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| 1 | +# 0.11 Closure Status Audit |
| 2 | + |
| 3 | +**Date:** 2026-07-01 |
| 4 | +**Scope:** 0.11 Phase Transitions |
| 5 | +**Audit type:** status reconstruction and Tier-A closure planning |
| 6 | + |
| 7 | +## Current Answer |
| 8 | + |
| 9 | +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. |
| 10 | + |
| 11 | +It is not closed as Tier A right now. |
| 12 | + |
| 13 | +The current controlled status is: |
| 14 | + |
| 15 | +```text |
| 16 | +Readiness: Draft |
| 17 | +Tier: B |
| 18 | +Claim level: selected internal beta benchmark plus diagnostic mechanism lanes |
| 19 | +Current controller: structure-factor / estimator-policy formula extraction and acceptance |
| 20 | +``` |
| 21 | + |
| 22 | +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. |
| 23 | + |
| 24 | +## What Is Already Working |
| 25 | + |
| 26 | +| Lane | What works | Boundary | |
| 27 | +| :-- | :-- | :-- | |
| 28 | +| 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. | |
| 29 | +| Spatial-coupled operator | Core opt-in spatial modes exist and pass engine/operator availability gates. | Dynamics stayed mean-field-like in the scaling artifact. | |
| 30 | +| 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. | |
| 31 | +| 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. | |
| 32 | + |
| 33 | +## Why It Still Cannot Close |
| 34 | + |
| 35 | +The blocker is not that nothing works. The blocker is that the claim-bearing scaling path is not yet accepted. |
| 36 | + |
| 37 | +The latest controlling evidence says: |
| 38 | + |
| 39 | +- The primary beta artifact can support only a selected beta-exponent benchmark. |
| 40 | +- The dynamics/scaling artifacts still block universality claims. |
| 41 | +- The current structure-factor RMS proxy is diagnostic-only and rejected as a source-backed second-moment estimator replacement. |
| 42 | +- The source-family lowest-mode estimator implementation exists, but current conserved-order snapshots do not provide an accepted `S(0)` susceptibility observable. |
| 43 | +- Policy-source candidates and abstract formula boundaries are packaged, but full-text formula extraction, UET normalization mapping, and estimator acceptance remain blocked. |
| 44 | +- The latest source-archive localization gate only confirms temporary arXiv source archives and TeX member discovery; it does not extract or accept formulas. |
| 45 | + |
| 46 | +## Current Machine-Readable Gate |
| 47 | + |
| 48 | +The audit gate is saved at: |
| 49 | + |
| 50 | +```text |
| 51 | +Result/artifacts/0_11_closure_status_audit.json |
| 52 | +``` |
| 53 | + |
| 54 | +The gate keeps the topic at `WARN` with: |
| 55 | + |
| 56 | +```text |
| 57 | +tier_a_closure_gate = BLOCKED |
| 58 | +primary_beta_gate = PASS |
| 59 | +scaling_claim_gate = BLOCKED |
| 60 | +estimator_formula_gate = BLOCKED |
| 61 | +source_archive_policy_gate = WARN |
| 62 | +``` |
| 63 | + |
| 64 | +## Drift Found |
| 65 | + |
| 66 | +The main documentation drift is in the tail of `UPDATE_LOG.md`. |
| 67 | + |
| 68 | +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. |
| 69 | + |
| 70 | +The current controlling status remains the artifact/gate chain, especially Wave 38 and this closure audit. |
| 71 | + |
| 72 | +## Path To Tier A |
| 73 | + |
| 74 | +Tier A should require a narrow, explicit closure route: |
| 75 | + |
| 76 | +1. Extract exact formula fragments from the localized TeX/PDF math sources for fixed-composition, canonical finite-size, and Cahn-Hilliard structure-factor estimators. |
| 77 | +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. |
| 78 | +3. Map the accepted estimator into UET normalized lattice units with unit/proxy boundaries. |
| 79 | +4. Rerun finite-size/exponent gates using only the accepted estimator policy. |
| 80 | +5. Require at least beta, nu/correlation-length behavior, finite-size consistency, and baseline separation before any dynamics-based universality claim. |
| 81 | +6. Keep material critical-point calibration and RG closure as separate gates; do not smuggle them into a beta-only pass. |
| 82 | +7. Only after the artifact chain passes should README/topic index wording move toward Tier A, and that promotion still needs human review. |
| 83 | + |
| 84 | +## Safe Claim Boundary |
| 85 | + |
| 86 | +Allowed now: |
| 87 | + |
| 88 | +```text |
| 89 | +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. |
| 90 | +``` |
| 91 | + |
| 92 | +Not allowed now: |
| 93 | + |
| 94 | +```text |
| 95 | +UET has solved phase transitions. |
| 96 | +Topic 0.11 is verified as a full theory. |
| 97 | +The current engine proves a 3D Ising universality shift. |
| 98 | +The analytical beta projection alone closes the topic as Tier A. |
| 99 | +``` |
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