28-EFT.WP.Propagation.PathRedshift v1.0 | Chapter 14 — Runtime & Streaming (Caching / Fallback / Panels)

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Chapter 14 — Runtime & Streaming (Caching / Fallback / Panels)

One-sentence goal: Within an execution graph G=(V,E), build a streaming runtime for z_path / T_arr* centered on windowing, caching, fallback, and panels, ensuring dual-form (analytic/config vs. observed/realized) consistency and dimensional compliance, and publish manifest-grade evidence.

I. Scope & Objects

1. Inputs
   • References & models: RefCond (Ch. 10); component models z_kin / z_grav / z_med / z_cos and path/integrals (Chs. 3–8).
   • Observation streams: z_meas(t) (Ch. 9) with timebase offset / skew / J; window/stride W/H, lateness, and watermark policy.
   • Caching & resources: cache.policy = { ttl, size, key }, algorithm signature algo.hash, rate/backpressure policy.
2. Outputs
   • Online artifacts: windowed z_path^{config}(W) and z_meas(W), T_arr^{form1/form2}(W), harmonized T_arr*(W), and dual-form online deltas delta_form_rt;
   • Panels & alerts: SLI/SLO quantiles, coverage/freshness, fallback trail;
   • Manifest: manifest.redshift.rt.*.
3. Boundary
   This chapter focuses on execution & publication; component modeling and calibration are in Chs. 2–13.

II. Terms & Variables

• Windowing & lateness: win_k = [ t_k, t_k+W ), stride H, overlap O = 1 − H/W, lateness; watermark wm(t).
• Cache key: K_cache = hash( RefCond.hash, path.hash, algo.hash, band, win_id ); hit rate hit, staleness stale_ratio.
• Online dual forms: configured/analytic metric^{config}(W) vs measured/realized metric^{meas}(W);
  delta_form_rt(metric) = | metric^{config}(W) − metric^{meas}(W) |.
• Resources & backpressure: arrival rate λ_in, service rate μ, queue depth q, drop rate drop_rate; token bucket (r,B).
• Dimensions: unit(W,H,lateness,latency) = [T], unit(z) = 1, unit(hit,stale_ratio,drop_rate) = 1.

III. Postulates P65-14x

• P65-1401 (Dual forms): For each window win_k, compute and publish z_path^{config}(W) & z_meas(W), T_arr^{form1/form2}(W), and delta_form_rt.
• P65-1402 (Temporal semantics & sealing): Seal a window when wm(t_proc) ≥ t_k + W − lateness; handle late data via patch recompute or a shadow pipeline, and persist the strategy used.
• P65-1403 (Traceable caching): The cache key includes RefCond hashes and algorithm/band; any change invalidates cache and triggers recompute.
• P65-1404 (Dimensional compliance): All published windowed quantities pass check_dim( y − f(x) ); record log↔linear conversions in scale.note.
• P65-1405 (Fail-Closed fallback): On SLO/contract violations or dual-form assertion failures, degrade / bypass / rollback and persist strategy cards with evidence URIs.
• P65-1406 (Privacy minimization): Runtime manifests keep only hashes/pointers/statistics—no raw sensitive data.

IV. Minimal Equations S65-14x

1. Window fusion & online dual forms

• S65-1401: window-fused configured redshift
• z_path^{config}(W) = compose( z_kin(W), z_grav(W), z_med(W), z_cos(W) )
• delta_form_rt(z) = | z_path^{config}(W) − z_meas(W) |
• S65-1402: arrival-time online gap
• delta_form_rt(T) = | T_arr^{form1}(W) − T_arr^{form2}(W) |
• ΔT_obs(W) = | T_arr*(W) − t̂_cont(W) |

2. Caching & staleness

• S65-1403 (Che approximation): with class arrival rates λ_u, find T_c s.t. ∑_u (1 − e^{−λ_u T_c}) = cache.size;
  hit ≈ ( ∑ λ_u(1 − e^{−λ_u T_c}) ) / ( ∑ λ_u ); stale_ratio = expired_used / used.

3. Rate limiting / backpressure

• S65-1404: token bucket (r,B); stability E[λ_in] < E[μ]; queue evolution q_{k+1} = max(0, q_k + a_k − s_k).

4. SLO decomposition

• S65-1405 (Gates & panel keys):
  p95(delta_form_rt(z)) ≤ tol_z_rt, p95(delta_form_rt(T)) ≤ tol_Tarr, p95(ΔT_obs) ≤ tol_align;
  panel keys: p95(| z_meas − z_path^{config} |), p95(ΔT_obs), hit, stale_ratio, drop_rate, panel_freshness.

5. Fallback sequence

• S65-1406: mode := scale_down → damping → lower_order → bypass → rollback_version; each step emits actions[] with metric deltas.

V. Metrology Pipeline M65-14 (Ready → Execute → Check → Fallback → Persist)

1. Ready: fix W/H/lateness/watermark, cache.policy, SLO and contract thresholds; load RefCond hashes, models, and algo.hash.
2. Execute: slide windows by H; check cache K_cache; on miss, compute z_path^{config}(W), z_meas(W), T_arr^{form1/2}(W), T_arr*(W); record latency / cpu / mem / hit / stale_ratio / watermark_lag.
3. Check:
   • Compute online dual-form gaps delta_form_rt(z/T) and ΔT_obs;
   • Validate SLO/contracts: latency_p95 / drop_rate / hit / stale_ratio and ρ / queue depth;
   • Ensure dimensional/mask/band consistency with prior chapters.
4. Fallback: on any critical failure, execute the strategy of S65-1406; persist actions, blast radius, and recovery outcome.
5. Persist:

manifest.redshift.rt = {

RefCond.hash, path.hash, algo.hash,

W,H,lateness,watermark,

cache:{ ttl, size, policy, hit, stale_ratio },

metrics:{ delta_form_rt_z, delta_form_rt_T, ΔT_obs_p{50,95,99},

resid_z_p95, latency_p{50,95,99}, drop_rate, watermark_lag },

resources:{ cpu_pct, mem_pct, gpu_util },

actions[], contracts.*, signature

}

VI. Contracts & Assertions C65-14x (suggested thresholds)

• C65-1401 (Dual-form gaps): p95(delta_form_rt_z) ≤ tol_z_rt, p95(delta_form_rt_T) ≤ tol_Tarr, p95(ΔT_obs) ≤ tol_align.
• C65-1402 (Latency / jitter): latency_p95 ≤ SLO.latency_p95, jitter_p95 ≤ 0.2•W.
• C65-1403 (Cache efficacy): hit ≥ hit_min (typ. ≥ 0.8), stale_ratio ≤ tol_stale.
• C65-1404 (Backpressure stability): E[λ_in] < E[μ] and drop_rate ≤ drop_max.
• C65-1405 (Freshness / coverage): panel update ≤ Δt_panel_max, window coverage ≥ cov_min; age(RefCond) ≤ Δt_max.
• C65-1406 (Dimensional compliance): pass check_dim( y − f(x) ); document log↔linear conversions.

VII. Implementation Bindings I65-14* (interfaces, I/O, invariants)

• I65-141 plan_stream_windows(W, H, lateness, watermark) -> { schedule, status }
• I65-142 query_or_compute(cache, K_cache, fn) -> { value, hit, stale, status }
• I65-143 enforce_rate(token_bucket:{ r,B }, now) -> { permit, state, status }
• I65-144 measure_runtime(stream) -> { latency, drop_rate, ρ, cpu_pct, mem_pct, gpu_util, watermark_lag, status }
• I65-145 compare_dual_runtime(cfg_metrics, meas_metrics) -> { delta_form_rt, resid_z_p95, status }
• I65-146 apply_fallback(mode, ctx) -> { actions[], status }
• I65-147 snapshot_panel(metrics, resources, U) -> { panel.uri, snapshot.hash, status }
• I65-148 emit_runtime_manifest(results, policy) -> { uri, status }
  Invariants: two_forms_present = true; the window schedule is monotone; cache keys include RefCond.hash and algo.hash; all fallbacks are replayable and auditable.

VIII. Cross-References

IX. Quality & Risk Control

• SLI / SLO: p95(delta_form_rt_z), p95(delta_form_rt_T), p95(ΔT_obs), latency_p95, drop_rate, hit, stale_ratio, ρ_p95, watermark_lag_p95, panel_freshness.
• Fallback gradient: scale_down → damping → lower_order → bypass → rollback_version (coordinated with Ch. 12 strategy cards).
• Audit: window signatures & cache keys, SLO breaches and dual-form gap distributions, fallback actions & blast radius, and manifest.redshift.rt signature chain with replayability.

Summary

• This chapter establishes the streaming runtime baseline for z_path / T_arr*: windowing, cache reuse, rate limiting/backpressure, fallback, and panels.
• With P65-14x / S65-14x / M65-14 / C65-14x / I65-14* and manifest.redshift.rt, runtime becomes traceable, auditable, and rollback-ready, and remains consistent with the component/mapping/integral/observation/fusion conventions across prior chapters.