — 20

• L4.5 Correct gate behavior (CLOSE on breach) — 15

Scoring I/O: scorecard.json

{
  "lab": "E3_cwa",
  "seed": 1337,
  "score": 92,
  "breakdown": {"L3.1":25,"L3.2":17,"L3.3":20,"L3.4":20,"L3.5":10},
  "metrics":{"cwa":0.86,"pri":0.22,"latency_drop":0.27}
}

---

E.5 Teacher & CI Harness

• Teacher pack: rubrics/*.yaml, hidden solutions under solutions/.

• CI: ci/run_all.yml runs labs nightly with fixed seeds; publishes artifacts to artifacts/ci/<date>/.

• Plagiarism/overfit guard: randomized seeds per student + hash of code cells; compare metric fingerprints.

GitHub Actions (snippet)

name: repro-labs
on: [workflow_dispatch, schedule]
jobs:
  run:
    runs-on: ubuntu-latest
    steps:
      - uses: actions/checkout@v4
      - uses: actions/setup-python@v5
        with: { python-version: '3.11' }
      - run: pip install -r labs/requirements.txt
      - run: make e1 e2 e3 e4
      - uses: actions/upload-artifact@v4
        with: { name: artifacts, path: artifacts/** }

---

E.6 What “done” looks like (per lab)

• ✅ artifacts/.../scorecard.json with score ≥ 80

• ✅ report.md (1–2 pages) incl. plots & short justifications

• ✅ Reproducible rerun with same seed ±1% metric variance

---

That’s a complete, classroom-and-CI-ready Repro Labs package: datasets (with schemas), scripts & CLIs, notebook index, and auto-gradable rubrics tied to ObserverOps invariants.

 

Appendix F — Safety & Compliance Mapping

(SOC/ISO control matrices and trace evidence)

Scope note: This appendix shows how ObserverOps’ invariants and artifacts satisfy common assurance frameworks. It is not legal advice—adapt with your GRC counsel.

---

F.0 Assurance Backbone (what auditors will look for)

ObserverOps ships three first-class, exportable evidence streams:

1. Immutable Trace Ledger (T): hash-chained, append-only records of measure → commit at tick τ with channel π and outcome y (internal collapse / latching).

2. Certificate & Gate Logs (CWA): permutation/flip/chunk panels, scores, PRI, and the decision (PASS/FAIL) including configured thresholds at decision time.

3. BeltOps Telemetry (PBHL): Five-Line KPI (Gap/Flux/Twist/Coherence/Residual), acceptance-check results (boundary, gluing, 4π), gates OPEN/CLOSE, and change history (α, controller gains).

Cross-cutting: Agreement checks, slot allocator events, sync metrics (ρ, Δτ). Together they provide who did what, when, with which policy, and whether safety gates acted.

---

F.1 Evidence Packs (ready-to-export bundles)

Pack types and contents

• Run Pack (/evidence/run/<run_id>.zip)
  /trace/*.jsonl (ledger slice) • /config/*.yaml (effective policy) • /agree/*.json • /slots/*.jsonl • /signing/manifest.json (hashes, BLAKE3) • /sig/chain.txt (prev_hash chain)

• CWA Pack (/evidence/cwa/<pool_id>.zip)
  /panels/*.jsonl (perm/flip/chunk draws + deltas) • /decision.json (score, PRI, thresholds, require_pass flag) • /fallback.json (if used) • /projector/ref.txt • /audit/plots/*

• Belt Review Pack (/evidence/belt/<belt_id>/<window>.zip)
  /kpi/*.json • /acceptance/*.json • /gate/*.json • /controller/*.json (Flux-gate PID trace, Twist-step ops) • /alpha/history.json

• Incident Pack (/evidence/incident/<incident_id>.zip)
  /timeline.md • /signals/*.json (KPIs crossing) • /root_cause/*.md • /remediation/*.yaml • /approvals/*.pdf (SoD evidence)

All packs include a manifest with digests, signer identity, and timestamping (RFC 3161-compatible if configured).

---

F.2 SOC 2 (Trust Services Criteria) — Control Matrix

SOC2 TSC	ObserverOps Mechanism	Primary Evidence	Frequency / Owner
CC1 – Control Environment	Org-level config repo; policy gates (cwa_gate, belt_gate, slots_gate)	Config PRs, approvals, change log	Per change / GRC
CC2 – Communication & Info	Webhooks + dashboards for AgreementFail, CWA.Fail, PolicyGate.Trigger	Event stream archives; alert receipts	Continuous / SRE
CC3 – Risk Assessment	PRI + CWA score risk bands; PBHL Residual thresholds	Risk register entries linked to metrics	Quarterly / Risk
CC4 – Monitoring Activities	Five-Line KPI & acceptance checks scheduler	KPI trends; acceptance reports	Weekly / Program Ops
CC5 – Control Activities	Hard gates on pooling & belts; back-pressure to Ô	Gate decisions; denied requests logs	Continuous / Runtime
CC6 – Logical Access	API scopes; token scopes (measure:write, …); trace read ACLs; field-level redaction	IAM policy export; access logs	Quarterly / SecOps
CC7 – System Ops	Health checks; Δτ & ρ monitors; autoscaling policies	SRE runbooks; on-call logs	Continuous / SRE
CC8 – Change Mgmt	Versioned configs; canary profiles (dev/stage/prod); idempotency guard	Release notes; diff & approvals	Per release / Eng
CC9 – Risk Mitigation	Incident playbooks (cwa_false_green, belt_residual_spike)	Incident packs; MTTR metrics	Per incident / IR

Processing Integrity (PI) → enforced by latching (immutable trace), agreement checks on commuting instruments, and certificate-gated pooling.
Confidentiality/Privacy → redaction policies (drop|mask|hash), PII field lists, and retention periods in org profile.

---

F.3 ISO/IEC 27001:2022 Annex A — Control Mapping (selected)

Annex A Control (2022)	ObserverOps Feature	Evidence
A.5.1 Policies for Information Security	Org config observerops.yaml with policy gates and thresholds	Policy file, approvals, policy reviews
A.5.7 Threat intelligence	PRI & phase-risk alerts; acceptance anomaly flags	Risk dashboard, alert history
A.5.10 Acceptable use of information	Redaction & minimization settings; slot budgets limiting data spread	Config + audit samples
A.5.18 Access control	API scopes, per-endpoint budgets, rate-limits	IAM export; WAF/rate logs
A.5.19 Identity management	OAuth2/PAT issuance, rotation policies	Token inventory; rotation proof
A.5.23 Cloud services	BeltOps exports to managed storage with integrity checks	Export manifests; S3/Azure immutability
A.5.30 ICT readiness for continuity	Belt fast/slow loops; acceptance checks; gate CLOSE on breach	DR runbook; test evidence
A.8.12 Data leakage prevention	Field-level redaction; telemetry sample rates	Redaction rules; sampling config
A.8.16 Monitoring activities	Five-Line KPIs; event taxonomy; Δτ/ρ	KPI dashboards; event archives
A.8.20 Protection of log information	Hash-chained trace; chain verification API; signed evidence packs	Hash audit, signer certs
A.8.21 Admin of logging	Retention & rotation; access to /trace gated by scope	Retention policy; access logs
A.8.28 Secure coding	Idempotency, append-only writes, compatibility guards	Unit/integration tests, coverage

---

F.4 ISO/IEC 42001:2023 (AI Management System) — Mapping (selected)

42001 Topic	ObserverOps Mapping	Evidence
AI Risk Management	CWA certificate + PRI bands; PBHL residual as macro-risk	CWA packs; risk register links
Data & Model Lifecycle	Projector refs (W_ref), versioned configs, fallback estimators	Model registry, /project logs
Traceability & Transparency	Immutable trace T; agreement diagnostics; belt acceptance	Evidence packs, API exports
Human Oversight	Gates produce explicit OPEN/CLOSE, require approvals for override	Approval records, SoD attestations
Monitoring & Response	Sync metrics, incident playbooks, SLOs for gates and recovery	Incident timelines, MTTR charts

---

F.5 NIST SP 800-53 Rev. 5 (cross-reference, short list)

Family	Relevant Controls	ObserverOps Support / Evidence
AC Access Control	AC-2, AC-3, AC-6	Scoped tokens; route-level RBAC; least-privilege exports
AU Audit & Accountability	AU-2, AU-6, AU-9	Trace ledger; hash chain; audit review procedures
CM Configuration Management	CM-3, CM-5	Versioned configs; enforced gates; canary
IR Incident Response	IR-4, IR-5	Incident packs + runbooks; postmortems
RA Risk Assessment	RA-3, RA-5	PRI, CWA score, residual trend; risk dashboards
SI System & Info Integrity	SI-4, SI-7	Certificate failure alerts; immutability guard; anomaly flags

---

F.6 GDPR / Data Protection Principles (operationalization)

• Minimization (Art. 5(1)(c)): PII redaction at trace-write; slot budgets and eviction policies reduce spread.

• Integrity & Confidentiality (Art. 5(1)(f)): hash-chained trace + scoped access; encryption at rest/in-transit.

• Storage Limitation (Art. 5(1)(e)): retention_days per profile; automatic purge jobs.

• Accountability (Art. 5(2)): Evidence packs + chain-of-custody (manifest digests, signer identity).

• DPIA Triggers: enable DPIA mode for new projectors/models or changes lifting PRI beyond band; attach risk assessment to the CWA pack.

---

F.7 Separation of Duties (SoD) & Approvals

• Policy changes (thresholds, gates) require two-person approval (Engineering + GRC).

• Emergency overrides log reason, ticket, duration, and auto-revert deadline.

• Production deploys: CI emits a signed config diff and links it into the next Evidence Pack.

Evidence: PR approvals, change request IDs, override logs, and /policy/version snapshots.

---

F.8 Auditor Playbook (queries & samples)

Sampling windows

• Daily light: 10 CWA decisions (mix PASS/FAIL), 5 belt updates, 20 trace writes across tools.

• Weekly deep: 100 CWA (borderline scores), all acceptance checks since last review, 10% of AgreementFail.

Query sketches (SQL/DSL)

• Show all PASS decisions within 1h before any incident:

SELECT pool_id, score, pri, thresholds, decided_at
FROM cwa_decisions
WHERE decision='PASS' AND decided_at BETWEEN incident_start - INTERVAL '1 hour'
                                   AND incident_start;

• Verify trace immutability (hash chain continuity):

SELECT t.trace_id
FROM trace t
LEFT JOIN trace p ON p.trace_id = t.prev_id
WHERE t.prev_hash <> p.hash;

• List gate closures with residual > max:

SELECT belt_id, residual, reason, window_start
FROM belt_gates
WHERE status='CLOSE' AND residual > residual_max;

• Agreement failures on commuting pairs:

SELECT a.key, a.reason
FROM agreement a
JOIN commute_matrix c ON c.key=a.key
WHERE c.commute=true AND a.pass=false;

---

F.9 Key Risk Indicators (KRIs) & Tests of Controls

KRI	Green	Amber	Red	Control Test
CWA false-green rate (PASS but downstream drift > 1%)	<0.5%	0.5–1%	>1%	Shadow evaluation weekly
Trace retro-edit attempts	0	1–3/mo	>3/mo	Tamper drills, chain verify
PBHL residual excursions (outside max)	<5% windows	5–10%	>10%	Gate closes; recovery < 3 windows
Agreement fail on commuting keys	<2%	2–5%	>5%	SBS redundancy check, mapping audit
Slot collision rate (tools)	<0.5%	0.5–1%	>1%	Back-pressure + capacity review

---

F.10 Retention, Deletion, and Chain-of-Custody

• Retention: per-profile retention_days (e.g., prod 365d, dev 14d).

• Deletion: redaction by key; tombstone append entry with reason and actor (no in-place delete).

• Chain-of-Custody: Every pack has manifest.json with file paths, sizes, BLAKE3 digests, signer, timestamp; verification tool emits a pass/fail report.

---

F.11 Minimal Auditor Checklist

1. Pull 3 Evidence Packs of each type; verify signatures and hash chains.

2. Recompute CWA decisions on sampled pools; confirm thresholds at decision time match config snapshots.

3. Verify belt acceptance checks replay to same results; inspect one residual spike, ensure gate CLOSED and recovery in ≤ 3 windows.

4. Confirm SoD: pick one policy change → trace approvals to production and corresponding effective-config hash in subsequent packs.

5. Confirm data minimization: spot-check that configured PII fields are absent or masked in traces.

---

Bottom line: ObserverOps turns safety constraints into auditable controls—with deterministic traces, certificate decisions, and belt closure evidence that plug straight into SOC/ISO audits.

 

Appendix G — Figures & Tables

(production-ready list with captions and source data)

G.0 Conventions (for all figures/tables)

• IDs: Figures F1–F7, Tables T1–T5.

• Exports: SVG (print), PNG@2x (web), PDF (archive).

• Fonts/Style: Inter 10–12pt (tables), Inter 12–14pt (figures); grid=off, axes ticks out; color-blind safe (Okabe–Ito).

• Metadata: embed source_path, git_commit, build_ts, seed.

• Column keys used repeatedly:

  • tau (tick), pi (channel), y (outcome), CWA_score, PRI, Gap, Flux, Twist, Alpha, Residual, rho, delta_tau_pXX, occupancy, collisions, agree_score.

• Repro seed: OBSERVEROPS_SEED=1337.

• Build: make figs (or command listed per item).

• Alt-text: provided per figure for accessibility.

---

G.1 Figures

F1. ObserverOps stack diagram (micro/meso/macro)

• Purpose: Visual overview of ObserverOps planes/modules.

• Caption: ObserverOps composes micro (observer + slots), meso (SMFT with Ô/τ), and macro (PFBT belts) under the CWA aggregation law and audit plane.

• Source: figsrc/F1_stack.drawio (vector), modules list from docs/modules.yaml.

• Build: export via draw.io CLI → assets/fig/F1_stack.svg.

• QA: All module names match Table T2 API summary.

Alt-text: “Block diagram showing three layers—micro, meso, macro—with data/control/audit planes and CWA gate.”

---

F2. Ô-first scheduling loop & latching point

• Purpose: Show control loop and where internal collapse (latching) occurs.

• Caption: The Ô-first loop selects a compatible channel, measures, then latches the outcome into the trace at tick τₖ; downstream control is conditioned on the latched record.

• Source data: labs/lab1_qubit/artifacts/<run>/trace_ring.csv (for tick markers).

• Columns: tau, event, pi, committed(bool).

• Plot: Step diagram with a lock icon at TraceWrite.

• Build: python labs/lab1_qubit/plot_loop.py --out assets/fig/F2_loop.svg.

• QA: Exactly one TraceWrite per tau.

Alt-text: “Flow from channel selection to measurement to immutable trace write (latching).”

---

F3. CWA decision tree + validity band

• Purpose: Visualize certificate branches (perm/flip/chunk) and pass band.

• Caption: CWA passes when perturbation panels keep pooled outcomes within the validity band and Phase-Risk Index (PRI) stays below the red line; otherwise fallback is engaged.

• Source data: labs/lab3_cwa_rag/artifacts/<run>/certificate_summary.json.

• Columns: panel, k, delta_max, score, pri, decision.

• Plot: Decision tree + band chart (score vs. PRI with PASS/FAIL regions).

• Build: python labs/lab3_cwa_rag/plot_cwa_tree.py -o assets/fig/F3_cwa.svg.

• QA: Boundaries reflect config thresholds in Appendix D.

Alt-text: “Branching certificate tests with a shaded green pass band in score-PRI space.”

---

F4. Belt worldsheet (Gap, Flux, Twist, Residual)

• Purpose: Depict PBHL variables over the program worldsheet.

• Caption: Across windows, Gap tracks planned–done delta, Flux captures throughput, Twist encodes structural changes; Residual quantifies closure error.

• Source data: labs/lab4_belt_pbhl/artifacts/<run>/windows.jsonl.

• Columns: window_id, Gap, Flux, Twist, Alpha, Residual.

• Plot: 4-panel line chart (Gap/Flux/Twist/Residual vs window).

• Build: python labs/lab4_belt_pbhl/plot_worldsheet.py -o assets/fig/F4_belt.svg.

• QA: Residual = |Gap − (Flux + Alpha*Twist)| holds numerically.

Alt-text: “Time series of PBHL variables with residual envelope.”

---

F5. Five-Line KPI dashboard (production)

• Purpose: Operations panel snapshot for a belt.

• Caption: Five-Line KPIs summarize belt health; gates close automatically when Residual exceeds policy thresholds.

• Source data: apps/beltops/artifacts/<run>/kpi_timeseries.csv.

• Columns: ts, Gap, Flux, Twist, Coherence, Residual, gate.

• Plot: Multi-line with shaded amber/red bands; gate status markers.

• Build: python apps/beltops/plot_kpi.py -o assets/fig/F5_kpi.svg.

• QA: Gate CLOSE markers align with residual breaches.

Alt-text: “Five layered lines over time with amber/red zones and gate status dots.”

---

F6. Agreement/SBS schematic

• Purpose: Show redundancy leading to cross-observer agreement.

• Caption: When commuting instruments write shared or SBS-redundant records, independent observers converge on effective outcomes (AB-fixedness).

• Source: figsrc/F6_agreement_sbs.svg (vector + callouts).

• Build: Export from source; labels cross-checked with agreement API fields.

• QA: Legend includes commuting/non-commuting pairs.

Alt-text: “Two observers reading redundant pointer channels leading to the same outcome.”

---

F7. Slot allocator with occupancy/collision heatmap

• Purpose: Visualize slot conservation under load.

• Caption: Integer, non-overlapping slots with back-pressure keep collision rates within SLA bands; heatmap shows occupancy and rare collisions.

• Source data: runtime/slot_alloc/artifacts/<run>/slot_metrics.csv.

• Columns: ts, pool(memory|tools|attention), occupancy, collisions.

• Plot: Heatmap over time×pool with collision annotations.

• Build: python runtime/slot_alloc/plot_slots.py -o assets/fig/F7_slots.svg.

• QA: occupancy ∈ [0,1]; collisions ≤ budget from config.

Alt-text: “Three-row heatmap of slot occupancy with occasional red collision dots.”

---

G.2 Tables

T1. Metric definitions & threshold bands

• Caption: Formal definitions and production bands for ObserverOps metrics.

• Source: docs/metrics.yaml (authoritative), rendered to table.

• Columns: metric, definition, estimator, green, amber, red.

• Build: python tooling/render_metrics_table.py > assets/table/T1_metrics.csv.

• QA: Bounds match Appendix D thresholds.

---

T2. API summary & event taxonomy

• Caption: Endpoint inventory and event types with schemas and scopes.

• Source: OpenAPI openapi/observerops.v1.yaml + docs/events.yaml.

• Columns: endpoint, method, scope, request_body, response, errors.

• Build: python tooling/openapi_to_table.py -o assets/table/T2_api.csv.

• QA: Error codes align with Appendix C.

---

T3. Ablation results (±Ô, ±slots, ±certificate)

• Caption: Effect sizes on disagreement, latency, and residual under ablations.

• Source data: bench/ablations/artifacts/<run>/results.csv.

• Columns: ablation, disagreement, latency_ms, residual, notes.

• Build: python bench/ablations/aggregate.py -o assets/table/T3_ablation.csv.

• QA: Seeds & configs logged in table footer.

---

T4. Commute vs conflict instrument pairs

• Caption: Instrument pairs classified by commutation on visited support.

• Source: runtime/agree/commute_matrix/*.json; expanded via frame map.

• Columns: pi_a, pi_b, commute(bool), comment.

• Build: python runtime/agree/expand_commute.py -o assets/table/T4_commute_pairs.csv.

• QA: Sample spot-checks in Lab 1.

---

T5. Policy gates & escalation ladders

• Caption: Gate conditions and automatic actions for CWA, belts, and slots.

• Source: config/policy_gates.yaml.

• Columns: gate, condition, action, severity.

• Build: python tooling/policy_to_table.py -o assets/table/T5_gates.csv.

• QA: Conditions parse and evaluate in dry-run.

---

G.3 Source Data Schemas (CSV/JSONL)

• trace_ring.csv: tau:int, event:str, pi:str, committed:bool, hash:str, prev_hash:str.

• certificate_summary.json: records with panel:str, k:int, delta_max:float, score:float, pri:float, decision:str.

• windows.jsonl: per line {"window_id":int,"Gap":float,"Flux":float,"Twist":float,"Alpha":float,"Residual":float}.

• kpi_timeseries.csv: ts:iso, Gap, Flux, Twist, Coherence, Residual, gate:str.

• slot_metrics.csv: ts:iso, pool:str, occupancy:float, collisions:int.

• results.csv (ablations): ablation:str, disagreement:float, latency_ms:float, residual:float, seed:int, config_hash:str.

---

G.4 Reproduction Commands (one-liners)

# Build all figures & tables
make figs tables

# Or selectively:
python labs/lab3_cwa_rag/plot_cwa_tree.py -o assets/fig/F3_cwa.svg
python labs/lab4_belt_pbhl/plot_worldsheet.py -o assets/fig/F4_belt.svg
python tooling/openapi_to_table.py -o assets/table/T2_api.csv

---

G.5 QC Checklist (per artifact)

• Source path & git commit embedded.

• Axes labeled with units; legends outside plot area; font ≥ 10pt.

• Color-blind palette applied; PASS/FAIL bands labeled.

• Numbers reproducible within ±1% across reruns with same seed.

• Tables round to 2–3 sig figs; include units column where relevant.

---

Deliverable: assets/fig/*.svg|png, assets/table/*.csv|md built from versioned sources above; each with deterministic seeds and embedded provenance.

 

 

 © 2025 Danny Yeung. All rights reserved. 版权所有 不得转载

 

Disclaimer

This book is the product of a collaboration between the author and OpenAI's GPT-5 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.