24-EFT.WP.Particle.TopologyAtlas v1.0 | Appendix B — Contract Library & Policy Cards (C90 Collection)

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Appendix B — Contract Library & Policy Cards (C90 Collection)

One-Sentence Goal
Provide an executable C90-* contract library and policy cards that guarantee consistency, stability, reproducibility, and auditability from data → complexes → atlas → retrieval → runtime.

I. Notes and Scope

• Objects covered: Field/θ/n, q(x), worldlines Γ, filtrations K(τ), diagrams D, landscapes λ_D, Atlas = { U_a, φ_a, ψ_a, T_ab }, invariants Q / Lk / Tw / Wr, runtime dashboards, and all manifest.topo.*.
• Contract strata: General (00x) → chapter-specific (04x–15x) → runtime (14x) → use-cases (15x).
• Action space: block / warn / degrade / recompute / postpone; all actions and evidence must be persisted.

II. Terms and Fields (common to contracts)

• unit(x), dim(x), check_dim; RefCond = { τ_policy, σ, p, window, norm }.
• non_decreasing(τ); d_B (bottleneck), W_p (Wasserstein), ||•||_p.
• Σ_a ψ_a ≡ 1; cycle error Δ_cyc; dual-form gap delta_form; streaming gap delta_form_rt.
• Minimal manifest keys: TraceID, data_hash, code.ver, deps, seed, RefCond, thresholds, decision, evidence, signature.

III. General Contracts C90-00x (cross-chapter)

• C90-001 (Units & dimensions) — Any field entering equations must declare unit(field) and dim(field) and pass check_dim( y − f(x) ).
  Violation: block with E_UNIT / E_DIM.
• C90-002 (RefCond completeness) — RefCond is required and must be written to manifests; missing → block.
• C90-003 (Reproducibility metadata) — { data_hash, code.ver, deps, seed } are mandatory; if any is missing, block.
• C90-004 (Parallel forms) — Wherever formA/B or stream/offline exists, record delta_form and assert delta_form ≤ tol_form.
• C90-005 (Evidence sufficiency) — Each topological object must carry ≥2 evidence types (geometric / persistence / local slice); otherwise warn → degrade.
• C90-006 (Input validity) — θ ∈ (−pi, pi] or is unwrapped; ||n|| = 1 ± ε_norm; out-of-range → degrade → project.

IV. Chapter-Specific Contracts

A. Ch. 4 — Field → Topological Density (C90-04x)

• C90-041 (Unwrap residual curl) — mean(| wrap(∇ × ∇θ) |) ≤ tol_curl.
• C90-042 (Orientation normalization) — mean(| ||n|| − 1 |) ≤ tol_norm; otherwise project and log correction energy E_proj.
• C90-043 (Density-integral integrity) — Q = ( ∫ q dA ) near-integer: | Q − round(Q) | ≤ tol_Qfrac.
• C90-044 (Jacobian stability) — quantile(| det(J) |, p_hi) ≤ J_max; mask exceptions and down-weight.

B. Chs. 3/5 — Defects & Worldlines (C90-05x / 06x)

• C90-051 (Minimum spacing) — defect min-distance d_min ≥ d_guard; violation → merge/suppress.
• C90-052 (Charge conservation) — with no boundary flux, ΔQ_window ≤ tol_Q.
• C90-061 (Trajectory continuity) — adjacent-frame pairing cost cost_track ≤ tol_track; excess triggers reconnection checks.
• C90-062 (Linking conservation) — off-event segments maintain Lk (|ΔLk| = 0); steps allowed only within E_reconn windows.

C. Chs. 7/8 — Complexes & Persistence (C90-07x / 08x)

• C90-071 (Monotone filtration) — enforce non_decreasing(τ); inversions → block.
• C90-072 (Sampling coverage) — κ_cover = |K(τ_max)| / |S| ≥ κ_min; otherwise degrade → coarsen_τ.
• C90-081 (Stability gate) — d_B(D, D') ≤ ε + α * scale_τ for known perturbation ε.
• C90-082 (Lifespan gate) — retain pairs with lifespan ≥ τ_pers_min; others → noise pool.

D. Chs. 9–11 — Atlas & Transitions (C90-09x–11x)

• C90-091 (Weight partition) — sup_x | Σ_a ψ_a(x) − 1 | ≤ 1e-6.
• C90-092 (Cycle error) — Δ_cyc ≤ tol_cyc; if exceeded, re-estimate T_ab or adjust cover.
• C90-093 (Distortion bound) — cond(∂φ) ≤ κ_max; else mark low-trust and restrict usage.
• C90-111 (Incremental coherence) — after merge(Atlas, patch), invariants change monotonically: | Inv_after − Inv_before | ≤ tol_patch (unless justified by events).

E. Ch. 10 — Invariant Metrology & Calibration (C90-10x)

• C90-101 (Integer rounding gate) — fractional parts of Q/Lk/Tw/Wr ≤ tol_int before rounding to publish.
• C90-102 (Bias regression residual) — || Inv_cal − Inv_ref ||_p ≤ tol_bias; else do not publish.
• C90-103 (Uncertainty coverage) — coverage ≥ γ_min (e.g., 95%); otherwise inflate U = k * u_c and warn.

F. Ch. 12 — Noise, Cleaning & Robustness (C90-12x)

• C90-121 (Type invariance) — d_B(D_before, D_after) ≤ tol_clean; topology must not flip under cleaning.
• C90-122 (Energy budget) — E_denoise ≤ E_budget; over-smoothing → weaker scheme.

G. Ch. 13 — Atlas Comparison & Retrieval (C90-13x)

• C90-131 (Index recall) — Recall@K ≥ R_min on calibration sets.
• C90-132 (Re-ranking consistency) — d_exact(Q, A_topK) ≤ tol_rank; otherwise enlarge candidates or change metric.
• C90-133 (Triangle inequality bound) — for metric embeddings, ensure d(x,z) ≤ d(x,y) + d(y,z) within error ε_tri.

H. Ch. 14 — Runtime (C90-14x)

• C90-141 (Watermark gate) — lag_wm_p95 ≤ tol_wm; else postpone closure.
• C90-142 (Stream/batch coherence) — delta_form_rt_p95 ≤ tol_rt; else recompute_subset.
• C90-143 (Cache gate) — H_cache ≥ H_min; else trigger manage_cache(policy).
• C90-144 (Backpressure gate) — β = r_in / r_proc ≤ β_max; otherwise follow degrade ladder.
• C90-145 (Replay coherence) — replay(trace) vs online differences ≤ tol_replay.

I. Ch. 15 — Use Cases (C90-15x)

• C90-151 (Phase singularity charge) — | Q_out − Q_in | ≤ 0.5.
• C90-152 (Skyrmion integral) — per-tile | Q − round(Q) | ≤ 0.2, global weighted ≤ 0.1.
• C90-153 (Reconnection evidence) — require ΔLk ≠ 0, local energy/curvature peaks, and continuity of objects.

V. Policy Cards (Playbooks)

1. SC90-01 High noise / unwrap failure
   • Trigger: C90-041 / C90-121 fail; var(wrap(Δθ)) > v_max.
   • Actions: quality-guided unwrapping → increase σ → local patching → if fail, reduce to H0 only.
   • Evidence: residual maps, parameters, region masks.
2. SC90-02 Sparse sampling / low coverage
   • Trigger: κ_cover < κ_min.
   • Actions: coarsen_τ, switch Alpha for Rips, augment samples or interpolate.
3. SC90-03 Atlas cycle error over-limit
   • Trigger: Δ_cyc > tol_cyc.
   • Actions: re-estimate T_ab (rigid → affine → nonlinear) → adjust overlap → local rebuild.
4. SC90-04 Stream/batch drift
   • Trigger: delta_form_rt > tol_rt.
   • Actions: recompute_subset(scope) → sync RefCond → lock versions and replay.
5. SC90-05 Reconnection ambiguity
   • Trigger: ΔLk step without energy evidence.
   • Actions: widen Δt window → raise track-pair thresholds → require third evidence (curvature/topo-density peak).
6. SC90-06 Backpressure / drops
   • Trigger: β > β_max or rising drop_late.
   • Actions: thin → coarsen_τ → postpone → drop_late; record impact areas.
7. SC90-07 Low retrieval recall
   • Trigger: Recall@K < R_min.
   • Actions: increase embedding dimension, change metric, raise K, enable rerank_with_exact.
8. SC90-08 Invariant bias anomaly
   • Trigger: || Inv_cal − Inv_ref ||_p > tol_bias.
   • Actions: refit regression, remove outliers, inflate U or withhold publication.
9. SC90-09 Excess orientation distortion
   • Trigger: cond(∂φ) > κ_max.
   • Actions: re-mesh locally or exclude tile from global comparisons.
10. SC90-10 Over-cleaning
    • Trigger: d_B(D_before, D_after) > tol_clean.
    • Actions: lower smoothing, switch to robust filters, enable topology-preserving projection.

VI. Contract Grouping & Priority

• Hard gates: C90-001/002/071/091/141 (units, RefCond, monotonicity, partition, watermark).
• Consistency gates: C90-004/092/142.
• Stability gates: C90-081/103/131.
• Performance gates: C90-143/144.
  Failures are handled by priority—lower tiers pause until higher-tier issues are resolved.

VII. Persistence & Audit (contracts.* structure)

• contracts[n] = { id, scope, inputs_hash, metrics, thresholds, status, decision, action, evidence.uri, ts, signature }.
• Every executed policy card produces playbook[n] = { sc_id, trigger, steps[], outcome }, and is written to manifest.topo.*.

VIII. Suggested Thresholds (domain/device-calibrated)

• tol_curl = 1e-3; tol_norm = 5e-3; tol_Qfrac = 0.1; J_max = 3 * p95(J).
• κ_min = 0.6; τ_pers_min = 0.02 * scale_τ; tol_cyc = 1e-3.
• tol_int = 0.15; tol_bias = 0.05 * scale_inv; γ_min = 0.95.
• tol_wm = 2 * τ_window; tol_rt = 0.03 * scale_τ; H_min = 0.8; β_max = 0.9; tol_replay = 1e-6.
  (All thresholds are to be validated on calibration sets and entered into RefCond.)

Summary
This appendix delivers the complete C90-* contract library and policy cards, closing the loop with I90-* and implementations across Chs. 7–15. With layered guardianship—hard → consistency → stability → performance—and auditable policy-card execution, every step from construction to serving is verifiable, traceable, and replayable.