06-EFT.WP.Core.DataSpec v1.0 | Chapter 10 — Cross-Volume Binding and Use Cases

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Chapter 10 — Cross-Volume Binding and Use Cases

I. Scope and Objectives

• Provide binding methods between a dataset D and the other volumes—Core.Parameters, Core.Equations, Core.Metrology, Core.Errors—so that an end-to-end, from-ingest-to-release data specification is enforceable and auditable.
• Center the chapter on T_arr as the canonical use case: standardize gamma(ell) path fields, the two arrival-time formulations, and manifest bindings to ensure dimensional closure and a complete provenance loop.
• Deliver a ready-to-run workflow Mx-6 spanning schema, contracts, computation, privacy, and versioned release.

II. Cross-Volume Anchors and Bindings

1. Anchor set: c_ref, gamma(ell), d ell, L_gamma = ( ∫_gamma 1 d ell ), n_eff(x,t), T_arr.
2. Binding map:
   • Core.Parameters: c_ref <- params[c_ref_ref]; n_eff may be sourced from params[n_eff_model_ref].
   • Core.Equations: T_arr is produced by the minimal equations defined in S610-*; path operators must explicitly state gamma(ell) and the measure d ell.
   • Core.Metrology: fields declare unit(field_i) and dim(field_i) and must pass check_dim(expr).
   • Core.Errors: exceptions raised during computation and validation are recorded via log_event(E.*,"ERROR", context) and included in the Trace.

III. Dataset Specification: DS.TARR.PathIntegral v1

1. Purpose: store arrival time T_arr computed via path integrals, together with both formulations and their discrepancy metric.
2. Primary key and indexes:
   pk = [pid, seg_id]; idx_k = [[ts], [sid, tid], [form]].
3. Core fields (suggested):
   • Identity & spatiotemporal: pid (path id), seg_id (segment id), ts (UTC), CRS, sid, tid.
   • Path characterization: ell_start, ell_end, L_seg = ( ell_end - ell_start ), ell_nondec ∈ {0,1}.
   • Medium properties: n_eff_mean, n_eff_std, n_eff_source ∈ {"meas","model"}.
   • Reference constant: c_ref_ref (pointer to parameter table), c_ref_value (resolved numeric), unit(c_ref_value)="m/s".
   • Arrival time (two forms):
     T_arr_const = ( 1 / c_ref_value ) * ( ∫_gamma n_eff d ell )。
     T_arr_integrand = ( ∫_gamma ( n_eff / c_ref_value ) d ell )。
   • Error & quality: delta_form = | T_arr_const - T_arr_integrand |, q_score ∈ [0,1], mask_seg ∈ {0,1}.
   • Provenance: hash_sha256(blob), signature, Trace = [source -> method -> artifact].
4. Units and dimensions:
   dim(T_arr_const) = dim(T_arr_integrand) = T；dim(n_eff) = 1；dim(c_ref) = L/T；dim( ( ∫_gamma • d ell ) ) = L。

IV. Path and Sampling Field Conventions

• Path parameterization: gamma(ell) with non-decreasing ell; each record must satisfy ell_start <= ell_end.
• Sampling window: record Delta_t and fs; if n_eff(x,t) is resampled, declare method ∈ {"mean","sum","median","first","last"}.
• Discrete approximations:
  T_arr_const approx ( 1 / c_ref_value ) * ( Σ_j n_eff_j * Δell_j )。
  T_arr_integrand approx ( Σ_j ( n_eff_j / c_ref_value ) * Δell_j )。
• Dimensional check: check_dim( T_arr_const - T_arr_integrand ) = T must pass.

V. Minimal Equations and Consistency (S610-*)

• S610-1 (Constant-factored form): T_arr = ( 1 / c_ref ) * ( ∫_gamma n_eff d ell )。
• S610-2 (General form): T_arr = ( ∫_gamma ( n_eff / c_ref ) d ell )。
• S610-3 (Discrepancy constraint): delta_form = | T_arr_const - T_arr_integrand | <= tol_Tarr。
• S610-4 (Segment composition): full-path T_arr_total = Σ_seg T_arr(seg_id)；L_gamma = Σ_seg L_seg。

VI. Contract and Validation Templates

• Primary key and path:
  unique(pk)；assert(ell_nondec == 1)；assert(ell_end >= ell_start)。
• Binding validity:
  exists(params where id = c_ref_ref)；abs(c_ref_value - params.value) <= tol_cref。
• Dimensional closure:
  check_dim( T_arr_const ) == T；check_dim( T_arr_integrand ) == T。
• Two-form consistency:
  delta_form <= tol_Tarr；segments failing the threshold must set mask_seg = 0 and degrade q_score.
• Quality gates:
  q_score >= q_min；hash_sha256 and signature present；Trace non-empty.
• Contract execution:
  assert_contract(ds, tests=[...]) -> dict；on failure, log_event(E.DS.CONTRACT,"ERROR", context).

VII. Cross-Volume Binding Workflow Mx-6 (End-to-End)

• Load schema: register_schema("DS.TARR.PathIntegral","1.0", ...) and complete unit/dim bindings.
• Bind parameters: bind_to_parameters(ds, params=["c_ref_ref","n_eff_model_ref"]).
• Bind equations: bind_to_equations(ds, eqn_refs=["S610-1","S610-2"]).
• Normalize arrival time: enforce_arrival_time_convention(ds) to produce T_arr_const and T_arr_integrand.
• Validate contracts: validate_dataset(schema, ds, strict=True) and assert_contract(ds, tests).
• Quality & drift: quality_metrics(ds)；monitor_drift(D_ref, ds, fields=["T_arr_const","T_arr_integrand"], method="KL")。
• Privacy & governance: apply anonymize or mask_fields as needed; update manifest.privacy.
• Publish & freeze: export_manifest(ds)；freeze_release(ds,"tarr_v1")。

VIII. Reference Implementation Notes (I60 Bindings)

1. enforce_arrival_time_convention(ds:any) -> None
   • Resolve c_ref_ref to c_ref_value;
   • Verify monotone ell and consistent CRS;
   • Compute both T_arr_* and delta_form;
   • Update mask_seg, q_score.
2. bind_to_equations(ds:any, eqn_refs:list[str]) -> bool
   • Check that S610-* are resolvable (symbols and units present);
   • Write manifest.equations = eqn_refs.
3. export_manifest(ds:any) -> dict
   Emit schema_version, fields, units/dims, privacy, governance, cryptography, equations, and checks.

IX. Use Case A — Ingest → Validate → Compute → Publish

1. Input: discrete samples of n_eff(x,t) along gamma(ell), and c_ref_ref.
2. Steps:
   • Aggregate by segment to obtain n_eff_mean and Δell.
   • Run enforce_arrival_time_convention to produce the two T_arr_*.
   • Trigger assert_contract and quality_metrics.
   • Segments with delta_form <= tol_Tarr are publishable; others set mask_seg=0.
   • freeze_release and sign.
3. Output: frozen DS.TARR.PathIntegral v1, with manifest containing equation references and the quality report.

X. Use Case B — Parameter Update Triggers Recompute and Version Upgrade

1. Trigger: c_ref changes in Core.Parameters (bump_version).
2. Flow:
   • diff_datasets(params_old, params_new, keys=["c_ref"])；
   • For affected pids, run enforce_arrival_time_convention to recompute;
   • If delta_form or key statistics undergo breaking changes, set schema_version = major+1;
   • Produce release notes and freeze_release a new tag.
3. Compatibility: offer an adapter view and manifest.migration from old to new.

XI. Use Case C — Privacy-Constrained Publication

1. Strategy:
   • Generalize paths: publish gamma(ell) via geohash(r>=6) or segment aggregation;
   • Aggregate T_arr: publish median/IQR/RMSE rather than per-point detail;
   • Differential privacy: apply (epsilon, delta) budgets to count-type derivatives and record them in the epsilon_ledger.
2. Verification: recompute q_score and drift, ensuring delta_form respects tol_Tarr.

XII. Failures and Recovery (Linked to Core.Errors)

1. Common failures:
   • Binding failure (missing c_ref_ref): log_event(E.DS.BIND.MISS,"ERROR", context) → fallback to a default c_ref for diagnostics, with explicit remediation notes.
   • Dimensional mismatch: write traceback_summary and block release; fix unit/dim mappings.
   • Two-form over-threshold: auto-downgrade mask_seg=0 and route to manual review.
2. Recovery strategies:
   • retry(policy={"max":3,"backoff":"exp"}) for transient I/O;
   • fallback(models=["interpolate","neighboring_path"], "weighted") for diagnostics only—not for official release.

XIII. Acceptance Metrics and Thresholds (Recommendations)

• delta_form: p95(delta_form) <= tol_Tarr (choose tol_Tarr per experiment design).
• Completeness: completeness(pid) >= 0.98; ell_nondec_violation = 0.
• Reproducibility: RMSE of recomputed T_arr under the same manifest ≤ tol_repro.
• Traceability: Trace coverage = 1.0; hash_sha256 verification rate = 1.0.

XIV. Best Practices for Path Fields and Computation

• Segment length: choose Δell to balance numerical error O(Δell^p) with observed noise; record p and the extrapolation regime.
• Reference constant: fix c_ref provenance (source, time, conditions) in the manifest; avoid mixing references within a batch.
• Endpoint alignment: when stitching gamma(ell) across devices, ensure consistent CRS and endpoint continuity.

XV. Interfaces to Neighboring Chapters

• With Chapter 2: field entries must include pii_level, unit/dim, and default-value strategy.
• With Chapter 4: both formulations and path contracts are expressed via assert_contract; reuse test templates.
• With Chapter 5: recommend parquet with row groups aligned to pid/seg_id for vectorized integration and indexing.
• With Chapter 8: monitor drift and q_score before and after release.
• With Chapter 9: publish path and spatiotemporal fields per classification; apply anonymize and mask_fields where needed.

XVI. Summary

• Workflow Mx-6 unifies DS.TARR.PathIntegral with parameters, equations, metrology, privacy & security, and error handling.
• Dual computation of T_arr with a strict delta_form constraint is the control variable of this cross-volume binding; the manifest carries the entire evidence chain and configuration.
• The pattern generalizes to any path-integral dataset (swap the integrand and reference quantity) while preserving the same reproducibility and governance bar.