07-EFT.WP.Core.Threads v1.0 | Chapter 9 — Cross-Volume Binding with Arrival Time

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Chapter 9 — Cross-Volume Binding with Arrival Time

I. Scope and Objectives

• Align the concurrency volume’s temporal semantics with the path and arrival-time anchors defined in Core.DataSpec, and standardize the data shape, computational conventions, and validation flow for T_arr.
• Define postulates P79-, minimal equations S79-, and the operational flow Mx-9, and realize the cross-volume binding interfaces from I70-9: bind_to_parameters, bind_to_equations, enforce_arrival_time_convention.
• For batch / online / streaming scenarios, provide timeout, scheduling, and clock-calibration strategies using T_arr as the reference, ensuring consistency across hb, timeout, retry, and SLOs.

II. Terminology and Anchors (Cross-Volume Reuse)

1. Path and measure: gamma(ell), ell, d ell, L_gamma = ( ∫_gamma 1 d ell ).
2. Dual conventions for arrival time
   • Constant-factored: T_arr = ( 1 / c_ref ) * ( ∫_gamma n_eff d ell ).
   • General integrand: T_arr = ( ∫_gamma ( n_eff / c_ref ) d ell ).
3. Clocks and ordering: tau_mono (monotonic clock), ts (UTC), hb (happens-before).
4. Concurrency objects: G=(V,E), chan, eid, pid_thr, K_thr.
5. Metrology: unit(T_arr)="s", dim(T_arr)="T"; standard uncertainty u(x), expanded uncertainty U = k * u_c (from Core.Metrology).

III. Postulates P79 (Formulation, Timing, Calibration)

• P79-1 (Formulation parity): any arrival-time dataset and derivation must report both conventions and the difference
  delta_form = | ( 1 / c_ref ) * ( ∫_gamma n_eff d ell ) - ( ∫_gamma ( n_eff / c_ref ) d ell ) |.
• P79-2 (Path closure): if gamma is concatenated from {gamma_k}, then T_arr(gamma) = ∑_k T_arr(gamma_k), ell is non-decreasing, and segments are continuous.
• P79-3 (Clock roles): use tau_mono for performance statistics and timeouts; use ts for cross-node alignment and audit, and constrain inter-node offsets with T_arr.
• P79-4 (Causal preservation): if eid_a hb eid_b, calibrated timestamps satisfy ts_a_cal <= ts_b_cal + epsilon_hb.
• P79-5 (Dimensional closure): check_dim( T_arr - ( ∫ n_eff d ell ) / c_ref ) = 0 must pass; field-level unit(x)/dim(x) must match the equations.
• P79-6 (Non-intrusive quota): the resources for T_arr sampling and calibration must be budgeted into R_cpu/R_mem/R_io and quota; observability must not invert backpressure.
• P79-7 (Auditable provenance): Trace = [source -> method -> artifact] must be complete; provide hash_sha256(blob) and signature.

IV. Minimal Equations S79 (Estimation, Composition, Calibration)

• S79-1 (Dual definitions)
  T_arr = ( 1 / c_ref ) * ( ∫_gamma n_eff d ell ) = ( ∫_gamma ( n_eff / c_ref ) d ell ) (ideally equal).
• S79-2 (Segment composition)
  T_arr(gamma) = ∑_{k=1..m} ( ∫_{gamma_k} ( n_eff / c_ref ) d ell ), with gamma = ⊕_k gamma_k.
• S79-3 (Uncertainty synthesis)
  u^2(T_arr) approx ( ∂T_arr/∂c_ref )^2 u^2(c_ref) + ∑ ( ∂T_arr/∂n_eff_k )^2 u^2(n_eff_k ) + ∑ u^2_intk.
• S79-4 (Arrival vs. observed delta)
  Let cross-node observable Delta_ts = ts_recv - ts_emit, then the relative skew
  Delta_skew = Delta_ts - T_arr is used for ts calibration and causal repair.
• S79-5 (Timeout floor)
  timeout >= T_arr + J + P99(service), with J the link-jitter budget.
• S79-6 (Critical-path constraint)
  T_make(G) >= ∑( w on crit(G) ) + ∑( c on crit(G) ), where edge cost c(e) may be approximated by T_arr(e).

V. Data Shape and Schema (Aligned with Core.DataSpec)

• Primary key and indexes
  pk = [pid, ts_emit, ts_recv]; secondary indexes: idx_1=[sid_src,sid_dst], idx_2=[gid,eid].
• Key fields (illustrative)
  pid, sid_src, sid_dst, gid, eid, method ∈ {"active_probe","passive_trace"};
  ts_emit, ts_recv, tau_emit, tau_recv;
  gamma_spec (serialized path), ell_seq (non-decreasing), L_gamma, CRS;
  n_eff_model, c_ref, T_arr_calc_const, T_arr_calc_general, delta_form, u(T_arr);
  m ∈ {0,1}, q_score ∈ [0,1], Trace, signature.
• Units/dimensions
  unit(T_arr)="s", unit(ell)="m", unit(c_ref)="m s^-1", dim(T_arr)="T".
• Integrity constraints
  ts_emit <= ts_recv + epsilon_clock; ell_seq non-decreasing; abs(delta_form) <= tol_form.

VI. Interface Bindings (I70-9 Realization)

1. Bind to parameters and equations
   bind_to_parameters(ds, params=["c_ref","n_eff_model"]) -> bool: validate unit/dim and defaults.
   bind_to_equations(eqn_refs=["S79-1","S79-3"]) -> bool: map dataset fields to equation terms and record provenance.
2. Arrival-time enforcement — enforce_arrival_time_convention(trace):
   • Parse gamma_spec and ell_seq to build a canonical path.
   • Compute both T_arr_calc_const and T_arr_calc_general in parallel.
   • Compute delta_form and u(T_arr) and write to Trace.
   • Calibrate timestamps via Delta_skew = ( ts_recv - ts_emit ) - T_arr, producing ts_cal, then verify/repair hb.
   • Feed updated timeout, retry, and rate_limit policies back into the runtime.

VII. Policy Coupling (Timeout, Scheduling, Limiting)

• Timeout & retry
  Use S79-5 for the floor; combine with Chapter 5’s upper bound W_retry <= timeout * ( retries + 1 ) + J_total, then select a robust timeout within the feasible band.
• Scheduling & concurrency
  Approximate c(e) by T_arr(e) on edges; for crit(G) optimize K_thr and affinity to reduce ∑ c(e).
• Limiting & backpressure
  If P99(Delta_skew) rises abnormally, first reduce ingress rps, then raise channel cap or adjust bp policy (Chapter 7).

VIII. Calibration and Audit Flow Mx-9

• Collect: for each link record {ts_emit, ts_recv, tau_emit, tau_recv, gamma_spec, ell_seq, CRS}.
• Compute: produce both T_arr_calc_const/general and delta_form; evaluate u(T_arr).
• Calibrate: compute Delta_skew, derive calibrated ts_cal, and verify hb.
• Contract: execute assertions (Section IX); on failure, trigger degradation and limiting.
• Report: emit structured metrics and logs for T_arr, Delta_skew, delta_form, u(T_arr), and alert states.
• Archive: update manifest, Trace, signature, and freeze schema_version.

IX. Contracts and Assertion Templates (I70-8 Alignment)

• Formulation consistency
  {"type":"arrival_form_consistency","tol_form_ms":0.1} requires delta_form <= tol_form.
• Causality after calibration
  {"type":"hb_after_cal","epsilon_ms":1.0} enforces hb within epsilon_ms.
• Timeout floor
  {"type":"timeout_floor","expr":"timeout >= T_arr + J + P99_service"}.
• Data integrity
  {"type":"ell_monotonic","field":"ell_seq","strict":true}.

X. Representative Use Cases

• Online service chain
  Calibrate cross-AZ ts via T_arr; set timeout = T_arr + P99(service) + J; perform near-placement for crit(G) edges.
• Event stream processing
  Align producer/consumer watermarks with T_arr to preserve hb and cross-node window consistency.
• Batch windows
  Use max(T_arr) as the lateness bound for cross-site joins; set deadline = SLA - max(T_arr) - safety_margin.

XI. Failure Semantics and Compensation

• Missing measurements: records with m=0 must not be used for calibration; impute with local-window median(T_arr) and annotate approx independence.
• Model drift: if drift(n_eff_model) > tau, re-estimate n_eff and recompute T_arr.
• Dedup & idempotency: cross-domain retries must carry idemp_key; set Delta_t_dedup >= max(T_arr) to avoid double-charging/execution under reordering.

XII. Observability and Reporting (Chapter 8 Coupling)

• Metrics
  arrival.t_arr_ms_bucket{link}, arrival.delta_form_ms{link}, arrival.skew_ms{link}.
  Trigger: when Burn_rate rises with concurrent skew_ms spikes, enter rollback gates.
• Logs
  Record {"eid","gid","gamma_spec_hash","T_arr","delta_form","u_T_arr","Delta_skew"} with sensitive IDs masked via mask_fields.

XIII. Implementation Notes (Developer Aide-Mémoire)

• Single numeric path: compute all integrals with the same gamma(ell) and d ell to avoid spurious delta_form from discretization drift.
• Bucket alignment: use the same bucket family for t_arr_ms_bucket and latency histograms to keep Pxx comparable.
• Cost control: run T_arr computation in a low-frequency control loop; in hot paths rely on near-edge caches and last u(T_arr).

XIV. Reference Numbers and Cross-Volume Links

• Equations: S79-1 … S79-6; Postulates: P79-1 … P79-7; Flow: Mx-9; Interfaces: I70-9.
• Cross-volume citation: “see the companion whitepaper Energy Threads Chapter 3 S/P/M/I …”, and Core.DataSpec Chapter 10 for the T_arr dataset example and path-field norms.

XV. Deliverables and Acceptance

• T_arr dataset schema & manifest; dual-form implementations & validation scripts; delta_form and u(T_arr) reports.
• Calibration & causality verification pipeline (Mx-9) and an assert_thread_contract assertion pack.
• Runbook: threshold library (tol_form, epsilon_hb, J), rollback gates, and dashboard links for observability.