23-EFT.WP.Metrology.PathCorrection v1.0 | Chapter 14 — Runtime and Streaming Corrections (Caching / Fallback / Dashboards)

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Chapter 14 — Runtime and Streaming Corrections (Caching / Fallback / Dashboards)

One-Sentence Goal
On an execution graph G = (V, E), produce T_corr and manifest.path.* in a streaming, low-latency, and auditable manner, using caching / fallback / alerting and dashboard SLIs to uphold business SLOs.

I. Scope and Objects

1. Inputs
   • Execution graph and operators: V = { geom, env, iono, tropo, fiber, ray, integ, inst, u, compose, emit }; edges E encode data dependencies.
   • Streaming data: obs(t), met_3D(t,x), TEC(t,lat,lon), temp_profile(t), Sparams(f), cfg(ver).
   • Runtime policy: policy = { cache, window, fallback, alarm, SLO }; time base tau_mono and publication clock ts.
2. Outputs
   • Streaming path-correction results T_corr(t) and components T_parts(t).
   • manifest.path and runtime-derived keys manifest.path.rt.
   • Dashboard metrics and audit logs.
3. Constraints & Boundaries
   Parallel dual-form evaluation with traceable RefCond; extrapolation is forbidden; every node obeys its invariants (see prior chapters and unified notation).

II. Terms and Variables

• L_rt: end-to-end streaming latency, unit = "s".
• W_t: time window (sliding/tumbling), unit = "s"; W_x: spatial window, unit = "m".
• TTL_k: time-to-live for cache layer k, unit = "s".
• age(src): data freshness, unit = "s".
• hit_k, miss_k: hit/miss for cache layer k.
• SLI.*: runtime indicators (see IX).
• delta_form: dual-form difference (published with the stream); tol_Tarr: threshold.
• wm: event-time watermark; lateness: late-data allowance, unit = "s".
• trace_id: traceable identifier for a single path solution.

III. Axioms P814-*

• P814-1 (Event-Time First) — Streaming computation aligns by event time; wm and lateness are explicit; processing time is for SLO monitoring only.
• P814-2 (Online Dual Forms) — Any published T_corr must include parallel T_form1 / T_form2 and delta_form on the same grid/window.
• P814-3 (Tiered Caching) — Use layered caches: L1 (in-memory objects), L2 (local durable), L3 (shared/remote); keys are hashes of physical equivalence classes.
• P814-4 (Justified Fallback) — Any fallback must declare level, trigger, and impact scope, and inflate uncertainty and guardbands.
• P814-5 (Dashboards Are Contracts) — Dashboard SLIs externalize runtime contracts; threshold breaches raise alarms and switch policies.
• P814-6 (Idempotent & Replayable) — Each node is idempotent per trace_id; inputs are replayable for exact reproduction.
• P814-7 (Minimum Viable Output) — When partially missing, publish the minimum viable product with tags.degraded and a recomputation plan.

IV. Minimal Equations S814-*

• S814-1 (End-to-End Latency Budget)
  L_rt = L_queue + ∑_{v∈V} L_v + L_io, with target L_rt ≤ SLO_latency.
• S814-2 (Cache Keys and Equivalence Classes)
  key = hash( gamma.hash, bucket(ts; W_t), bucket(x; W_x), f, RefCond.ver, model_tag );
  hit rule: same_hash ∧ within_TTL.
• S814-3 (Freshness and Coverage)
  age(src) = ts_now - ts_src; coverage cov(gamma) = ( |{ell: data_valid}| / |{ell: all}| );
  contract: age(src) ≤ Delta_t, cov(gamma) ≥ cov_min (see Chapter 11).
• S814-4 (Window Aggregation)
  For x(t) over W_t: ⟨x⟩_{W_t} = ( ∫_{t-W_t}^{t} x(τ) dτ ) / W_t;
  publish x_pub = ⟨x⟩_{W_t} or x(t*) (window end in event time).
• S814-5 (Online Dual-Form Monitoring)
  delta_form = | ( 1 / c_ref ) * ( ∫ n_eff d ell ) - ( ∫ ( n_eff / c_ref ) d ell ) |;
  online gate: delta_form ≤ tol_Tarr, otherwise trigger re-integration or degrade.
• S814-6 (Fallback Inflation Factor)
  At fallback level r ∈ {1…R}, inflate uncertainty: U_r = U_base * ( 1 + α_r ), with α_r from policy.
• S814-7 (Expedited Publication Rules)
  If miss_L1 ∧ hit_L2: allow synchronous backfill; if miss_L1 ∧ miss_L2 ∧ hit_L3: async backfill and delay publish to deadline ≤ SLO_latency.
• S814-8 (Alarm Thresholds)
  Let p = P( delta_form > tol_Tarr | W_t ); when p ≥ p_thr for N_w consecutive windows, raise alarm.form.
  Similarly, age(src) > Delta_t raises alarm.freshness.

V. Metrological Workflow M80-14

• Ready — Build G and node invariants; register policy, SLO, window { W_t, W_x }, TTL { TTL_L1, TTL_L2, TTL_L3 }, and wm/lateness.
• Keys & Caches — Implement S814-2 keys; assign cache layers and TTLs for env/iono/tropo/fiber/ray/integ/u/inst.
• Ingest & Align — Event-time alignment and late-data handling for streams; apply Chapter 11 windowing/interpolation policies.
• Streaming Solve — Execute along G: geom → env/iono/tropo/fiber → ray → integ (dual forms) → inst → u (GUM/MC) → compose.
• Fallback Decision — On misses or contract failures, follow fallback_matrix from live → model → climatology → RefCond0, applying S814-6 inflation to U and guardbands.
• Publish & Persist — Emit manifest.path and manifest.path.rt (including cache hit spectra and fallback tags) at ts.
• Dashboards & Alarms — Compute SLI/SLI_p in real time; on breach, raise alarms and switch policies (e.g., shrink W_t / extend TTL / prioritize warmups).
• Audit & Replay — Persist trace_id, inputs.hash, seeds, wm/lateness; enable full trace-level replay.
• Self-Heal & Warmup — Background warming of hot keys; reallocate resources and grow caches based on dashboard hotspots.

VI. Contracts and Assertions (C80-141x)

• C80-1411 Freshness — max(age(src)) ≤ Delta_t; violations degrade with degraded.freshness.
• C80-1412 Coverage — cov(gamma) ≥ cov_min; otherwise fallback or delay publication.
• C80-1413 Dual Forms — delta_form ≤ tol_Tarr; if over limit for N_w consecutive windows, force re-integration and alarm.
• C80-1414 Latency — L_rt ≤ SLO_latency, p99(L_rt) ≤ SLO_latency_p99; sustained breach enters degraded mode (cache-first / relaxed windows).
• C80-1415 Idempotency — Repeated inputs with the same trace_id yield identical outputs (hash check); else tag idempotency_breach.
• C80-1416 Traceability — manifest.path.rt must include { cache_hits, ttl, wm, lateness, fallback_level }; missing → trace_missing and refuse publication.
• C80-1417 Numerical Floor — u_num ≥ u_floor (see Chapter 13); below floor, raise precision or adjust windows.
• C80-1418 Panel Consistency — Dashboard metrics match persisted statistics within ≤ 1%.

VII. Implementation Bindings I80-*

• I80-141 build_exec_graph(spec) -> G (nodes/edges, resources, and invariant init).
• I80-142 cache_getset(layer, key, compute_fn, TTL) -> value, meta (multi-tier cache wrapper).
• I80-143 decide_fallback(context) -> level, alpha_r, tags (driven by contracts and live dashboard state).
• I80-144 stream_align(inputs, wm, lateness) -> aligned_streams (event-time alignment and late-data handling).
• I80-145 run_pipeline(G, streams, policy) -> { T_corr, T_parts, delta_form, u, tags }.
• I80-146 publish_panel(metrics) -> ack (dashboard + alert bus).
• I80-147 emit_path_manifest(results, policy) -> manifest.path (reuse existing).
• I80-148 emit_runtime_manifest(rt_meta, policy) -> manifest.path.rt.
• Invariants: non_decreasing(ell); delta_form ≤ tol_Tarr; check_dim(T_arr) = "[T]"; RefCond and method are traceable.

VIII. Cross-References

• Path integration and dual forms: Chapter 10.
• Environmental fusion and windowing/interpolation: Chapter 11.
• Instruments and processing chain: Chapter 12.
• Uncertainty / guardband and degradation inflation: Chapter 13.
• Time base, timestamp semantics, and sync: EFT.WP.Metrology.TimeBase v1.0, …Sync v1.0.
• Cleaning and tagging: EFT.WP.Methods.Cleaning v1.0.

IX. Quality and Risk Control

1. Suggested SLO / SLI Targets
   • SLI_latency = p95(L_rt): free-space links ≤ 1.0 s, indoor fiber ≤ 0.2 s.
   • SLI_freshness = p95( max(age(src)) ) ≤ Delta_t.
   • SLI_delta_form = p99(delta_form) ≤ tol_Tarr.
   • SLI_cache_hit_L1 ≥ 0.8, SLI_cache_hit_total ≥ 0.95.
   • SLI_u = p95(U) ≤ U_target (see Chapter 13).
2. Risk Scenarios & Actions
   • Source outage: raise fallback_level, shrink W_t, enlarge TTL, tag degraded.source.
   • Integration instability: densify adaptive grids, add step-size guards, or fall back to empirical models.
   • Jitter spikes: weighted smoothing, delayed publish, trigger re-calibration (see Chapter 12).
3. Audit & Rollback
   Log all alarm/degrade/fallback events; provide trace-level replay scripts and a “shadow publish” channel.

Summary
This chapter defines a streaming mechanism for path corrections on G = (V, E): event-time alignment, tiered caching, a fallback matrix, online dual-form monitoring, and dashboard alerting.
Minimal key set:
manifest.path.rt = { trace_id, ts, L_rt, cache:{ L1,L2,L3,hits,TTL }, wm, lateness, window:{ W_t,W_x }, fallback:{ level,alpha_r,tags }, contracts:{ freshness,cov,delta_form }, SLI:{ latency,hit,freshness }, seeds, inputs.hash }.
Together with Chapters 10–13, the system maintains low-latency, traceable, and compliant publication of T_corr under resource and data perturbations.