Add 0.11 closure status audit gate

docs/topics/0.11_Phase_Transitions/CLOSURE_STATUS_AUDIT.md

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+# 0.11 Closure Status Audit
+
+**Date:** 2026-07-01
+**Scope:** 0.11 Phase Transitions
+**Audit type:** status reconstruction and Tier-A closure planning
+
+## Current Answer
+
+Topic 0.11 is important because it is one of the first places where UET tries to move from conceptual equation behavior into a physics benchmark: phase-transition critical behavior.
+
+It is not closed as Tier A right now.
+
+The current controlled status is:
+
+```text
+Readiness: Draft
+Tier: B
+Claim level: selected internal beta benchmark plus diagnostic mechanism lanes
+Current controller: structure-factor / estimator-policy formula extraction and acceptance
+```
+
+This means the topic has useful internal evidence, but it cannot yet claim a full phase-transition theory, RG closure, universal critical behavior, or accepted dynamics-based 3D Ising scaling.
+
+## What Is Already Working
+
+| Lane | What works | Boundary |
+| :-- | :-- | :-- |
+| Primary beta benchmark | `Research_Critical_Exponents.py` writes a `PASS` artifact for the selected beta comparison. | This is a selected benchmark, not a full exponent-set or RG result. |
+| Spatial-coupled operator | Core opt-in spatial modes exist and pass engine/operator availability gates. | Dynamics stayed mean-field-like in the scaling artifact. |
+| Conserved-order spectral core | `conserved_order_spectral_v1` repaired the core implementation bridge to the topic Cahn-Hilliard engine. | Later finite-size/exponent gates remained blocked. |
+| Structure-factor work | The blocker was narrowed from vague estimator uncertainty to specific formula/source-policy gates. | The accepted estimator formula and normalization mapping are still missing. |
+
+## Why It Still Cannot Close
+
+The blocker is not that nothing works. The blocker is that the claim-bearing scaling path is not yet accepted.
+
+The latest controlling evidence says:
+
+- The primary beta artifact can support only a selected beta-exponent benchmark.
+- The dynamics/scaling artifacts still block universality claims.
+- The current structure-factor RMS proxy is diagnostic-only and rejected as a source-backed second-moment estimator replacement.
+- The source-family lowest-mode estimator implementation exists, but current conserved-order snapshots do not provide an accepted `S(0)` susceptibility observable.
+- Policy-source candidates and abstract formula boundaries are packaged, but full-text formula extraction, UET normalization mapping, and estimator acceptance remain blocked.
+- The latest source-archive localization gate only confirms temporary arXiv source archives and TeX member discovery; it does not extract or accept formulas.
+
+## Current Machine-Readable Gate
+
+The audit gate is saved at:
+
+```text
+Result/artifacts/0_11_closure_status_audit.json
+```
+
+The gate keeps the topic at `WARN` with:
+
+```text
+tier_a_closure_gate = BLOCKED
+primary_beta_gate = PASS
+scaling_claim_gate = BLOCKED
+estimator_formula_gate = BLOCKED
+source_archive_policy_gate = WARN
+```
+
+## Drift Found
+
+The main documentation drift is in the tail of `UPDATE_LOG.md`.
+
+Wave 39-41 wording says the topic is formally verified at the analytical projection level. That wording is not supported by the current topic index, verification spec, formula audit, or latest estimator/source gates. Treat those entries as historical notes that require claim-boundary correction, not as the current topic status.
+
+The current controlling status remains the artifact/gate chain, especially Wave 38 and this closure audit.
+
+## Path To Tier A
+
+Tier A should require a narrow, explicit closure route:
+
+1. Extract exact formula fragments from the localized TeX/PDF math sources for fixed-composition, canonical finite-size, and Cahn-Hilliard structure-factor estimators.
+2. Decide an accepted estimator policy for conserved-order phase-transition fields: conserved susceptibility, finite-k/canonical estimator, or explicit rejection with a dynamics/window repair route.
+3. Map the accepted estimator into UET normalized lattice units with unit/proxy boundaries.
+4. Rerun finite-size/exponent gates using only the accepted estimator policy.
+5. Require at least beta, nu/correlation-length behavior, finite-size consistency, and baseline separation before any dynamics-based universality claim.
+6. Keep material critical-point calibration and RG closure as separate gates; do not smuggle them into a beta-only pass.
+7. Only after the artifact chain passes should README/topic index wording move toward Tier A, and that promotion still needs human review.
+
+## Safe Claim Boundary
+
+Allowed now:
+
+```text
+Topic 0.11 has a passing internal selected-beta benchmark and several diagnostic operator lanes. The strongest open blocker is accepted structure-factor/correlation-length estimator policy for conserved-order scaling. The topic is promising but not closed.
+```
+
+Not allowed now:
+
+```text
+UET has solved phase transitions.
+Topic 0.11 is verified as a full theory.
+The current engine proves a 3D Ising universality shift.
+The analytical beta projection alone closes the topic as Tier A.
+```

docs/topics/0.11_Phase_Transitions/Result/artifacts/0_11_closure_status_audit.json

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+{
+  "schema_version": "0.1",
+  "topic": "0.11_Phase_Transitions",
+  "audit_date": "2026-07-01",
+  "audit_type": "closure_status_reconstruction",
+  "status": "WARN",
+  "current_readiness": "Draft",
+  "current_tier": "B",
+  "claim_class": "selected_internal_beta_benchmark_plus_diagnostic_mechanism_lanes",
+  "controlling_blocker": "accepted_structure_factor_estimator_policy_missing",
+  "source_of_truth_order": [
+    "docs/topics/README.md",
+    "docs/topics/0.11_Phase_Transitions/VERIFICATION_SPEC.md",
+    "docs/topics/0.11_Phase_Transitions/Result/artifacts/*.json",
+    "docs/topics/0.11_Phase_Transitions/FORMULA_AUDIT.md",
+    "docs/topics/0.11_Phase_Transitions/UPDATE_LOG.md"
+  ],
+  "gates": {
+    "primary_beta_gate": {
+      "status": "PASS",
+      "evidence": "Result/artifacts/0_11_phase_transitions_verification.json",
+      "boundary": "selected beta benchmark only"
+    },
+    "scaling_claim_gate": {
+      "status": "BLOCKED",
+      "evidence": [
+        "Result/artifacts/0_11_spatial_coupling_scaling.json",
+        "Result/artifacts/0_11_conserved_order_spectral_scaling.json"
+      ],
+      "boundary": "dynamics artifacts do not yet support universality-shift or RG-closure claims"
+    },
+    "estimator_formula_gate": {
+      "status": "BLOCKED",
+      "evidence": [
+        "Result/artifacts/0_11_structure_factor_policy_formula_boundary_gate.json",
+        "Result/artifacts/0_11_structure_factor_full_text_formula_readiness_gate.json",
+        "Result/artifacts/0_11_structure_factor_source_archive_localization_gate.json"
+      ],
+      "boundary": "formula extraction, UET normalization mapping, and accepted estimator policy remain open"
+    },
+    "source_archive_policy_gate": {
+      "status": "WARN",
+      "evidence": "Result/artifacts/0_11_structure_factor_source_archive_localization_gate.json",
+      "boundary": "temporary arXiv source archives are localized but raw sources are not repo-archived"
+    },
+    "tier_a_closure_gate": {
+      "status": "BLOCKED",
+      "reason": "Tier A requires an accepted estimator policy plus finite-size/exponent rerun with correlation-length and baseline-separation gates passing"
+    }
+  },
+  "drift_notes": [
+    {
+      "location": "UPDATE_LOG.md Wave 39-41 tail entries",
+      "issue": "wording says formally VERIFIED at analytical projection level",
+      "resolution": "treat as historical drift; this audit and current artifacts control status"
+    }
+  ],
+  "tier_a_required_next_steps": [
+    "extract exact TeX/PDF formula fragments from localized source archives",
+    "accept or reject conserved-order estimator policy with source-backed formula boundaries",
+    "map accepted estimator into UET normalized lattice units",
+    "rerun finite-size/exponent gates using the accepted estimator policy",
+    "require beta, nu/correlation-length behavior, finite-size consistency, and baseline separation before universality wording",
+    "keep material calibration and RG closure as separate gates"
+  ],
+  "allowed_claim_now": "0.11 has a passing internal selected-beta benchmark and diagnostic operator/mechanism lanes; the strongest open blocker is accepted structure-factor/correlation-length estimator policy for conserved-order scaling.",
+  "blocked_claims": [
+    "UET solved phase transitions",
+    "0.11 is verified as a full phase-transition theory",
+    "current engine proves a 3D Ising universality shift",
+    "analytical beta projection alone closes Tier A"
+  ]
+}