https://osf.io/yj5aw/files/osfstorage/68d30242dd3f77699b3c315f
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ObserverOps Technical Blueprint - II & III

Part II — Reference Architecture & APIs

Chapter 9 — System Overview (Planes & Modules)

Goal

Blueprint the data, control, and audit planes and the boundaries among six core modules:
Observer Runtime, CWA Engine, Slot Allocator, Tick & Sync, BeltOps Dashboard, and Policy Gates. Provide end‑to‑end flows, canonical contracts, SLOs, and production diagrams (architecture + dependency graph).

What You’ll Implement in This Chapter

A 3‑plane deployment model with responsibilities, invariants, and SLO bands per plane.
A module map with clear inputs/outputs/state for each core component.
A baseline event taxonomy spanning the stack (data/control/audit).
Two reference flows (observational data path; governance gate path).
Production artifacts: Architecture diagram (Mermaid), dependency graph (Mermaid), module boundary table, and configuration snippets.

9.1 The Three Planes

Separation of concerns: keep measurement & transformation hot‑path in the Data Plane; scheduling/cadence and policy in the Control Plane; immutability, lineage, and exports in the Audit Plane.

9.1.1 Data Plane

Purpose. Carry measurements and projections from instruments to pools; enforce internal collapse at write time and CWA at aggregation time.

Canonical objects. Measurement, Projection, Certificate, PoolResult.

Hot‑path services.

Observer Runtime (/measure, /agree, /trace/:id)
CWA Engine (/project, /pool)

Invariants.

Latching: TraceWrite(τ_k) is in‑frame irreversible; edits require a new tick τ_{k+1}.
Certificate‑gated pooling: additive pooling only if CWA.score ≥ θ.
Slot conservation (data buffers/tools): non‑fractional, non‑overlap writes.

SLOs (typical starting bands).

p95 measure→trace write: ≤ 50 ms
p95 project: ≤ 25 ms
p95 pool (when CWA pass): ≤ 30 ms; fallback path ≤ 120 ms
Availability (monthly): ≥ 99.9%

Failure modes & guards.

False‑green certificate: mitigate via conservative θ, multi‑panel tests, and audit sampling.
Buffer spill/collisions: back‑pressure via Slot Allocator; drop policies must be explicit events.

9.1.2 Control Plane

Purpose. Decide what to observe next (Ô policy), advance ticks τ, manage fleet synchronization (ρ, Δτ), and apply Policy Gates that throttle or halt risky runs.

Canonical objects. Tick, Schedule, GatePolicy, GateDecision.

Core services.

Tick & Sync (cadence manager; fleet sync metrics ρ, Δτ)
Policy Gates (thresholds on CWA score, PBHL Residual, black‑hole detectors)

Invariants.

Ô‑first scheduling: channel selection precedes measurement; compatibility checks run before actuation.
Tick monotonicity: τ_{k+1} > τ_k; retries are new ticks or explicitly same‑tick idempotent (retry_id).
Sync safety: cross‑agent Δτ bounded by policy; if exceeded, degrade to safe mode.

SLOs.

p95 Ô decision latency: ≤ 15 ms (cached), ≤ 60 ms (field‑aware)
Fleet sync order parameter ρ: ≥ 0.85
Gate evaluation latency: ≤ 10 ms inline; ≤ 100 ms async fan‑out

9.1.3 Audit Plane

Purpose. Provide immutable Trace Ledger, Certificate Logs, and Belt Telemetry with export hooks to GRC systems. This plane is the source of truth for cross‑observer agreement checks and PBHL governance.

Canonical objects. TraceRecord, CertPanel, AgreementReport, BeltKPI, ExportBundle.

Core services.

Observer Runtime — Trace Ledger (hash‑chained, append‑only)
CWA Engine — Cert Log (panels, seeds, CI/drift)
BeltOps Dashboard — KPI Store (Gap/Flux/Twist, Residual, EEI/SI)

Invariants.

Immutability: append‑only with hash chain and content‑addressed blobs.
Agreement evidence: agreement tests reference shared records; no private deltas.
Exportability: every decision has a proof trail (ids for trace, cert, gate, belt update).

SLOs.

Write durability: ≥ 11×9s (cloud multi‑AZ); RPO: 0; RTO: < 5 min tier‑wise
Retention: configurable; typical 90–365 days hot, 7 years cold

9.2 Module Map & Boundaries

The six modules are independently deployable with narrow interfaces and explicit state ownership.

Module	Owns	Ingests	Emits	Hard Invariants	Typical SLO
Observer Runtime	Trace Ledger; Channel Registry; Commute Matrix	`Measure`, `Schedule`	`TraceWrite`, `AgreementReport`	Internal collapse; compatibility checks pre‑actuation	p95 measure→write ≤ 50 ms
CWA Engine	Projector library; Cert Panel configs; Cert Logs	`ProjectionRequest`	`Certificate{score}`, `PoolResult`	Certificate‑gated add; reproducible panels (seeded)	p95 project ≤ 25 ms; pool ≤ 30/120 ms
Slot Allocator	Slot budgets for memory/attention/tools	`SlotRequest`	`SlotGrant/Refuse`, `CollisionEvent`	Integer slots; non‑overlap; explicit eviction	Decision ≤ 5 ms
Tick & Sync	Tick index τ; fleet sync metrics ρ, Δτ	`Heartbeat`, `ScheduleNeed`	`TickStart`, `Schedule`, `DesyncAlert`	Monotone τ; bounded Δτ	Ô decision ≤ 60 ms
BeltOps Dashboard	PBHL worldsheet (Gap, Flux, Twist, α), EEI/SI	`PoolResult`, `AgreementReport`	`PBHL.Update`, KPIs, `Residual`	Gap≈Flux+α·Twist within residual band	KPI refresh ≤ 1 s
Policy Gates	Gate configs; escalation ladders	`Certificate`, `Residual`, `BlackHoleIndex`	`GateDecision{allow	throttle	block}`

Shared services (cross‑cutting): Identity & Auth (service→service tokens, user claims), Config & Secrets (versioned), Telemetry Bus (events), Data Catalog/Lineage.

9.3 Canonical Interfaces & Events (Overview)

HTTP/gRPC Endpoints (preview)

POST /measure           // {pi, S, T_ref}
POST /project           // {x, policy, projector}
POST /pool              // {projected[], cert_config, min_score}
POST /agree             // {Ta_ref, Tb_ref, commute_matrix_id}
POST /belt              // {edges:{plan,do}, alpha, mesh, gates}
GET  /trace/:id         // immutable record by id

Event Taxonomy

TickStart(τ), ChannelSelected(π), TraceWrite(τ, π, y)
AgreementPass/Fail{score}
CWA.Pass/Fail{score, panels}
PBHL.Update{Gap, Flux, Twist, α, Residual}
PolicyGate.Trigger{metric, threshold, action}
DesyncAlert{Δτ, ρ}
CollisionEvent{slot_id}

Idempotency keys: trace_id, retry_id, cert_seed, pool_id, belt_update_id.

9.4 Reference Flows

9.4.1 Observational Data Path (Hot‑Path)

Tick & Sync emits TickStart(τ_k) and a Schedule with selected channel (Ô policy).
Observer Runtime invokes instrument π, obtains y, and latches via TraceWrite(τ_k, π, y).
CWA Engine receives a ProjectionRequest from Runtime, computes Projection and runs certificate panels → emits Certificate{score}.
If score ≥ θ, CWA Engine performs additive /pool and returns PoolResult; otherwise switches to order‑aware fallback and returns PoolResult{fallback:true}.
BeltOps Dashboard ingests PoolResult and AgreementReport to update PBHL worldsheet and KPIs; Policy Gates evaluate whether to throttle/stop subsequent schedules.

Sequence (Mermaid)

sequenceDiagram
  participant Sync as Tick & Sync
  participant OR as Observer Runtime
  participant CWA as CWA Engine
  participant Belt as BeltOps Dashboard
  participant Gate as Policy Gates
  Sync->>OR: TickStart(τ_k) + Schedule(π)
  OR->>OR: measure(π) → y
  OR->>OR: TraceWrite(τ_k, π, y) // latch
  OR->>CWA: /project{x, policy}
  CWA-->>OR: Projection φ(x)
  OR->>CWA: /pool{φ[], cert}
  CWA-->>OR: Certificate{score} + PoolResult
  OR-->>Belt: PoolResult, AgreementReport
  Belt-->>Gate: PBHL.Update{Gap,Flux,Twist,Residual}
  Gate-->>Sync: GateDecision{allow|throttle|block}

9.4.2 Governance Gate Path (Control‑to‑Data feedback)

Trigger: Residual > R_max or CWA.score < θ_min for N consecutive windows.
Policy Gates emit GateDecision=throttle|block with rationale and evidence ids.
Tick & Sync lowers cadence (increase inter‑tick), narrows channel set, or pauses schedules until Residual/CWA recover; all changes are recorded as PolicyGate.Trigger and Schedule deltas.

9.5 Deployment Topologies

Topology A — Compact (single cluster). All modules as services on one mesh; shared telemetry bus; storage split by plane (hot: Data Plane, immutable: Audit Plane).

Topology B — Federated (multi‑team, multi‑region). Data Plane per domain; shared Control Plane with global Tick & Sync; Audit Plane centralized with regional appenders. Agreement runs cross‑domain by referencing shared trace ids.

Capacity & Latency Planning.

Hot‑path budget: 50–100 ms end‑to‑end on CWA‑pass path.
Fallback budget: up to 150–250 ms, flagged and rate‑limited by Policy Gates.
Throughput: size to 10× peak with back‑pressure from Slot Allocator.

Back‑pressure & Degradation.

Prefer shed projections over dropping traces; no silent loss.
Auto‑degrade: reduce channel cardinality; widen tick spacing; disable expensive panels.

9.6 Failure Domains & Safe Modes

Data Plane

Failure: instrument timeouts → Action: mark as conflict; skip with explicit TraceWrite(timeout); request retry via new τ.
Failure: certificate service cold → Action: block additive pool; fallback estimator with GateDecision=throttle.

Control Plane

Failure: desync (ρ↓, Δτ↑) → Action: pause schedules except commuting‑safe channels; resync protocol.
Failure: gate storm → Action: exponential back‑off; consolidate triggers; operator override path.

Audit Plane

Failure: ledger ingestion lag → Action: spill to local WAL; block exports; raise amber status.

Safe Modes

Read‑only audit; CWA‑off (no additive pooling); Ô‑reduced (commuting‑only); Tick slow‑roll. All are reversible with clear exit criteria.

9.7 Security, Privacy, and Compliance Hooks

AuthZ scopes per plane: data.write, control.schedule, audit.read/export.
PII/secret handling: projection artifacts tagged; redaction policies; lineage in audit.
Tamper‑evidence: hash‑chain for traces/cert logs; signed exports; reproducible seeds for panels.
Least privilege runners: Slot Allocator and Policy Gates run with minimal scopes; BeltOps is read‑mostly with signed writes for KPIs.

9.8 Production Artifacts

9.8.1 Architecture Diagram (Mermaid)

flowchart LR
  subgraph CONTROL[Control Plane]
    TS[Tick & Sync]
    PG[Policy Gates]
  end
  subgraph DATA[Data Plane]
    OR[Observer Runtime]
    CWA[CWA Engine]
    SA[Slot Allocator]
  end
  subgraph AUDIT[Audit Plane]
    TL[Trace Ledger]
    CL[Cert Logs]
    BD[BeltOps Dashboard]
  end

  TS -- Schedule/τ --> OR
  OR -- measure→TraceWrite --> TL
  OR -- /project,/pool --> CWA
  CWA --> CL
  OR -- Slot requests --> SA
  SA -. grants/refuse .-> OR
  OR --> BD
  BD --> PG
  PG -- GateDecision --> TS

  classDef plane fill:#0b7285,stroke:#0b7285,color:#fff;
  class CONTROL,DATA,AUDIT plane;

9.8.2 Module Dependency Graph (Mermaid)

graph TD
  SA[Slot Allocator]
  OR[Observer Runtime]
  CWA[CWA Engine]
  TS[Tick & Sync]
  PG[Policy Gates]
  BD[BeltOps Dashboard]

  TS --> OR
  OR --> CWA
  OR --> BD
  CWA --> BD
  BD --> PG
  PG --> TS
  SA --> OR

  %% Notes: all modules write to Audit Plane stores (not shown as edges here).

9.8.3 Boundary Checklist (Copy‑Paste into Design Reviews)

Each module declares owned state and no hidden side effects
All cross‑module calls carry idempotency keys
Retries either advance τ or use explicit retry_id
CWA thresholds and fallback policies versioned + auditable
Slot budgets defined; collisions observable; eviction policy explicit
Gate configs reproducible; escalation ladders documented
PBHL Residual bands defined; BeltOps panel shows Five‑Line KPI
Exports signed; lineage attached; privacy redactions applied

9.9 Summary

This chapter pins down the planes, modules, and contracts that make ObserverOps buildable. The next chapters (10–13) dive into per‑module APIs, data schemas, algorithms, and operational runbooks.

Chapter 10 — Observer Runtime

Goal

Implement the hot‑path service that executes measurements, enforces internal collapse at trace‑write, evaluates instrument compatibility, and produces agreement evidence using SBS‑style redundancy.

Scope. This chapter defines the Observer Runtime’s public interfaces, on‑disk/over‑the‑wire schemas, operational guardrails (idempotency/retries/latching), and the event taxonomy that other modules consume.

10.1 Responsibilities & Boundaries

Owns

Trace Ledger: append‑only, hash‑chained records of (τ, π, y) with provenance.
Channel Registry: instrument metadata, costs, slot needs, semantic pointers.
Commute Matrix: compatibility & preflight constraints among channels.

Collaborates with

Tick & Sync (receives TickStart, Schedule).
CWA Engine (calls /project, /pool).
Policy Gates (consumes GateDecision hints for degraded modes).
BeltOps Dashboard (emits AgreementReport, feeds KPIs).

Non‑Goals

Does not implement certificates or pooling algorithms (delegates to CWA Engine).
Does not compute PBHL controllers (BeltOps).

10.2 Public Interfaces (HTTP/gRPC)

10.2.1 `/measure`

Method	Path	Purpose	Idempotency	SLO	Auth
`POST`	`/measure`	Invoke instrument π on current state, return outcome `y`, and latch to Trace Ledger at tick τ.	`Idempotency-Key` (semantic: same tick + same π dedup)	p95 ≤ 50 ms	`data.write`

Request (JSON)

{
  "tau": 1042,
  "pi": "tools.search.web",
  "state_ref": "S:7f1b...",
  "schedule_id": "sched-1b2c",
  "idempotency_key": "m-1042-tools.search.web-1"
}

Response

{
  "trace_id": "t-01HZXJ...",
  "tick": 1042,
  "channel": "tools.search.web",
  "outcome_ref": "blob:sha256:ab38...",
  "write": {"hash": "sha256:9f2e...", "prev": "sha256:...", "ts": "2025-09-22T10:41:12Z"},
  "status": "latched"
}

Errors

409 Conflict — non‑commuting with locked channel at same τ
412 Precondition Failed — schedule mismatch or missing slot grant
425 Too Early — tick not opened by Tick & Sync

10.2.2 `/agree`

Method	Path	Purpose	Idempotency	SLO	Auth
`POST`	`/agree`	Compute cross‑observer agreement score using commute matrix & shared records (SBS redundancy).	`agree_id` deterministic over inputs	p95 ≤ 40 ms	`data.read`

Request

{
  "Ta_ref": "tset:replica-A:week39",
  "Tb_ref": "tset:replica-B:week39",
  "commute_matrix_id": "cm:v1.12",
  "pointer": "support.answer",
  "window": {"start": 1030, "end": 1045}
}

Response

{
  "agree_id": "ag-6c91...",
  "score": 0.94,
  "redundancy": {"R": 3.6, "channels": ["kb.vector", "kb.keyword", "kb.cached"]},
  "evidence": ["t-01HZXJ...", "t-01HZXL..."],
  "sbs": {"pass": true, "reason": "pointer redundancy ≥ 3"}
}

10.2.3 `/trace/:id`

Method	Path	Purpose	Caching	SLO	Auth
`GET`	`/trace/:id`	Retrieve immutable trace record with provenance & hash chain links.	CDN‑cacheable (immutable)	p95 ≤ 20 ms	`audit.read`

Response (abbrev.)

{
  "trace_id": "t-01HZXJ...",
  "tick": 1042,
  "channel": "tools.search.web",
  "outcome": {"kind": "json", "bytes": 2312},
  "write": {"hash": "sha256:...", "prev": "sha256:...", "writer": "or-0"},
  "lineage": {"schedule_id": "sched-1b2c", "idempotency_key": "m-1042-tools.search.web-1"}
}

10.3 Instrument Compatibility (Preflight)

Commute Matrix C is a sparse symmetric map over channel pairs with optional contextual predicates.

Entry form

{ "a": "sensors.qubit.Z", "b": "sensors.qubit.X", "commute": false, "predicate": "same_object && Δτ < 3" }

Preflight algorithm (pseudo‑code)

# inputs: schedule S = [π1, π2, ...], tick τ_k, matrix C
for (i,j) in pairs(S):
    if not C.commute(π_i, π_j, context):
        raise Conflict(pi=π_j, with_=π_i, tick=τ_k)

Conflict handling

Re‑order to a commuting sequence if available.
Defer non‑commuting channel to τ_{k+1} (Tick & Sync request).
Annotate TraceWrite with conflict=true when a measured channel times out and is skipped.

10.4 SBS Redundancy (Pointer Agreement)

Pointer variable. A semantic target (e.g., support.answer) with one or more pointer channels that redundantly encode it.

Redundancy factor (R). Effective count of independent channels carrying the same pointer:
R = ((Σ w_i)^2) / (Σ w_i^2), where w_i are channel reliability weights.

Agreement score. Jaccard/soft‑Jaccard or cosine similarity over pointer‑projected outcomes aggregated across observers within the window [τ_s, τ_e].

Runtime role.

Maintains a Pointer Map: {pointer → channels}
Emits AgreementReport with {score, R, evidence_trace_ids}

10.5 Data Schemas

10.5.1 Trace Ledger (append‑only, hash‑chained)

{
  "$schema": "https://observerops.io/schemas/trace.v1.json",
  "trace_id": "t-...",
  "tick": 1042,
  "channel": "tools.search.web",
  "slot_id": "slot:mem:3",
  "outcome_ref": "blob:sha256:...",
  "meta": {"duration_ms": 18, "cost": {"tokens": 1200}},
  "write": {"hash": "sha256:...", "prev": "sha256:...", "ts": "...", "writer": "or-0"},
  "lineage": {"schedule_id": "...", "idempotency_key": "...", "retry_id": null},
  "flags": {"timeout": false, "conflict": false}
}

10.5.2 Commute Matrix

{
  "$schema": "https://observerops.io/schemas/commute-matrix.v1.json",
  "matrix_id": "cm:v1.12",
  "default": true,
  "pairs": [
    {"a": "sensors.qubit.Z", "b": "sensors.qubit.X", "commute": false},
    {"a": "retriever.vector", "b": "retriever.keyword", "commute": true}
  ],
  "predicates": {
    "same_object": "ctx.object_a == ctx.object_b",
    "Δτ<3": "(ctx.tau_b - ctx.tau_a) < 3"
  }
}

10.5.3 Channel Registry

{
  "$schema": "https://observerops.io/schemas/channel-registry.v1.json",
  "channels": [
    {
      "id": "tools.search.web",
      "kind": "tool",
      "pointer": ["support.answer"],
      "requires_slot": {"type": "mem", "units": 1},
      "cost_model": {"latency_ms_p95": 40, "tokens_p95": 1500}
    }
  ]
}

10.6 Ops: Idempotency, Retries, Latching Guardrails

Latching rule (internal collapse): once TraceWrite(τ_k, π, y) commits, downstream control must condition on y. Retro‑edit requires a new tick τ_{k+1} and produces a new trace id.
Per‑tick single‑write: at most one successful TraceWrite per (τ, π).
Idempotency keys: dedup same‑tick duplicates; retry_id marks replays after transient errors.
Retry policy:
- 5xx / network → retry with same τ and retry_id (idempotent);
- 409 Conflict → request reschedule to τ_{k+1};
- 412/425 → wait for TickStart or fetch latest Schedule.
Back‑pressure: integrate with Slot Allocator; when refused, emit CollisionEvent and reschedule.

10.7 Event Taxonomy (Runtime‑Scoped)

Preflight.Compatibility{τ, π, ok, reason}
Measure.Start{τ, π} / Measure.Result{τ, π, y_ref, duration}
TraceWrite{trace_id, hash, prev, ts}
Retry{τ, π, retry_id, cause}
Agreement.Pass/Fail{agree_id, score, R}
Pointer.Redundancy{pointer, R, channels[]}

Event keys: run_id, observer_id, schedule_id, trace_id, agree_id.

10.8 Worked Examples

10.8.1 Qubit Toy (non‑commuting)

Channels: sensors.qubit.Z, sensors.qubit.X; C[Z,X]=false for same object.
Schedule proposes [Z, X] at τ_k. Preflight blocks X at τ_k; Tick & Sync defers X to τ_{k+1}.
TraceWrite(τ_k, Z, y_z) latches; TraceWrite(τ_{k+1}, X, y_x) records the second measurement.
/agree compares two observers with shared records → low agreement when orders differ (documented counterexample).

10.8.2 Tool‑Using Agent (commuting, SBS pass)

Channels: retriever.vector, retriever.keyword, kb.cached commute and point to support.answer.
Three traces at τ_k produce redundant pointers (R≈3.6). /agree across replicas A/B yields high score.

Sequence (Mermaid)

sequenceDiagram
  participant TS as Tick & Sync
  participant OR as Observer Runtime
  participant SA as Slot Allocator
  participant CWA as CWA Engine
  TS->>OR: Schedule(τ_k, [retriever.vector])
  OR->>SA: SlotRequest(mem=1)
  SA-->>OR: SlotGrant(slot:mem:3)
  OR->>OR: Preflight.Compatibility(ok=true)
  OR->>OR: measure → y
  OR->>OR: TraceWrite(τ_k, retriever.vector, y)
  OR->>CWA: /project{x, projector}

10.9 SLOs, Alerts, and Dashboards

Runtime SLOs

p95 measure→write ≤ 50 ms; error rate ≤ 0.5%
Agreement pipeline p95 ≤ 40 ms; stale commute matrix < 0.1%
Trace durability ≥ 11×9s; export lag p95 ≤ 2 s

Alerts

Latching violations (duplicate (τ, π) writes)
Desync dependency (received /measure before TickStart)
Commute drift (runtime observes conflicts for pairs marked commuting)

Dashboards

Hot‑path latency; per‑channel error bars; redundancy factor R over time; agreement heatmap.

10.10 Configuration (YAML)

runtime:
  cwa:
    min_score: 0.82
    panels:
      permutation: 128
      sign_flip: 64
      chunk_shuffle: 32
  latching:
    per_tick_single_write: true
  retries:
    max_attempts: 3
    backoff_ms: [50, 200, 800]
  slots:
    require_grant: true
  pointers:
    support.answer: [retriever.vector, retriever.keyword, kb.cached]
  commute_matrix: cm:v1.12

10.11 Artifacts

API Tables: /measure, /agree, /trace/:id (above)
Schemas: Trace Ledger v1, Commute Matrix v1, Channel Registry v1
Event Taxonomy: Runtime‑scoped events (10.7)
Diagrams: Sequence (10.8), plus plane‑context in Ch.9

Chapter 11 — CWA Engine (Projection → Certificate → Pool)

Goal. Decide when project→add (mean/sum pooling) is provably safe after projection, and when to auto-fallback to order-aware aggregators. Provide deterministic certificates, risk outputs, and tight latency budgets suitable for hot-path use.

11.1 Responsibilities & Boundaries

Owns

Projector Library P(·): deterministic projection policies (e.g., embedding models, pointer extractors, feature maps).
Certificate Panels: permutation, sign-flip, and chunk-shuffle test batteries with seeds.
Cert Logs: panel outcomes, seeds, CI/drift summaries.

Collaborates with

Observer Runtime (input vectors/records; calls /project, /pool).
Policy Gates (consumes certificate scores, Phase-Risk Index, drift alerts).
BeltOps Dashboard (receives risk KPIs).

Non-Goals

Doesn’t write traces (Observer Runtime does).
Doesn’t implement governance gates (Policy Gates do).

11.2 Interfaces (HTTP/gRPC)

11.2.1 `POST /project`

Project raw observations into a pooled space under a specified projector policy.

Request

{
  "policy": "embeddings.e5-large",
  "inputs": [{"ref":"t-01HZXJ..."}, {"ref":"t-01HZXL..."}],
  "params": {"normalize": true, "dtype": "float32"},
  "seed": 4271
}

Response

{
  "projection_id": "φ-9a12...",
  "vectors_ref": "blob:sha256:1f2c...",     // array of d-dim vectors
  "meta": {"n": 18, "dim": 1024, "normalize": true, "policy": "embeddings.e5-large"}
}

SLO p95 ≤ 25 ms. Auth data.write.

11.2.2 `POST /pool`

Pool a set of projected vectors with certificate gating.

Request

{
  "projection_id": "φ-9a12...",
  "vectors_ref": "blob:sha256:1f2c...",
  "aggregator": "mean",                      // desired fast path
  "min_score": 0.82,                         // θ
  "panels": {"perm": 128, "flip": 64, "chunk": 32},
  "chunk_meta": {"boundaries": [0,3,7,12,18]}, // optional for text/audio
  "seed": 4271
}

Response (fast-path pass)

{
  "pool_id": "pool-7c0b...",
  "aggregator_used": "mean",
  "vector_ref": "blob:sha256:b1a4...",
  "certificate": {
    "score": 0.91,
    "panels": {
      "perm":{"n":128,"median_delta":0.04},
      "flip":{"n":64,"median_delta":0.03},
      "chunk":{"n":32,"median_delta":0.05}
    },
    "phase_risk_index": 0.09,
    "ci95": [0.88, 0.93],
    "drift": {"p_value": 0.74, "ref_window": "W38"}
  },
  "fallback": {"used": false}
}

Response (fallback)

{
  "pool_id": "pool-7c0b...",
  "aggregator_used": "attention",
  "vector_ref": "blob:sha256:5ae9...",
  "certificate": {
    "score": 0.61,
    "phase_risk_index": 0.39,
    "ci95": [0.57, 0.66],
    "reason": "score<threshold or chunk panel median_delta>τ"
  },
  "fallback": {"used": true, "policy": "attention.kv", "latency_ms": 92}
}

SLO p95 ≤ 30 ms (pass path), ≤ 120 ms (fallback). Auth data.write.

11.3 Certificate Design

Let $V=\{v_i\}_{i=1}^N$ , $v_i\in\mathbb{R}^d$ be projected vectors. Baseline additive pool:

\mu_0 = \frac{1}{N}\sum_{i=1}^N v_i \quad\text{(or sum)}

Define a stability distance between any pooled vector $\mu$ and baseline $\mu_0$ :

\delta(\mu,\mu_0)=\min\!\left(1,\ \frac{\lVert \mu-\mu_0\rVert_2}{\lVert \mu_0\rVert_2 + \varepsilon}\right)

Score contribution from a panel with samples $\{\mu_j\}$ :

s = 1 - \mathrm{median}_j\ \delta(\mu_j,\mu_0) \in [0,1]

Panels

Permutation Panel (order wash-out)
- Draw permutations $\pi_j$ of indices; pool in permuted order (for additive mean, the order itself shouldn’t matter; this detects hidden order effects in the projection or pre-pool normalization).
- Produce $\mu^{(perm)}_j$ , compute $s_{perm}$ .
Sign-Flip Panel (orientation wash-out)
- Sample Rademacher signs $s_i\in\{\pm1\}$ per sample and/or small per-dimensional masks; form $v'_i = s_i v_i$ ; pool to $\mu^{(flip)}_j$ .
- Rationale: truly additive observables shouldn’t invert under local orientation flips after projection; sensitivity indicates phase-like coherence not erased by $P(·)$ .
- Compute $s_{flip}$ .
Chunk-Shuffle Panel (chunk boundary wash-out)
- Randomly perturb chunk boundaries or merge/split neighboring chunks consistent with chunk_meta.
- Pool perturbed sets → $\mu^{(chunk)}_j$ ; compute $s_{chunk}$ .

Aggregate certificate.

\text{CWA.score} = w_p s_{perm} + w_f s_{flip} + w_c s_{chunk},\quad w_p+w_f+w_c=1.

Defaults: $w_p=0.4, w_f=0.3, w_c=0.3$ .

Phase-Risk Index. A complementary risk value emphasizing order/phase sensitivity:

\mathrm{PRI} = 1 - \min(s_{perm}, s_{flip}, s_{chunk})

Low PRI (≈0) is safe; high PRI (→1) risky.

Confidence Interval (CI). Bootstrap the panel deltas; report 95% CI for the aggregate score.

11.4 Algorithms

11.4.1 Evaluator Pseudocode

def cwa_certificate(vectors, panels, seed, eps=1e-9, weights=(0.4,0.3,0.3)):
    rng = PCG64(seed)
    V = np.array(vectors)                      # N x d
    mu0 = V.mean(axis=0)                       # baseline
    norm0 = np.linalg.norm(mu0) + eps

    def delta(mu): return min(1.0, np.linalg.norm(mu - mu0) / norm0)

    def panel_perm(n):
        ds = []
        for _ in range(n):
            rng.shuffle(V)                     # permute in-place copy in real code
            mu = V.mean(axis=0)
            ds.append(delta(mu))
        return 1 - np.median(ds), ds

    def panel_flip(n):
        ds = []
        for _ in range(n):
            signs = (rng.random(V.shape[0]) < 0.5).astype(np.float32) * 2 - 1
            mu = (V * signs[:,None]).mean(axis=0)
            ds.append(delta(mu))
        return 1 - np.median(ds), ds

    def panel_chunk(n, boundaries):
        ds = []
        for _ in range(n):
            b = jitter_boundaries(boundaries, rng)  # small merges/splits
            subvects = [V[b[k]:b[k+1]].mean(axis=0) for k in range(len(b)-1)]
            mu = np.mean(subvects, axis=0)
            ds.append(delta(mu))
        return 1 - np.median(ds), ds

    sp, dsp = panel_perm(panels["perm"])
    sf, dsf = panel_flip(panels["flip"])
    sc, dsc = panel_chunk(panels["chunk"], panels.get("boundaries", [0, len(V)]))

    score = weights[0]*sp + weights[1]*sf + weights[2]*sc
    pri   = 1 - min(sp, sf, sc)
    ci_lo, ci_hi = bootstrap_ci([*dsp, *dsf, *dsc])  # on deltas → map to score CI

    return {
      "score": score, "phase_risk_index": pri,
      "panels": {"perm":{"median_delta":1-sp},
                 "flip":{"median_delta":1-sf},
                 "chunk":{"median_delta":1-sc}},
      "ci95": [ci_lo, ci_hi]
    }

11.4.2 Drift & CI

Maintain rolling distribution of panel deltas and scores per policy, domain.
Drift test: two-sample KS or AD test vs. reference window (e.g., week-over-week).
Alarm: p_value < 0.05 and |mean score shift| ≥ 0.05 → raise CWA.Drift.

11.5 Auto-Fallback Policies

Inputs: score, ci95, phase_risk_index, panels.*.median_delta, latency_budget_ms.

Default thresholds

Green (pass): score ≥ θ_pass (0.82) AND PRI ≤ 0.20
Amber (sampling pass): θ_warn ≤ score < θ_pass (0.75–0.82) → allow mean if latency critical and ci95[0] ≥ θ_warn; log amber
Red (fallback): score < θ_warn OR any panel.median_delta > τ_panel (0.25) OR PRI > 0.5

Fallback choices (by domain)

Text: attention.kv (length-aware), else cnn.1d
Time-series: rnn.gru or tcn
Multi-modal: late fusion with per-modality attention

Escalation

If Red persists ≥ K windows (default 3), emit PolicyGate.Trigger(block) and slow ticks.

11.6 Data & Logs

Certificate Log (immutable, append-only)

{
  "$schema": "https://observerops.io/schemas/cert.v1.json",
  "pool_id": "pool-7c0b...",
  "projection_policy": "embeddings.e5-large",
  "n": 18, "dim": 1024,
  "score": 0.91, "phase_risk_index": 0.09, "ci95": [0.88,0.93],
  "panels": {"perm":{"n":128,"median_delta":0.04},
             "flip":{"n":64,"median_delta":0.03},
             "chunk":{"n":32,"median_delta":0.05}},
  "weights": {"perm":0.4,"flip":0.3,"chunk":0.3},
  "seed": 4271, "ts": "2025-09-22T10:51:03Z",
  "drift": {"p_value": 0.74, "ref_window": "W38"},
  "fallback_used": false
}

Risk Outputs (for Policy Gates)

CWA.score (0–1), ci95, phase_risk_index
panel_max_delta, perm_delta, flip_delta, chunk_delta
drift.p_value, ref_window
Recommended action: {allow|throttle|block} with rationale

11.7 Latency Budget (Guide)

Path	Work	Typical Panel Counts	p50	p95	p99	Notes
`/project`	Model forward + norm	—	12 ms	25 ms	40 ms	cache models; FP16/INT8 ok if invariant
`/pool` (pass)	panels + mean	P=64, F=32, C=16	18 ms	30 ms	55 ms	vectorized panels; reuse μ₀
`/pool` (strict)	panels + mean	P=128, F=64, C=32	32 ms	55 ms	90 ms	use if high-stakes
`/pool` (fallback)	attention / rnn	—	55 ms	120 ms	220 ms	throttle if sustained

Complexity. O(N·d) for pooling; panels scale O((P+F+C)·d) with small constants; chunk panel mildly super-linear if boundary search.

11.8 Event Taxonomy (CWA-Scoped)

CWA.Project{projection_id, policy, n, dim, duration_ms}
CWA.Panel.Start/End{pool_id, perm|flip|chunk, n}
CWA.Pass{pool_id, score, pri, ci95}
CWA.Fail{pool_id, score, pri, reason}
CWA.Fallback{pool_id, policy, latency_ms}
CWA.Drift{policy, p_value, ref_window}
CWA.Export{pool_id, cert_log_ref}

Keys: pool_id, projection_id, cert_seed, domain, observer_id.

11.9 Worked Example (Text RAG Pooling)

Runtime sends 18 chunk vectors (E5 projector).
CWA computes μ₀ (mean) and panels (P=128, F=64, C=32).
Results: s_perm=0.96, s_flip=0.92, s_chunk=0.85 → score=0.91, PRI=0.15.
/pool returns additive mean; logs certificate; Policy Gates allow.
A week later, chunk deltas drift to 0.28 → score=0.78 (Amber); attention fallback engages on long docs while short docs stay additive.

11.10 Configuration (YAML)

cwa:
  thresholds:
    score:
      pass: 0.82
      warn: 0.75
    panel_delta_max: 0.25
    pri_max: 0.50
  panels:
    perm: 128
    flip: 64
    chunk: 32
  weights:
    perm: 0.4
    flip: 0.3
    chunk: 0.3
  fallback:
    text: attention.kv
    timeseries: rnn.gru
    multimodal: late_fusion.attn
  drift:
    ref_window: "Wk-1"
    pvalue_alert: 0.05
  reproducibility:
    seed: 4271
    log_all: true

11.11 Implementation Notes & Guardrails

Determinism: all panels seeded; record cert_seed.
Numerics: add ε in norms; clamp deltas to [0,1]; FP16 safe if ε≥1e-6.
Safety on failure: if certificate fails, never return additive mean; must return fallback or HTTP 409 with GateDecision=block.
Privacy: vectors tagged with lineage; redact raw content in Cert Logs.
Testing: synthetic coherent sequences should fail; permutation-stable bags should pass with high scores.

11.12 Artifacts

Config YAML (11.10)
Evaluator pseudocode (11.4.1)
Latency budget table (11.7)
Schemas & Events (11.6, 11.8)
API Contracts (/project, /pool)

Next: Chapter 12 — Slot Allocator & Tick/Sync (priority tiers, back-pressure, fleet cadence).

Chapter 12 — Slot Allocator & Tick/Sync (Capacity → Cadence → Cohesion)

Goal. Guarantee quantized capacity (slots) and coordinated cadence (ticks) across a fleet so observers stay reliable under load. Provide APIs for slot grants, a cadence manager for ticks, fleet-sync metrics (ρ, Δτ), and policies for priority, back-pressure, and safe degradations.

12.1 Responsibilities & Boundaries

Slot Allocator (SA) owns

Integer slot budgets for memory, attention, and tools (mem, attn, tool).
Leases (grants with TTL), collision logs, and eviction policy.

Tick & Sync (TS) owns

Global/cluster tick index τ, target cadence (ms between ticks), phase anchors.
Fleet-sync metrics: order parameter ρ and desynchrony Δτ.
Schedules (Ô decisions) or cadence hints to the Observer Runtime.

Collaborates with

Observer Runtime (requests slots; consumes schedules; emits heartbeats).
Policy Gates (consume ρ, Δτ, occupancy; issue throttle/stop).
CWA Engine (may request temporary “panel budget” slots).

12.2 Interfaces (HTTP/gRPC)

12.2.1 Slot APIs

POST /slots/request — ask for a lease.

{
  "tenant": "team-support",
  "observer_id": "obs-A42",
  "type": "mem",              // mem | attn | tool
  "units": 2,                 // integer
  "ttl_ms": 120000,
  "priority": "P1",           // P0|P1|P2
  "purpose": "retriever.batch",
  "idempotency_key": "slots-obs-A42-1042-mem-2"
}

Response

{
  "grant_id": "gnt-7af1...",
  "slot_ids": ["slot:mem:3","slot:mem:4"],
  "lease_expiry": "2025-09-22T11:03:10Z",
  "decision": "granted"       // granted | queued | refused
}

POST /slots/heartbeat

{"grant_id":"gnt-7af1...","extend_ms":30000}

POST /slots/release

{"grant_id":"gnt-7af1..."}

GET /slots/occupancy

Returns per-type {total, used, queued, collisions_per_min, by_tenant[]} (for dashboards).

SLOs: decision p95 ≤ 5 ms; release ≤ 3 ms.

12.2.2 Tick & Sync APIs

POST /tick/heartbeat — observer heartbeat + last applied tick.

{"observer_id":"obs-A42","tau":1042,"lag_ms":18}

GET /sync/status

{
  "tau_current": 1042,
  "cadence_ms": 80,
  "rho": 0.91,
  "delta_tau": 2,            // max tick gap across fleet
  "jitter_ms_p95": 14
}

POST /cadence/config — update target cadence & bounds (role-gated).

{"cadence_ms": 80, "min_ms": 60, "max_ms": 120, "phase_anchor": "now"}

SLOs: status p95 ≤ 10 ms; config p95 ≤ 25 ms.

12.3 Core Metrics

Occupancy per type: used / total.
Collision rate: refused grants per minute due to lack of contiguous slots (or budget).
ρ (order parameter): Kuramoto-style sync of tick phases
$\rho = \left|\frac{1}{N}\sum_{j=1}^N e^{i\theta_j}\right|$ , where $\theta_j$ is observer j’s tick phase in $[0,2\pi)$ .
Interpretation: 1=perfect sync, 0=uniformly desynced.
Δτ (desynchrony): max tick index difference in the fleet (or 95th–5th percentile gap).
Tick jitter: p95 absolute deviation from target cadence.

12.4 Slot Allocator — Algorithms & Policies

12.4.1 Priority & Admission

Priority tiers: P0 (critical), P1 (default), P2 (batch).
Budget splits: hard min-reserves per tier (P0_min, P1_min), with steal from lower tiers when idle.
Admission rule (simplified):
1. If free ≥ units and within tenant quota → grant.
2. Else if tier < victim tier and preemptible grants exist → evict lowest-value lease (starting with P2, then P1).
3. Else queue (FIFO within tier) or refuse with back-pressure hint.

12.4.2 Eviction & Back-Pressure

Eviction: mark evicted grants, emit CollisionEvent, allow 1 grace heartbeat (e.g., 1 s) for cleanup.
Back-pressure hints in refusal:
- reduce_parallelism: decrease concurrent channels.
- widen_ticks: ask TS to increase cadence_ms.
- switch_estimator: hint CWA to use lower-cost fallback.

12.4.3 Lease & Renewal

Leases must heartbeat before lease_expiry. Miss → auto-release.
Hard invariant: non-overlap writes per slot; allocator logs all grants/releases.

Pseudocode (admission)

def request(type, units, tier, tenant):
    pool = pools[type]
    if pool.free() >= units and within_quota(tenant, units):
        return grant(units)
    victims = find_preemptible(pool, tier, units)
    if victims.total_units >= units:
        evict(victims); return grant(units, preempt=True)
    return queue_or_refuse()

12.5 Tick & Sync — Algorithms & Policies

12.5.1 Cadence Controller

Target cadence $C^*$ (ms between ticks). Use PI control on jitter:
- error $e_k = C^* - \text{observed\_cadence}_k$
- update $C_{k+1} = C_k + K_P e_k + K_I \sum e$
Guardrails: clamp to $[min\_ms, max\_ms]$ .

12.5.2 Phase Sync & Resynchronization

Periodic phase anchors (e.g., every 1–5 s) broadcast τ_anchor + wall-clock.
Observers compute phase error and nudge their local timers (slew, no jumps).
If ρ < ρ_min or Δτ > Δτ_max, enter Resync Mode:
- temporarily widen cadence (reduce rate) and trim outlier observers (delay their next tick).
- restrict schedules to commuting-safe channels until sync recovers.

12.5.3 Schedule Shaping

When under back-pressure (from SA or Policy Gates), TS narrows channel set and increases inter-tick.
Burst smoothing: token bucket per observer and per tenant; overflows delay next TickStart.

Pseudocode (resync)

if rho < rho_min or delta_tau > dtau_max:
    cadence_ms = min(cadence_ms * 1.25, max_ms)
    schedule = schedule.filter(commuting_safe=True)
    broadcast("RESYNC", cadence_ms, schedule)

12.6 Degradation Modes (Safe States)

D0 Normal: full cadence; all channels; panels at default counts.
D1 Gentle: widen cadence by 10–25%; reduce parallelism; downscale panel counts (perm/flip/chunk ÷2).
D2 Strict: commuting-only channels; additive pooling allowed only if CWA.score ≥ θ_strict; others fallback.
D3 Quiescent: stop tick advancement except health checks; accept critical P0 only.

Entry conditions (any):

Occupancy > 0.9 for ≥ 60 s (by type).
ρ < 0.8 for ≥ 10 s or Δτ > 5 for ≥ 10 s.
Collision rate > threshold AND grant latency p95 > 30 ms.

Exit conditions: ρ ≥ 0.9 and Δτ ≤ 2 and occupancy < 0.7 for 30 s.

12.7 SLA Bands & Desync Alerts

12.7.1 SLA Bands (Green / Amber / Red)

Metric	Green	Amber	Red	Action
Slot occupancy (mem/attn/tool)	≤ 0.70	0.70–0.90	> 0.90	D1 at Amber; D2 at Red
Grant latency p95	≤ 5 ms	5–20 ms	> 20 ms	Increase reserves / throttle
Collision rate (per min)	≤ 2	3–10	> 10	Investigate evictions; widen cadence
ρ (order parameter)	≥ 0.90	0.80–0.90	< 0.80	Resync; scheduling restrictions
Δτ (ticks)	≤ 2	3–5	> 5	Trim outliers; slow cadence
Tick jitter p95	≤ 15 ms	16–40 ms	> 40 ms	PI retune; anchor more often

12.7.2 Desync Alert Thresholds

ALERT-SYNC-AMBER: ρ < 0.9 for 5 s or Δτ ≥ 3 for 5 s → enter D1.
ALERT-SYNC-RED: ρ < 0.8 for 10 s or Δτ ≥ 6 for 10 s → enter D2 + notify Policy Gates.
ALERT-SYNC-CRIT: ρ < 0.6 for 20 s or Δτ ≥ 10 for 20 s → D3; block non-P0.

12.8 Event Taxonomy (SA/TS-Scoped)

Slots.Request{grant_id, type, units, priority, decision}
Slots.Heartbeat{grant_id, extend_ms}
Slots.Release{grant_id}
Slots.Collision{type, tenant, needed_units}
TickStart{τ, schedule_id}
TickAnchor{τ_anchor, wallclock, cadence_ms}
DesyncAlert{rho, delta_tau, level}
Cadence.Update{cadence_ms, reason}
Degrade.Enter/Exit{mode, reason}

Keys: observer_id, tenant, schedule_id, grant_id.

12.9 Worked Examples

12.9.1 RAG Surge (Evening Traffic)

Occupancy(mem) climbs to 0.92; grant p95 → 28 ms; collision rate 12/min.
SA signals back-pressure; TS enters D2: cadence +20%, commuting-only channels, CWA strict threshold.
Within 45 s, occupancy falls to 0.74 and ρ stays ≥0.9 → exit to D0.

12.9.2 Multi-Robot Sync

Field bots drift due to poor NTP; ρ drops to 0.77 and Δτ=7.
TS broadcasts RESYNC with anchors every 500 ms; trims fast outliers; slows cadence to 110 ms.
After 12 s, ρ=0.92, Δτ=2; normal cadence restored; schedules reopened to full set.

12.10 Configuration (YAML)

slots:
  pools:
    mem:   {total: 128, reserve: {P0: 32, P1: 64, P2: 32}}
    attn:  {total: 64,  reserve: {P0: 16, P1: 32, P2: 16}}
    tool:  {total: 24,  reserve: {P0: 8,  P1: 12, P2: 4}}
  eviction:
    preemptible: ["P2","P1"]
    grace_ms: 1000
  quotas:
    team-support: {mem: 48, attn: 24, tool: 8}
    team-search:  {mem: 64, attn: 32, tool: 12}

ticksync:
  cadence_ms: 80
  bounds_ms: {min: 60, max: 140}
  pi_gains: {kp: 0.12, ki: 0.02}
  anchors:
    period_ms: 1000
    jitter_target_p95_ms: 15
  thresholds:
    rho_min: 0.90
    delta_tau_max: 2
    amber: {rho: 0.90, delta_tau: 3, duration_s: 5}
    red:   {rho: 0.80, delta_tau: 6, duration_s: 10}
    crit:  {rho: 0.60, delta_tau:10, duration_s: 20}
  degradation:
    d1: {cadence_factor: 1.1, panel_scale: 0.5}
    d2: {cadence_factor: 1.25, commuting_only: true, cwa_strict: 0.86}
    d3: {pause_non_p0: true}

12.11 Guardrails & Testing

Integer slots only; assert non-overlap, and log all evictions.
Idempotent grants via idempotency_key.
Monotone τ; no tick jumps; only slew during resync.
Load tests: ramp to 95% occupancy; verify D1/D2/D3 transitions and recovery.
Sync tests: inject clock skew; confirm alert ladder and convergence of ρ/Δτ.

Artifacts delivered: SLA bands (12.7.1), desync alert thresholds (12.7.2), slot & cadence configs (12.10), event taxonomy (12.8), algorithms/pseudocode (§12.4–12.5).

Next: Chapter 13 — BeltOps Dashboard & Policy Gates (panels, webhooks, audits, thresholded gates).

Chapter 13 — BeltOps Dashboard & Policy Gates (Closure → Telemetry → Control)

Goal. Close the macro loop with Purpose-Flux Belt Theory (PFBT) telemetry and deterministic gates that throttle or block risky runs. Surface Five-Line KPIs (Gap/Flux/Twist/Coherence/Residual), EEI/SI indices, and a clean webhook + export story for audits.

13.1 Responsibilities & Boundaries

BeltOps Dashboard (BD) owns

The belt worldsheet: $\textbf{Gap}, \textbf{Flux}, \textbf{Twist}, \alpha$ .
Residual: $R = \left| \text{Gap} - (\text{Flux} + \alpha\cdot\text{Twist}) \right|$ .
Five-Line KPI time series + EEI (Effectiveness/Execution Index) and SI (Sustainability Index).
KPIs export (pull via API / scheduled pushes).

Policy Gates (PG) owns

Gate configs & thresholds; evaluation engine; allow|throttle|block decisions.
Triggers on CWA score, Phase-Risk Index (PRI), PBHL Residual, and sync/capacity hints (ρ, Δτ, occupancy).
Signed webhooks and deterministic decision logs.

Collaborators

Observer Runtime (Agreement reports, pool results).
CWA Engine (scores, PRI, drift).
Tick & Sync (applies gate decisions; cadence shaping).
GRC/Audit (exports).

13.2 Interfaces (Overview)

13.2.1 `POST /belt`

Update belt worldsheet from fresh data (usually per tick/window).

Request

{
  "belt_id": "support-v2025Q3",
  "window": {"start": "2025-09-22T11:00:00Z", "end": "2025-09-22T11:01:00Z"},
  "gap": 0.62,
  "flux": 0.48,
  "twist": 0.12,
  "alpha": 1.1,
  "inputs": {
    "pool_ids": ["pool-7c0b..."],
    "agree_ids": ["ag-6c91..."]
  },
  "notes": "release sprint W39"
}

Response

{
  "pbhl": {"residual": 0.062, "status": "green"},
  "kpis": {"gap": 0.62, "flux": 0.48, "twist": 0.12, "coherence": 0.91},
  "indices": {"eei": 0.73, "si": 0.81},
  "update_id": "beltupd-92af..."
}

SLO p95 ≤ 60 ms. Auth control.write.

13.2.2 KPIs Export (Pull)

GET /belt/:id/kpi?from=...&to=...&format=parquet|jsonl
Returns Five-Line KPIs + EEI/SI + Residual with lineage (ids of contributing pool/agreement updates).
SLO p95 ≤ 200 ms (server-side range aggregation).

13.2.3 Gate Evaluation & Triggers

POST /gate/evaluate (optional explicit call; normally auto on belt/cert events)

{
  "belt_id": "support-v2025Q3",
  "metrics": {
    "cwa_score": 0.77,
    "pri": 0.36,
    "residual": 0.11,
    "rho": 0.86,
    "delta_tau": 4,
    "occupancy_mem": 0.82
  },
  "context": {"domain":"support-kb","risk":"standard"}
}

Response

{
  "decision": "throttle",
  "reasons": ["cwa_score_below_warn","residual_amber","rho_below_target"],
  "actions": {"cadence_factor": 1.15, "commuting_only": false},
  "gate_id": "gate-4d1e...",
  "effective_for_s": 60
}

Webhooks fire on any decision (see §13.7).

13.3 Data & Schemas

13.3.1 Belt Worldsheet

{
  "$schema": "https://observerops.io/schemas/belt.v1.json",
  "belt_id": "support-v2025Q3",
  "window": {"start":"...","end":"..."},
  "gap": 0.62,
  "flux": 0.48,
  "twist": 0.12,
  "alpha": 1.1,
  "residual": 0.062,
  "coherence": 0.91,            // agreement/coherence proxy at macro layer
  "indices": {"eei": 0.73, "si": 0.81},
  "lineage": {"pool_ids":["..."], "agree_ids":["..."], "cert_refs":["..."]},
  "hash": "sha256:..."
}

13.3.2 Gate Policy Config

{
  "$schema": "https://observerops.io/schemas/gate-config.v1.json",
  "bands": {
    "residual": {"green": [0,0.08], "amber": [0.08,0.15], "red": [0.15, 1.0]},
    "cwa_score": {"pass": 0.82, "warn": 0.75},
    "pri_max": 0.50,
    "rho_min": 0.90,
    "delta_tau_max": 2
  },
  "actions": {
    "amber": {"cadence_factor": 1.1, "panel_scale": 0.7},
    "red": {"cadence_factor": 1.25, "commuting_only": true, "block_if_score_lt": 0.70}
  },
  "debounce_s": 10,
  "hold_s": 60,
  "escalation": {"amber_windows": 3, "red_windows": 2}
}

13.3.3 Decision Log

{
  "gate_id": "gate-4d1e...",
  "belt_id": "support-v2025Q3",
  "ts": "2025-09-22T11:05:03Z",
  "decision": "throttle",
  "reasons": ["residual_amber","cwa_warn"],
  "inputs": {"residual":0.11,"cwa_score":0.77,"pri":0.36,"rho":0.86,"delta_tau":4},
  "signature": "HMAC-SHA256:..."
}

13.4 Evaluation Logic (Deterministic)

13.4.1 Rule Set (conceptual)

CWA gate
- If cwa_score < warn or pri > pri_max → at least throttle.
- If cwa_score < block_if_score_lt → block additive pooling; force fallback.
PBHL gate
- If residual ∈ Amber → throttle (widen cadence, reduce panels).
- If residual ∈ Red → block risky schedules and request Twist analysis.
Sync/Capacity gate
- If rho < rho_min or delta_tau > max or occupancy > 0.9 → throttle or commuting-only.
Escalation/debounce
- Require N consecutive windows before raise; M green windows before lower (hysteresis).
Determinism
- Same inputs → same gate_id (hash). All thresholds versioned.

13.4.2 Pseudocode

def evaluate(m, cfg, now):
    reasons, actions = [], {}
    decision = "allow"

    if m["cwa_score"] < cfg["bands"]["cwa_score"]["warn"] or m["pri"] > cfg["bands"]["pri_max"]:
        decision, reasons = "throttle", reasons + ["cwa_warn_or_pri"]

    if m["cwa_score"] < cfg["actions"]["red"]["block_if_score_lt"]:
        decision, reasons = "block", reasons + ["cwa_block"]

    res = m["residual"]
    rband = band(res, cfg["bands"]["residual"])
    if rband == "amber":
        decision = max_decision(decision, "throttle"); reasons += ["residual_amber"]
    elif rband == "red":
        decision = "block"; reasons += ["residual_red"]

    if m["rho"] < cfg["bands"]["rho_min"] or m["delta_tau"] > cfg["bands"]["delta_tau_max"]:
        decision = max_decision(decision, "throttle"); reasons += ["sync_issue"]

    actions = prescribe(decision, cfg["actions"])
    gate_id = stable_id(m, cfg)
    return gate_id, decision, reasons, actions

13.5 Dashboards (Panel Specs)

13.5.1 Five-Line KPI (time series, 1-min granularity)

Lines: Gap, Flux, Twist, Coherence, Residual.
Bands: green/amber/red based on configured thresholds.
Features: hover to show contributing pool/agree ids; click to open Cert Logs.

13.5.2 EEI / SI Panels

EEI: weighted blend of outcome quality, throughput, and agreement stability.
Example $\text{EEI} = 0.5\cdot Q + 0.3\cdot \text{ThroughputNorm} + 0.2\cdot \text{Agreement}$ .
SI: energy/compute cost per accepted unit + variance + slot pressure proxy.

13.5.3 Residual Trend

Rolling residual with change points and Twist annotations (reorg, policy change).
Correlate with cadence changes and gate states.

Panel spec (JSON)

{
  "panel_id": "kpi-five-line",
  "layout": {"w": 12, "h": 6},
  "series": [
    {"metric":"gap"}, {"metric":"flux"}, {"metric":"twist"},
    {"metric":"coherence"}, {"metric":"residual"}
  ],
  "bands": {"residual":[0.08,0.15], "coherence":[0.85,0.9]}
}

13.6 SLA Bands & Actions (Macro)

Metric	Green	Amber	Red	Default Gate Action
Residual	≤ 0.08	(0.08, 0.15]	> 0.15	Allow / Throttle / Block
CWA Score	≥ 0.82	[0.75, 0.82)	< 0.75	Allow / Throttle / Block (fallback)
PRI	≤ 0.20	(0.20, 0.50]	> 0.50	Allow / Throttle / Block
ρ	≥ 0.90	[0.80, 0.90)	< 0.80	Allow / Throttle / Commute-only/Block
Δτ (ticks)	≤ 2	3–5	> 5	Allow / Throttle / Block

13.7 Webhook Schema (Signed)

Endpoint registration

{
  "url": "https://ops.example.com/observerops/webhooks",
  "events": ["Gate.Decision","Belt.Update","CWA.Drift"],
  "secret": "********",   // HMAC key
  "retry": {"max": 5, "backoff_ms": [500, 2000, 5000]}
}

Event — Gate.Decision

{
  "event": "Gate.Decision",
  "id": "evt-8b2d...",
  "ts": "2025-09-22T11:06:30Z",
  "belt_id": "support-v2025Q3",
  "decision": "throttle",
  "reasons": ["cwa_warn_or_pri","residual_amber"],
  "actions": {"cadence_factor": 1.15, "panel_scale": 0.7},
  "signature": "HMAC-SHA256:base64(...)"
}

Verification: X-ObserverOps-Signature header (HMAC of payload). Retries are idempotent by id.

13.8 Audit Export Format

Exports are bundles with a manifest + referenced artifacts (parquet/jsonl). Signed and hash-addressed.

Manifest

{
  "export_id": "exp-W39-beltops",
  "created": "2025-09-22T11:10:05Z",
  "belt_id": "support-v2025Q3",
  "windows": [{"start":"2025-09-22T10:00:00Z","end":"2025-09-22T11:00:00Z"}],
  "files": [
    {"path":"kpi.parquet","sha256":"..."},
    {"path":"decisions.jsonl","sha256":"..."},
    {"path":"cert_logs.parquet","sha256":"..."}
  ],
  "lineage": {"pool_ids":[...], "agree_ids":[...], "cert_refs":[...]},
  "signature": "ed25519:..."
}

Contents

kpi.parquet: time series (Gap/Flux/Twist/Coherence/Residual, EEI/SI).
decisions.jsonl: Gate.Decision with inputs/reasons/actions.
cert_logs.parquet: referenced CWA certificates (subset).
Optional: privacy_map.json (redactions), schema_versions.json.

Retention: hot 90–365 days; cold 7 years.

13.9 Worked Scenarios

13.9.1 CWA Amber, Residual Amber → Throttle

Score = 0.79, PRI = 0.28, Residual = 0.11 (Amber bands).
PG returns throttle: cadence_factor=1.15, panel_scale=0.7.
TS widens cadence; CWA reduces panel counts; after 3 windows, Residual=0.07 (Green) → auto-lift.

13.9.2 Residual Red → Block Risky Schedules

Residual spikes to 0.18 after org Twist (reorg); Score=0.84.
PG blocks non-critical workloads and restricts schedules to commuting-safe channels until Residual < 0.10 for 4 windows. Twist annotation appears on Residual panel.

13.10 Configuration (YAML)

beltops:
  kpi:
    coherence_source: "agreement.rate"
    window_s: 60
  pbhl:
    residual_bands: {green: [0,0.08], amber: [0.08,0.15], red: [0.15,1.0]}
  indices:
    eei_weights: {quality: 0.5, throughput: 0.3, agreement: 0.2}
    si_weights:  {energy: 0.5, variance: 0.3, slots: 0.2}
  export:
    schedule_cron: "*/15 * * * *"
    format: "parquet"
    sign: "ed25519"
    include: ["kpi","decisions","cert_logs"]

gates:
  thresholds:
    cwa_score: {pass: 0.82, warn: 0.75}
    pri_max: 0.50
    rho_min: 0.90
    delta_tau_max: 2
  actions:
    amber: {cadence_factor: 1.1, panel_scale: 0.7}
    red:   {cadence_factor: 1.25, commuting_only: true, block_if_score_lt: 0.70}
  debounce_s: 10
  hold_s: 60
  escalation: {amber_windows: 3, red_windows: 2}

webhooks:
  url: "https://ops.example.com/observerops/webhooks"
  secret: "env:WEBHOOK_SECRET"
  events: ["Gate.Decision","Belt.Update","CWA.Drift"]

13.11 SLOs, Alerts, and Guardrails

SLOs

/belt p95 ≤ 60 ms; KPI export p95 ≤ 200 ms (range ≤ 1 h).
Gate evaluation ≤ 10 ms inline (≤ 100 ms async fan-out).
Dashboard refresh ≤ 1 s.

Alerts

Residual.Red sustained ≥ 2 windows.
Gate-Flap (> 3 decisions flip-flop within 5 min).
Export-Lag (> 2 min after schedule).

Guardrails

Deterministic evaluation (versioned thresholds).
Hysteresis (debounce + hold) prevents flapping.
Signed webhooks + signed exports for tamper-evidence.
Privacy: KPI exports contain ids only; raw content redacted at source.

Artifacts delivered: Panel specs (§13.5), webhook schema (§13.7), audit export format (§13.8), interfaces (§13.2), configs (§13.10), evaluation pseudocode (§13.4.2), SLA bands (§13.6).

Next: Part III — Implementation Patterns & Recipes (apply BeltOps + Gates to real fleets).

Chapter 14 — Tool-Using LLM Agents (Pattern → Recipes → KPIs)

Goal. Turn an LLM that calls external tools into a buildable observer: tools map to channels Π; Ô (scheduler) picks the next channel; τ (ticks) commit decisions; traces latch; replicas run agreement checks; pooling is CWA-gated. You’ll get safe-retry patterns, SBS logging, multi-agent quorum, KPIs, and ablations you can run this week.

14.1 Pattern (Tools ↔ Channels; Ô/τ; Latching)

Mapping.

Channel set Π ≙ tool registry (e.g., web.search, kb.retriever.vector, kb.retriever.keyword, code.exec, calc, summarize).
Ô policy selects next channel based on state S and recent trace T.
τ advances per committed step; TraceWrite(τ_k, π, y) is the latching point.

Minimal loop (pseudocode)

def observer_loop(goal):
    tau = tick.start()
    while not done(goal):
        pi = O_hat.select_channel(S, T)        # Ô policy
        grant = slots.request(type=need(pi))   # mem/attn/tool slots
        preflight.check_commute(pi, T)         # conflict graph C
        y = tools.invoke(pi, S)                # MEASURE
        trace_id = trace.write(tau, pi, y)     # LATCH
        if pi in PROJECTABLE:
            phi = cwa.project(y, policy="embeddings.e5-large")
            pooled = cwa.pool(phi, min_score=theta)  # cert-gated
            S = update_state(S, pooled)
        T = append(T, (tau, pi, y))
        tau = tick.next()
    return finalize(S, T)

What this guarantees

Internal collapse: downstream control conditions on latched y.
Agreement hooks: shared records + commuting sequences enable cross-observer checks.
Capacity safety: quantized slots; explicit back-pressure.

14.2 Tool Registry & Compatibility (Commute Matrix C)

Tool (channel π)	Typical conflicts (non-commuting)	Notes
`web.search`	`web.search` (same query, same τ)	de-duplicate via idempotency key
`kb.retriever.vector`	— (commutes with `kb.keyword`)	pointer→`support.answer`
`kb.retriever.keyword`	— (commutes with `kb.vector`)	pointer→`support.answer`
`summarize`	`summarize` (same input at same τ)	idempotent if content-hash matches
`code.exec`	often non-commuting with stateful tools	run after read-only steps
`calc`	commutes (pure)	deterministic
`write.kb`	non-commuting with any read of same object	defer to τ+1

Recipe: Preflight before MEASURE:

If C[π_i, π_j]==false for same object/window → reorder or push to τ_{k+1}.
Reserve tool slots for stateful tools to serialize writes.

14.3 Ô Scheduling Policies (choose next tool)

Scoring components (example)

Information gain: expected reduction in AL / Collapse Entropy $S_c$ .
Cost: slot + latency budget.
Risk: panel deltas from last CWA; phase-risk PRI.
Compatibility: penalize potential conflicts.

def select_channel(S, T):
    cands = filter_enabled(Π)
    score = {}
    for pi in cands:
        ig   = est_info_gain(pi, S, T)
        cost = cost_model(pi)
        risk = last_pri(pi)
        compat = compat_margin(pi, T)  # 1.0 if safe
        score[pi] = 0.6*ig - 0.3*cost - 0.1*risk + 0.1*compat
    return argmax(score)

Cadence: start at 60–120 ms between ticks; widen if slots hot or gates throttle.

14.4 Recipes

R1. Safe Retries (idempotent, latching-aware)

Idempotency keys per (τ, π, input_hash).
Retry matrix:
- 5xx/timeout → same τ, retry_id set; dedup by idempotency key.
- 409 Conflict → request reschedule to τ+1.
- 412/425 (precondition/tick-early) → wait for TickStart.
Never mutate a latched trace; publish a new TraceWrite at τ+1 with reason.

R2. SBS Logging (pointer redundancy)

Define pointer support.answer → channels {kb.vector, kb.keyword, kb.cached}.
On each τ, record pointer outcomes; compute redundancy $R$ and emit AgreementReport.
Store evidence ids so replicas can agree on shared objects.

R3. Multi-Agent Quorum

Run 3 replicas (A/B/C) with same Ô policy and shared registry.
Accept result if agree(A,B) ≥ θ or agree(B,C) ≥ θ (2-of-3).
If quorum fails:
1. restrict to commuting channels,
2. elevate to human or retry at τ+1 with narrowed schedule.

R4. Certificate-Gated RAG

After kb.* measurements, call /project, then /pool with panels (e.g., P=128,F=64,C=32).
If score ≥ 0.82 & PRI ≤ 0.20 → mean; else attention fallback.
Log certificate for audit and BeltOps KPIs.

R5. Desync Hygiene (Δτ, ρ)

If ρ < 0.9 or Δτ ≥ 3: slow ticks by 10–25%, reduce parallelism, prefer commuting channels.
Gate raises to normal when ρ ≥ 0.9 and Δτ ≤ 2 for 30 s.

14.5 KPIs (definitions & targets)

KPI	Definition	Green Target	Notes
Disagreement	1 − mean(agreement score across replicas)	≤ 0.08	pointer-conditioned
Mis-exec	tool errors / tool invocations	≤ 1.0%	include timeouts
Δτ	fleet tick spread (95th–5th)	≤ 2 ticks	alert ≥ 3
Trace half-life	time until 50% of traces are overwritten/invalidated by updates	≥ 24 h	signals stability
Cert pass-rate	fraction of pools with `score ≥ θ`	≥ 80%	domain-dependent
Latency (E2E)	user→answer p95	target SLO	depends on fallback mix

14.6 Worked Example (Support Q&A)

Ô picks kb.retriever.vector at τ_0; Slot Allocator grants mem=1.
Measure→Latch: TraceWrite(τ_0, kb.vector, y_v).
Ô picks kb.keyword (commuting) at τ_1; latch y_k.
Runtime calls CWA: project+pool on {y_v,y_k,y_cached} (redundant set).
- Panels pass: score=0.90, PRI=0.12 → mean vector retained.
summarize at τ_2 condenses retrieved passages; latch summary.
Replica B mirrors steps; /agree between A/B on pointer support.answer returns 0.94.
BeltOps ingests KPIs; Policy Gates stay allow.

14.7 Playbooks

P1. Mis-exec spike

Symptom: mis-exec > 2% for 5 min.
Actions: freeze code.exec, prefer read-only; raise tool timeouts; enable retries (max 2); widen ticks by 10%; open incident if sustained.

P2. Certificate amber wall

Symptom: CWA pass-rate drops < 60%.
Actions: reduce chunk size variance; bump panel counts (P+32/F+16/C+16); enable attention fallback for long docs; schedule feature rollbacks if drift persists.

P3. Quorum failures

Symptom: Disagreement > 0.15 across replicas.
Actions: enforce commuting-only schedule for one window; elevate to human checker; cache accepted pointer; log counterexample set.

14.8 Ablations (±Ô, ±slots, ±certificate)

Design. 3× runs on the same traffic (A/B/C), 1 week each:

Baseline (Ô+slots+cert)
No-Ô (greedy tool order)
No-slots (unbounded parallelism)
No-certificate (always mean)

Ablation	Expected shift	Interp
No-Ô	Disagreement ↑ 5–10%; latency ↑	poor channel order & conflicts
No-slots	Mis-exec ↑; Δτ ↑; E2E latency variance ↑	collisions & back-pressure storms
No-certificate	Accuracy ↓ on coherent corpora; latency ↓	unsafe pooling saves time but harms quality

14.9 Config (YAML)

agent:
  goal: "answer_support_q"
  channels:
    - id: web.search           # tool → channel
      type: tool
      cost: {latency_ms_p95: 200}
    - id: kb.retriever.vector
      type: retriever
      pointer: [support.answer]
    - id: kb.retriever.keyword
      type: retriever
      pointer: [support.answer]
    - id: summarize
      type: llm
  commute_matrix: cm:v1.12
  O_hat:
    policy: "ig-cost-risk"
    weights: {ig: 0.6, cost: 0.3, risk: 0.1}
  tau:
    cadence_ms: 90
    bounds_ms: {min: 70, max: 140}

cwa:
  thresholds: {pass: 0.82, warn: 0.75, pri_max: 0.5}
  panels: {perm: 128, flip: 64, chunk: 32}
  fallback: {text: attention.kv}

quorum:
  replicas: 3
  agree_threshold: 0.90
  pointer: "support.answer"

slots:
  pools: {mem: {total: 64}, tool: {total: 16}}
  require_grant: true

alerts:
  misexec_rate: {warn: 0.01, crit: 0.02}
  disagreement: {warn: 0.12, crit: 0.18}
  delta_tau: {warn: 3, crit: 5}

14.10 Tests

Unit: idempotent /measure under retries; per-tick single-write; commute preflight.
Property: permutation stability on bag-like inputs (should pass CWA); coherent chain (should fail CWA).
Integration: 3-replica quorum; SBS redundancy R≥3; agreement ≥ 0.9 on stable topics.
Load: occupancy 80–95%; confirm no latching violations; Δτ stays ≤ 2 in green.

14.11 Artifacts

Playbooks: P1–P3 (mis-exec, certificate amber, quorum failures).
Ablations: ±Ô, ±slots, ±certificate with expected effect sizes.
Dashboards: Disagreement, mis-exec, Δτ, CWA pass-rate, trace half-life.
Configs: Agent + CWA + slots + quorum YAML (14.9).

Next: Chapter 15 — RAG & Embeddings (project→CWA-gate→pool; chunking as instrument design; latency/accuracy fronts).

Chapter 15 — RAG & Embeddings (Project → CWA-Gate → Pool)

Goal. Make retrieval-augmented generation (RAG) observer-safe: project first, run a CWA certificate to decide if additive pooling is valid, else auto-fallback to order-aware pooling. Treat chunking as instrument design, integrate cleanly with vector DBs, and track accuracy ↔ latency with Phase-Risk KPIs.

15.1 Pattern (End-to-End)

Data path.

Measure (retrieve) with commuting channels: kb.retriever.vector + kb.retriever.keyword (pointer → support.answer).
Project each candidate passage/snippet to vector space via policy $P(·)$ .
Certificate the set $V=\{v_i\}_{i=1}^N$ with panels (perm/flip/chunk) → CWA.score and PRI.
Pool:
- if score ≥ θ and PRI ≤ PRI_max → mean/sum (fast path);
- else → attention/CNN (order-aware).
Generate with pooled representation as context/features; latch traces and certificate.

Why it works. Projection erases phase/order if the projector truly collapses nuisance structure. Certificate checks that this holds for the current set (not just in general), guarding against “unsafe mean.”

15.2 Chunking as Instrument Design

Treat the chunker as part of the instrument $π_\theta$ with orientation $\theta$ (size, stride, boundary rule).

Design knobs

Size/stride (e.g., 512/128 tokens)
Overlap window (Hann/flat)
Boundary policy (sentence-aware, heading-aware)
Orientation: per-domain templates (FAQ vs narrative vs code)

Commutativity windows.

Chunkers with the same boundary policy commute; mixed policies may induce order sensitivity → chunk panel will detect it.

Redundancy. For SBS-style pointer objectivity, maintain 2–3 redundant chunkers (e.g., size 256, size 512, sentence) mapped to the same pointer; improves agreement and pass-rate.

15.3 Vector-DB Integration (Index & Query)

Upsert schema (generic)

{
  "id": "doc:123#ch:05",
  "vector": [ ... d floats ... ],
  "metadata": {
    "doc_id": "doc:123",
    "chunk_id": "05",
    "projector": "embeddings.e5-large",
    "norm": "l2",
    "chunk": {"size": 512, "stride": 128, "policy": "sentence"},
    "pointer": ["support.answer", "entity.X"],
    "ts_ingested": "2025-09-15T10:05:02Z"
  }
}

Partitions.

By projector (projector=…) to avoid mixing spaces.
By domain (knowledge area / locale).
Optional by orientation (chunk policy) to stage panel-specific retrievals.

Query path

KNN/ANN search (per projector/partition).
Join with keyword/graph hits (commuting channels).
Produce candidate set $V$ with provenance (doc, chunk meta).
Hand to CWA for certificate + pooling.

Tip: persist projection_id and chunk_meta alongside vectors so chunk panel can jitter boundaries without re-reading raw text.

15.4 Recipes

R1. Permutation Budget (panel counts)

Choose perm/flip/chunk sample sizes to balance CI vs latency.

Heuristic:

P = \min(128,\ \max(32,\ 8\cdot \lceil \log_2(N\cdot d) \rceil)),\quad F = \lfloor P/2 \rfloor,\quad C = \max(16,\ \lfloor P/4 \rfloor)

Clamp up (strict) on safety-critical domains; clamp down on mobile/edge.

R2. Phase-Risk Bands (actions)

Green: PRI ≤ 0.20 → allow additive mean.
Amber: 0.20 < PRI ≤ 0.50 → allow mean only if score ≥ θ_warn and latency budget tight; else attention.
Red: PRI > 0.50 → force attention/CNN, reduce chunk variability, widen ticks.

R3. Fallback to Attention Pooling

Text: attention.kv with position encodings; cap context by slots.
Time-series: rnn.gru / tcn with dilation; per-channel normalization.
Cache fallback outputs for identical candidate sets (content-hash key).

R4. Mixed-Mode Retrieval (commuting set)

Use {vector, keyword, cached} as redundant channels for the same pointer.

Raise redundancy $R$ ≥ 3 → improves agreement and stabilizes pass-rate.
Weight channels by historical reliability in ranking fusion.

R5. Precompute vs On-the-Fly

Precompute document vectors; on-the-fly per-query projection of short snippets (e.g., synthesized queries) if they influence pooling risk.
Always record projector and seed in Cert Log for reproducibility.

15.5 KPIs & Targets

KPI	Definition	Target / Band	Interpretation
Accuracy	task score (EM/F1/nDCG@k)	maximize	primary quality
Latency (E2E)	user→answer p95	meet SLO	certificate adds small fixed overhead
CWA Pass-Rate	`% pools with score ≥ θ_pass`	≥ 75–85%	higher means more fast-path
Phase-Risk Index (PRI)	1 − min(panel scores)	Green ≤ 0.20	coherence/order risk
Fallback Rate	`% answers using attention/CNN`	≤ 25% (steady)	too high → revisit chunking
Agreement	pointer agreement across replicas	≥ 0.90	SBS/objectivity proxy
Panel Cost	ms per pool (pass vs fallback)	within budget	capacity planning

Plot accuracy vs latency Pareto with markers by pass/fallback—aim to shift the frontier down/right with better chunking & redundancy.

15.6 Pipeline Pseudocode (Reference)

def rag_answer(query):
    # 1) Retrieve via commuting channels
    Vv = vdb.knn(query_vec, k=K, projector="e5-large")        # vectors
    Vk = keyword.search(query, k=Kk)                           # keywords
    C  = fuse(Vv, Vk)                                          # merge, dedup

    # 2) Project (if any raw needs projection)
    phi = project_if_needed(C, policy="e5-large", normalize=True)

    # 3) Certificate: decide pooling mode
    cert = cwa.certificate(phi, panels=choose_panels(len(phi)))
    if cert["score"] >= θ_pass and cert["phase_risk_index"] <= PRI_max:
        pooled = mean(phi)
        mode = "mean"
    elif cert["score"] >= θ_warn and latency_budget_tight():
        pooled = mean(phi); mode = "mean-amber"
    else:
        pooled = attention_pool(C)  # order-aware
        mode = "attention"

    # 4) Generate
    answer = llm.generate(query, context=pooled, mode=mode)

    # 5) Log
    log_cert(cert); log_pool(mode); log_answer(answer)
    return answer

15.7 Config Templates (YAML)

projectors:
  default: "embeddings.e5-large"
  policies:
    embeddings.e5-large:
      normalize: true
      dtype: float32
      cache: memory+disk

chunkers:
  - id: "sent-512@128"
    size: 512
    stride: 128
    boundary: "sentence"
  - id: "sent-256@64"
    size: 256
    stride: 64
    boundary: "sentence"

retrieval:
  knn:
    index: "qdrant://kb-support"
    space: "cosine"
    shard_by: ["projector","domain"]
    k: 20
  keyword:
    engine: "bm25"
    k: 20
  fusion:
    method: "rrf"
    weights: {knn: 0.6, keyword: 0.4}

cwa:
  thresholds: {pass: 0.82, warn: 0.75, pri_max: 0.50}
  panels: {perm: auto, flip: auto, chunk: auto}
  weights: {perm: 0.4, flip: 0.3, chunk: 0.3}
  fallback:
    text: "attention.kv"

kpis:
  report_window_s: 60
  accuracy_metric: "nDCG@10"
  latency_slo_ms_p95: 800

15.8 Benchmark Harness

Purpose. Measure accuracy ↔ latency under controlled phase/order conditions; stress certificate decisions.

Datasets

FAQ Bag (orderless): short independent Q/A pairs → should pass CWA easily.
Narrative Chain: long documents with causal order (chapters) → fail chunk panel unless chunking aligned.
Mixed Domain: support KB with both FAQs and tutorials.

Scenarios

Chunk Sweep: sizes {256, 512, 1,024}, strides {1/4, 1/8}; measure pass-rate and accuracy.
Panel Budget: P/F/C in {(64,32,16), (128,64,32)}; observe CI and latency.
Fallback Mix: attention vs mean; record frontier.

Outputs

CSV/Parquet with: accuracy, p95 latency, pass-rate, PRI, fallback rate, agreement.
Plots: accuracy–latency Pareto; pass-rate by chunk policy; PRI histogram.

Harness CLI

observerops-bench rag \
  --dataset narrative-chain \
  --chunkers sent-256@64 sent-512@128 \
  --panels 64,32,16 128,64,32 \
  --theta_pass 0.82 --theta_warn 0.75 \
  --pri_max 0.50 --trials 3 \
  --out results/chain_w39.parquet

15.9 Worked Examples

15.9.1 FAQ Corpus (Bag-like → Fast Path)

N=12 chunks per query, sent-256@64.
Panels: P=64,F=32,C=16 → score=0.93, PRI=0.08.
Mean pooling used; p95 latency 420 ms; nDCG@10 = 0.72; pass-rate 92%.

15.9.2 Tutorial Chapters (Coherent → Fallback)

N=18 chunks, sent-512@128.
Panels: P=128,F=64,C=32 → score=0.73, PRI=0.41, chunk.median_delta=0.27.
Attention fallback; p95 latency 720 ms; nDCG@10 = 0.75 (better accuracy despite higher cost); pass-rate 48%.

15.10 Artifacts

Config templates (§15.7).
Benchmark harness (CLI & scenarios; §15.8).
Pseudocode (§15.6).
KPIs and targets (§15.5).

Next: Chapter 16 — RL/Robotics (sensors as instruments; compatibility; fleet sync; belt-level objectives).

Chapter 16 — RL/Robotics (Sensors → Schedules → Synchronized Fleets)

Goal. Make RL/robotics stacks observer-safe: treat sensors as instruments (channels Π), encode action compatibility (commute/conflict), drive control on ticks τ, and coordinate fleets by sync ρ with closure at the belt layer (Gap/Flux/Twist/Residual). Use CWA to certify when sensor features can be additively fused; otherwise fall back to order-aware filters.

16.1 Pattern (single robot → fleet)

Channels Π (sensors & tools): lidar.scan, cam.rgb, imu, encoders, gripper.open/close, base.move, arm.movej, ee.force, …
Ô (scheduler): chooses next measure or act given state S and trace T, obeying the commute matrix C (sensor read–read often commutes; act–act rarely).
τ (ticks): fixed-rate control commits (e.g., 20 ms/50 Hz); TraceWrite(τ_k, π, y) latches outcomes; actions are latched intents with ack.
ρ (fleet sync): keep robot phases aligned for team behaviors; bound Δτ across the swarm.
CWA on fusion: after projecting sensor data to features, use certificate panels (perm/flip/chunk) to gate additive fusion; otherwise apply EKF/particle/attention fusion.

16.2 Robot Observer Tuple

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

S: estimator (pose, map, task), controller states, RL policy state.
T: append-only traces of (τ, channel, outcome) plus action acks.
Ô: policy mixing (state estimator needs vs. policy needs vs. safety checks).
Π: sensors/actuators as channels.
C: compatibility graph; edges when simultaneous use is safe/commuting.

Tick budget example (mobile manipulator): 50 Hz control (20 ms), 10 Hz mapping (100 ms), 2 Hz high-level planning (500 ms). Lower-rate loops schedule inside higher-rate ticks via sub-plans.

16.3 Action & Sensor Compatibility (C)

Typical conflicts (non-commuting):

arm.movej ↔ arm.teach (servo vs impedance mode).
base.move ↔ arm.movej at high speed (coupled dynamics; restrict envelope).
gripper.close ↔ ee.force.calibrate (block until calibration done).
write.map ↔ read.map (same object at same τ) → push write to $τ_{k+1}$ .
High-power sensor bursts (structured-light) ↔ cam.rgb (glare) → sequence.

Preflight: for proposed schedule $S=[π_1,π_2,...]$ , reject any pair with C[π_i,π_j]==false in current context; re-order to commuting sequence or shift to $τ_{k+1}$ .

16.4 Multi-Robot Sync via τ and ρ

Phase model: each robot j has phase $\theta_j \in [0,2\pi)$ for its control tick.
Order parameter: $\displaystyle \rho = \left|\frac{1}{N}\sum_{j=1}^N e^{i\theta_j}\right|$ (1=perfect sync).
Desynchrony: $\Delta\tau = \max_j \tau_j - \min_j \tau_j$ .
Resync: broadcast anchors each 0.5–1 s; slew clocks (no jumps); when $\rho<\rho_{min}$ or $\Delta\tau>\Delta\tau_{max}$ , restrict to commuting-safe actions and widen cadence until recovered (per Ch.12).

16.5 Recipes

R1. Conflict-Aware Schedules

Encode actuation envelopes (max combined speed/torque) as predicates in C.
Before issuing an action, compute compatibility margin; if negative, re-order or split across ticks.
For mixed base+arm motion, treat planner outputs as a single composite channel to avoid hidden conflicts.

R2. Certified Sensor Fusion

Project raw streams $x_i$ to features $v_i = P(x_i)$ (e.g., BEV features, learned embeddings).
Run CWA panels:
- perm over packet arrival order,
- flip sign/orientation jitter (e.g., minor frame inversions),
- chunk sub-scan re-binning.
If score ≥ θ & PRI ≤ PRI_max → fuse by mean/sum (grid/logit add).
Else fall back to EKF/UKF/particle or attention fusion.

R3. Fleet Belts Tied to Task Gap

Define belt worldsheet per mission: Gap (task error), Flux (work rate), Twist (reconfigs).
Use Residual = |Gap − (Flux + α·Twist)| to judge plan–do closure.
Gates: throttle when Residual Amber; block tactical pushes when Red.

R4. Safe Exploration & Rollback (RL)

Exploration actions run under Ô-sandbox with reduced cadence and hard C constraints.
Latch roll-back poses; if safety near-miss triggers, halt at $τ_{k+1}$ and return.

R5. Hot-Swap Sensors

If a sensor drops, keep fusion green via redundancy: LiDAR + depth + stereo pointing at same pointer (e.g., occupancy).
CWA pass with lower panel counts permits additive keep-alive until repair.

16.6 KPIs (targets depend on platform domain)

KPI	Definition	Green	Amber	Red
Task Success	episode success rate	≥ 0.9	0.8–0.9	< 0.8
Safety Incidents	stops/near-misses per hour	≤ 0.2	0.2–1.0	> 1.0
PBHL Residual		≤ 0.08	0.08–0.15	> 0.15
ρ	sync order parameter	≥ 0.9	0.8–0.9	< 0.8
Δτ	fleet tick spread (ticks)	≤ 2	3–5	> 5
Cert Pass-Rate	CWA pass on fusion calls	≥ 0.8	0.6–0.8	< 0.6
Loop Latency	control loop p95	≤ 20 ms	20–35 ms	> 35 ms

16.7 Control Loop (pseudocode)

def control_tick(robot):
    tau = tick.current()
    # 1) Sense (commuting reads first)
    scans = []
    for pi in ["lidar.scan","cam.rgb","imu","encoders"]:
        if commute_ok(pi, T): scans.append(measure(pi))
    trace.write(tau, "sense", ref=scans)  # latch

    # 2) Project → Certificate → Fuse
    V = [project(s) for s in scans]
    cert = cwa.certificate(V, panels=choose_panels(len(V)))
    fused = (np.mean(V, axis=0) if is_pass(cert) else ekf_fuse(V))
    trace.write(tau, "fused", ref=fused)  # latch

    # 3) Plan/Act with compatibility preflight
    candidate_actions = planner(fused, goal)
    safe_actions = preflight(candidate_actions, C)
    for a in safe_actions:
        act(a); trace.write(tau, a.kind, y="ack")

    # 4) Belt update (windowed)
    belt.update(metrics_from_tick())
    tick.next()

16.8 Simulation Checklist (pre-deployment)

Physics & Timing

Controller rate & jitter (20–50 Hz), sensor latencies, async delivery.
Contact models, friction cones, actuator limits & saturation.

Scenarios

Nominal, corner cases, adversarial clutter.
Sensor dropouts, glare, motion blur, LiDAR rain/fog models.
Domain randomization (textures, lighting, mass, delay).

ObserverOps Hooks

Trace latching & hash chain; per-tick single-write asserts.
Commute matrix validation (block non-commuting pairs).
CWA harness on fusion sets; fallback path exercised.
Tick sync under skew; ρ/Δτ alert ladder.
Belt KPIs and Residual response (D1/D2/D3 modes).

Safety

Soft/hard E-stops; geofences; speed caps under low ρ.
Near-miss detectors & log enrichment.

16.9 Log Schema (robotics JSONL)

One line per event.

{
  "ts": "2025-09-22T11:28:03.142Z",
  "robot_id": "bot-07",
  "tau": 431025,
  "event": "TraceWrite",
  "channel": "lidar.scan",
  "outcome_ref": "blob:sha256:...",
  "hash": "sha256:...",
  "prev": "sha256:...",
  "meta": {"duration_ms":12}
}

{
  "ts":"2025-09-22T11:28:03.160Z",
  "robot_id":"bot-07",
  "tau":431025,
  "event":"CWA.Pass",
  "score":0.88,
  "pri":0.12,
  "panels":{"perm":{"n":64,"median_delta":0.05},"flip":{"n":32,"median_delta":0.04},
      "chunk":{"n":16,"median_delta":0.06}},
  "pool_id":"pool-9aa1"
}

{
  "ts":"2025-09-22T11:28:03.180Z",
  "robot_id":"bot-07",
  "tau":431025,
  "event":"Act.Ack",
  "action":"base.move",
  "args":{"vx":0.3,"wz":0.1},
  "status":"ok"
}

{
  "ts":"2025-09-22T11:28:03.200Z",
  "robot_id":"bot-fleet",
  "event":"Sync.Status",
  "rho":0.91,
  "delta_tau":2
}

{
  "ts":"2025-09-22T11:29:00.000Z",
  "event":"PBHL.Update",
  "belt_id":"pickpack-W39",
  "gap":0.32,"flux":0.26,"twist":0.05,"alpha":1.1,
  "residual":0.021
}

16.10 Example Config (YAML)

robot:
  ticks:
    control_hz: 50         # 20 ms
    mapping_hz: 10
    plan_hz: 2
  channels:
    - lidar.scan
    - cam.rgb
    - imu
    - encoders
    - base.move
    - arm.movej
    - gripper.close
  commute_matrix: cm:mobile-manip:v3
  fusion:
    projector: "bev-resnet18"
    cwa:
      thresholds: {pass: 0.82, warn: 0.75, pri_max: 0.50}
      panels: {perm: 64, flip: 32, chunk: 16}
      fallback: "ekf"
  safety:
    e_stop_topic: "/estop"
    speed_caps: {normal: 1.0, desync: 0.4}
    near_miss_thresh: 0.2

fleet:
  sync:
    cadence_ms: 20
    rho_min: 0.90
    delta_tau_max: 2
    anchors_ms: 500
  belts:
    id: "pickpack-W39"
    residual_bands: {green:[0,0.08], amber:[0.08,0.15], red:[0.15,1.0]}
  gates:
    on_residual_red: {restrict: "commuting_only", block_non_p0: true}

16.11 SLOs & Alerts

SLOs

Control loop p95 ≤ 20 ms; mapping p95 ≤ 100 ms.
Fusion pass path ≤ 5 ms; fallback filter ≤ 20 ms.
Sync status broadcast ≤ 10 ms; gate decision ≤ 10 ms.

Alerts

LatchingViolation (duplicate (τ,π) write).
CommuteConflict rate > X/min.
CWA.Red or Drift sustained ≥ N windows.
Sync.Red (ρ < 0.8 or Δτ > 5).
Safety.NearMiss > threshold.

16.12 Artifacts

Sim checklist (§16.8).
Log schema (§16.9).
Config templates (§16.10).
Pseudocode control loop (§16.7).
KPIs with bands (§16.6).

Next: Chapter 17 — Governance & Ops (BeltOps) — program belts, gates, and board-ready rollups for robotics deployments.

Chapter 17 — Governance & Ops (BeltOps)

Goal. Run initiatives as program belts with measurable closure—keep PBHL Residual in band, raise EEI/SI (effectiveness & sustainability), and use Policy Gates to throttle or block risky runs. Deliver repeatable SOPs, an incident playbook for Residual excursions, and a board-ready one-pager.

17.1 Pattern (how BeltOps governs)

Wrap an initiative as a Belt with a worldsheet: Gap, Flux, Twist, α, and Residual = |Gap − (Flux + α·Twist)|.
Instrument the pipeline so pool results, agreement reports, and certificate logs roll up into the belt KPIs.
Drive by gates: deterministic rules on CWA score/PRI, Residual, and sync/capacity metrics (ρ, Δτ, occupancy) produce allow | throttle | block actions (Ch.13).
Operate on cadences: daily belt standups, weekly checkpoint, monthly residual review, quarterly PBHL review.

17.2 Roles & RACI

Role	Responsibilities	R	A	C	I
Belt Owner (BO)	Objectives, α tuning, OKRs → KPIs	✓	✓
Gatekeeper (GK)	Gate config/versioning, overrides	✓	✓
ObserverOps SRE (OSRE)	Runtime reliability, slots/ticks	✓		✓
Data/Model Lead (DML)	Projectors, chunkers, drift	✓		✓
Security/GRC	Exports, evidence, audits			✓	✓
Product/Stakeholders	Requirements, impact				✓

17.3 KPIs & Thresholds (governance view)

Five-Line KPI: Gap, Flux, Twist, Coherence (agreement proxy), Residual.
EEI (Effectiveness/Execution Index) — weighted composite:
$\text{EEI} = 0.5\cdot Q + 0.3\cdot \text{ThroughputNorm} + 0.2\cdot \text{Agreement}$
SI (Sustainability Index) — cost & stability composite:
$\text{SI} = 0.5\cdot \text{CostNorm}^{-1} + 0.3\cdot \text{Variance}^{-1} + 0.2\cdot (1-\text{SlotPressure})$
Targets (typical):
- Residual: Green ≤ 0.08, Amber (0.08–0.15], Red > 0.15
- EEI/SI uplift: ≥ +10% QoQ
- Audit pass-rate: ≥ 98% (evidence completeness & signature checks)

17.4 Operating Cadences

Daily (15 min): Belt standup — review Residual band, cert pass-rate, any gate actions; approve α micro-tune if needed.
Weekly: KPI checkpoint — compare against OKRs; freeze gate thresholds unless incident.
Monthly: Residual review — look for step changes; align Twist annotations (org changes, releases).
Quarterly (PBHL Review) — formal worldsheet analysis, EEI/SI uplift, incidents & actions, α retune with rationale.

17.5 Residual Incident Playbook (SOP)

Trigger. Any of:

Residual Red for ≥ 2 consecutive windows
Residual Amber for ≥ 4 windows with negative trend
Coherence drop > 0.1 while Flux ramps

Runbook.

Triage (T+0–5 min)
- Auto-throttle via gates (cadence ↑, panel_scale ↓); restrict to commuting-safe schedules.
- Capture snapshot bundle: recent pool_ids, cert logs, gate decisions.
Contain (T+5–30 min)
- Roll back last Twist if recent (feature flag/rollout).
- Force fallback pooling in high-risk domains.
Diagnose (T+30–120 min)
- Compare Gap vs Flux deltas; inspect α drift.
- Check cert drift p-values; examine chunk panel deltas.
Correct (T+2–24 h)
- Fix projector/chunker; re-tune α; adjust gate bands.
- Backfill data & re-run KPIs if necessary.
Verify & Close
- Residual returns to Green for ≥ 3 windows.
- File post-incident with evidence ids and signed export.

Exit criteria. Residual ≤ 0.08 (3 windows) and EEI/SI not degraded > 5%.

17.6 Policy Gates (governance presets)

Bands & actions (summary)

CWA: score<0.75 → block additive; 0.75–0.82 + PRI≤0.5 → throttle; ≥0.82 & PRI≤0.2 → allow.
PBHL: Residual Amber → throttle; Red → block risky (non-P0).
Sync/Capacity: ρ<0.9 or Δτ>2 or occupancy>0.9 → throttle (narrow channels, widen cadence).

Override/Waiver process

Gatekeeper raises temporary waiver (≤ 24 h) with reason & risk sign-off from BO + Security.
All overrides are signed, versioned, and exported.

17.7 Audit & Compliance

Evidence: Trace ids, Cert Logs, Gate Decisions, Belt updates; all signed (HMAC or ed25519) with hash-addressed blobs.
Exports: rolling hourly & on-demand bundles (see Ch.13 §13.8).
Audit pass-rate = verified artifacts / expected artifacts for the audit scope.
Retention: hot 90–365 days; cold 7 years; PII redaction maps included.

17.8 Dashboards & Board Package

Ops dashboard

Five-Line KPI with thresholds; cert pass-rate; PRI histogram; gate states timeline; α changes log.

Board-ready one-pager (template)

ObserverOps Belt — Q# Executive Summary  (Program: <name>)

1) Headline
   - EEI: <current>  (QoQ: +<%>)
   - SI : <current>  (QoQ: +<%>)
   - Residual: <value>  [Band: Green/Amber/Red]  α=<value>
   - Audit pass-rate: <value>%  (evidence bundles: <n>)

2) Outcomes & Throughput
   - Quality (task metric): <value>  | Throughput: <value>/day
   - Coherence (agreement): <value>

3) Risks & Controls
   - CWA: pass-rate <value>%  | PRI p95 <value>
   - Sync/Capacity: ρ=<value>, Δτ=<value>, occupancy p95=<value>

4) Incidents & Actions
   - Residual incidents: <count>  | Mean time to green: <h>
   - Actions taken: <bullets> (rollbacks, α-tunes, gate changes)

5) Next Quarter
   - Objectives (Gap↓, Flux↑, Twist budget)
   - Gating plan (bands & thresholds)
   - Investments (indexing, redundancy, simulation)

17.9 SOPs (ready to adopt)

SOP-A: Quarterly PBHL Review

Inputs: last-quarter belt exports; α change log; incident reviews.
Agenda (60–90 min)
1. Worldsheet walk-through (Gap, Flux, Twist, Residual)
2. EEI/SI uplift; cost & variance trends
3. Certificate & drift summary; pass-rate, PRI tails
4. α tuning proposal → decision & commit
5. Policy gate bands for next quarter
6. Risks & mitigations; action register
Outputs: signed minutes; updated α; gate config version bump.

SOP-B: Gate Change Control

Change ticket with: rationale, before/after bands, expected effect, rollback.
Shadow mode 24–72 h (evaluate decisions without enforcing).
Promote if false-positive/negative rates within target; else revert.

SOP-C: Evidence Export

Schedule: hourly rolling + on-request.
Validate signatures; manifest completeness; cross-check counts vs telemetry.
Distribute to GRC vault; alert on lag > 2 min.

17.10 Governance KPIs & Targets

KPI	Target	Notes
EEI uplift (QoQ)	≥ +10%	mix-adjusted
SI uplift (QoQ)	≥ +10%	capacity normalized
Residual time-in-band (Green)	≥ 85%	per quarter
Audit pass-rate	≥ 98%	evidence completeness
Gate accuracy (decisions vs post-hoc labels)	≥ 95%	shadow-labeling
Override volume	≤ 2 / quarter	indicates clear policy

17.11 Config Snippets

Belt config (YAML)

belt:
  id: "support-v2025Q4"
  residual_bands: {green: [0,0.08], amber: [0.08,0.15], red: [0.15,1.0]}
  alpha: 1.1
  kpi_window_s: 60
  indices:
    eei_weights: {quality: 0.5, throughput: 0.3, agreement: 0.2}
    si_weights: {cost: 0.5, variance: 0.3, slots: 0.2}

Gate policy (YAML)

gates:
  thresholds:
    cwa_score: {pass: 0.82, warn: 0.75}
    pri_max: 0.50
    rho_min: 0.90
    delta_tau_max: 2
  actions:
    amber: {cadence_factor: 1.1, panel_scale: 0.7}
    red: {cadence_factor: 1.25, commuting_only: true, block_if_score_lt: 0.70}
  override:
    waiver_ttl_h: 24
    approvers: ["belt_owner","security"]
  audit:
    export_cron: "*/15 * * * *"
    sign: "ed25519"

17.12 Benchmarking & Acceptance

Acceptance gates for go-live
- Residual Green ≥ 90% over a 2-week pilot
- EEI/SI uplift ≥ +8% vs baseline
- Audit dry-run pass-rate ≥ 99%
- Gate shadow accuracy ≥ 95%, flap rate < 2%/day
What to do if you miss
- Raise redundancy (pointer channels), reduce chunk variability, retune α, tighten gate hysteresis.

17.13 Artifacts

SOPs: Residual Incident (17.5), PBHL Review (17.9-A), Gate Change (17.9-B), Evidence Export (17.9-C).
Board template: one-pager (17.8).
Configs: belt & gate YAML (17.11).
KPIs: governance targets & acceptance (17.10 & 17.12).

Next: Part IV — Metrics & Telemetry (definitions → estimators → thresholds).

Chapter 18 — Education & Labs (Hands-On ObserverOps)

Goal. Give students and teams a classroom-ready path to build observers: practice internal collapse (latching), agreement under commuting effects, Ô/τ scheduling, CWA certificates, and PBHL belts. Each lab ships with: a notebook spec, tiny datasets, instructor notes, and an auto-grader outline.

18.0 Lab Logistics (common to all)

Stack: Python 3.10+, NumPy, JAX or PyTorch, Matplotlib/Plotly.
Extras: qutip (Lab 1 alt), networkx, pandas.
Repro: SEED=4271 (fix RNG), float32 unless noted, record cert_seed for CWA panels.

Trace format (all labs):

{ "tick": τ, "channel": "…", "outcome_ref": "blob:sha256:…",
  "write": {"hash":"…","prev":"…","ts":"…"}, "flags":{"conflict":false}}

Grading I/O: Auto-grader reads a JSONL events stream and a metrics.json produced by each notebook.

18.1 Lab A — Qubit Toy (Commuting vs Non-Commuting)

Learning objectives

Implement latching: no retro-edits within a tick.
Observe order effects with non-commuting instruments (X, Z).
Demonstrate agreement when effects commute and records are shared (SBS-style).

Background (minimal)

Pauli projective measurements on a single qubit; Born rule.
Commutativity: [Z,Z] commute; [X,Z] do not.

Dataset

Synthetic: initial states $|0\rangle, |1\rangle, |+\rangle, |-\rangle$ sampled 1k times.

Tasks

Implement measure(ρ, op) returning outcome $y∈{−1,+1}$ and post-measurement state (collapse).
Build a tiny Observer Runtime with /measure, /trace/:id, tick τ, and latching.
Run two sequences on $|+\rangle$ :
- S1: Z→X at the same object.
- S2: X→Z at the same object.
  Compare distributions and agreement across replicas that share traces.
Repeat with commuting pair: Z on Q₁ then Z on Q₂ (different objects) or Z→Z.

Reference snippets

def proj(op):  # Pauli 'X' or 'Z'
    return (np.eye(2)+pauli[op])/2, (np.eye(2)-pauli[op])/2

def measure(rho, op, rng):
    Pp, Pm = proj(op)
    p = np.real(np.trace(Pp @ rho))
    y = +1 if rng.random() < p else -1
    P = Pp if y==+1 else Pm
    rho_post = P @ rho @ P / max(1e-9, np.trace(P @ rho))
    return y, rho_post

Expected results

$|+\rangle$ : Z→X vs X→Z produce different joint histograms (order sensitivity).
Z→Z (same object, same basis): second outcome repeats first with prob. ~1.0 (up to numerical noise).
Agreement score across observers rises toward 1.0 only on commuting setups with shared records.

Auto-grader checks (10 pts)

(3) Latching: no duplicate (τ,π) writes; hash chain valid.
(3) Order effect: KL divergence between Z→X and X→Z joint ≥ 0.3.
(2) Agreement(commuting) ≥ 0.95.
(2) Non-commuting counterexample: agreement ≤ 0.7.

Instructor notes

Time: 60–90 min.
Common pitfall: “measuring without updating state.” Emphasize internal collapse.

18.2 Lab B — Gridworld SMFT Agent (Ô as Scheduler, τ as Commit Rhythm)

Learning objectives

Implement Ô to choose orientation/channel by field score.
Advance on discrete ticks τ, log latching writes.
Track Collapse Entropy $S_c$ and Attractor Load (AL), and observe Δτ effects.

Environment

10×10 grid; agent must locate a goal emitting a scalar field with noise.
Channels Π = {lookN, lookS, lookE, lookW} returning noisy gradients.

Tasks

Define SMFT field $\Psi_m(x,\theta,\tau)$ as a score map; Ô picks next look*.
Implement cadence manager: base cadence 100 ms; allow injected jitter to study Δτ.
Metrics per window: $S_c$ (entropy of chosen channels), AL (peak/mean of $\Psi_m$ ), success steps.

Policy (example)

score(pi) = w1*expected_gain(pi) - w2*latency(pi) - w3*conflict(pi)
pi* = argmax score

Expected results

$S_c$ decreases as agent homes in; AL increases; success in < 40 steps on average.
Injected desync (Δτ≥3) increases steps to goal and mis-exec rate.

Auto-grader (10 pts)

(3) Ô selection correctness: greedy improvement in AL per 5 ticks.
(3) Latching & traces: zero retro-edits; per-tick single-write.
(2) Cadence: jitter within configured bounds; Δτ alarm triggers when forced.
(2) Success: mean steps ≤ threshold (e.g., 45).

Instructor notes

Time: 90 min.
Extension: add a non-commuting “disturb” channel that corrupts local field → show schedule reordering.

18.3 Lab C — RAG Pooling Battery (CWA)

Learning objectives

Treat chunking as instrument design and measure its effect on pooling safety.
Use CWA panels (perm/flip/chunk) to gate additive mean vs attention fallback.
Draw accuracy↔latency frontiers; track Phase-Risk Index & pass-rate.

Datasets

FAQ-Bag (orderless; 2k Q–A snippets).
Narrative-Chain (10 long tutorials with chapter order).

Tasks

Retrieve K passages via vector + keyword (commuting).
Project with “e5-large”; run panels: P=128,F=64,C=32 (strict) and P=64,F=32,C=16 (fast).
Pool: if score≥0.82 & PRI≤0.20 use mean; else attention fallback.
Evaluate nDCG@10 and p95 latency; compute pass-rate, PRI distribution.

CLI (reference)

observerops-bench rag --dataset FAQ-Bag Narrative-Chain \
  --chunkers sent-256@64 sent-512@128 \
  --panels 64,32,16 128,64,32 --theta_pass 0.82 --pri_max 0.50

Expected results

FAQ-Bag: pass-rate ≥ 85%, PRI ≈ 0.1; mean pooling dominates (fast).
Narrative-Chain: pass-rate ≤ 55%, PRI ≈ 0.35–0.5; attention yields higher accuracy with more latency.

Auto-grader (10 pts)

(3) Certificate correctness: panel deltas decrease with bag-like data.
(3) Routing: fallback triggered on Narrative-Chain ≥ 35% of queries.
(2) Accuracy: attention ≥ mean on Narrative-Chain by ≥ +2 nDCG points.
(2) Telemetry: emit CWA.Pass/Fail and record seeds.

Instructor notes

Time: 90–120 min incl. plots.
Tip: have students vary chunk overlap; watch chunk panel sensitivity.

18.4 Lab D — Belt Simulator (PBHL Macro Closure)

Learning objectives

Simulate a program belt with Gap/Flux/Twist and Residual control.
Use Policy Gates to throttle when Residual leaves band.
Run a PBHL review and justify α tuning.

Simulator

Discrete time; Gap $G_t$ decays with Flux $F_t$ and reacts to Twist $T_t$ :
$G_{t+1}=G_t - \beta F_t + \eta_t + \xi T_t$ .
Belt closure target: $G_t \approx F_t + \alpha T_t$ (Residual small).

Tasks

Implement controllers: Flux-gate (fast) and Twist-step (slow).
Inject a Twist spike (reorg) at t=200; observe Residual excursion.
Configure gates: Residual Amber → throttle; Red → block; measure time to green.
Produce a board-ready one-pager (auto-filled).

Expected results

With gates on, Residual returns to Green within N windows; without gates, it lingers (counterfactual).

Auto-grader (10 pts)

(3) Residual control: time-to-green ≤ threshold (e.g., 12 windows).
(3) Gate determinism: identical inputs → identical decisions (hash match).
(2) Export: signed bundle with KPIs & decisions.
(2) PBHL review: α proposal consistent with observed drift (simple rule check).

Instructor notes

Time: 60–90 min.
Pitfall: over-aggressive α changes create oscillations; discuss hysteresis.

18.5 Deliverables (what you ship)

Notebooks

LabA_QubitToy.ipynb — latching + agreement; commuting vs non-commuting.
LabB_Gridworld_SMFT.ipynb — Ô/τ loop, AL & S_c, Δτ stress.
LabC_RAG_CWA.ipynb — certificates, pooling, accuracy/latency plots.
LabD_BeltSimulator.ipynb — PBHL + gates + incident drill.

Datasets

/data/qubit_states.npz — vectors for $|0\rangle, |1\rangle, |+\rangle, |-\rangle$ .
/data/gridworld/*.npz — maps, noise profiles.
/data/faq_bag.jsonl, /data/narrative_chain.jsonl — small corpora (2–20MB).
/data/belt_sims/*.json — seed configs for Gap/Flux/Twist.

Instructor Notes (PDF/MD)

Timing, pitfall list, variants, and grading rubrics; answer-key plots.

Auto-Grader

grader.py with:
- Parse: events.jsonl, metrics.json.
- Checks: latching, agreement, certificate routing, Residual control.
- Report: grade.json (per-criterion scores) + concise feedback.

grade.json schema

{
  "student_id": "…",
  "lab": "LabC_RAG_CWA",
  "score": 9.0,
  "breakdown": {
    "certificate": 3,
    "routing": 3,
    "accuracy": 2,
    "telemetry": 1
  },
  "notes": "Chunk panel tuned well; attention fallback used appropriately."
}

18.6 Safety & Fairness Notes

No PII: corpora are synthetic; verify redaction and lineage tags.
Determinism: seed all RNG; store cert_seed and config versions in logs.
Compute fairness: cap tokens/steps/slots across students.

18.7 Extension Paths

Lab A: add depolarizing noise and demonstrate redundancy (SBS) improving agreement.
Lab B: multi-agent gridworld; measure ρ under shared anchors.
Lab C: add multilingual projector and compare pass-rates across languages.
Lab D: couple two belts; show cross-belt Residual dynamics.

Artifacts delivered: notebooks, tiny datasets, instructor notes, and an auto-grader schema, all aligned to Chapters 2–7 (invariants), 10–13 (APIs & gates).

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.

Tuesday, September 23, 2025