# NS_GSM v0.4 — Proof-Authority Review Batch Closure Report

**Runtime:** CSM Reference Runtime 0.4.0  
**Date:** 2026-08-28  
**Scope:** observed-relative  
**Status:** curated source-internal authority audit / bounded native asset promotion

## 1. Purpose

v0.4 is the first phase that moves selected deferred theorem/no-go candidates through an explicit source-hash, statement, scope, assumptions, nonclaim, and certificate-authority audit.

It does **not** independently prove the audited mathematics. Source-internal results are capped at `AUDIT` authority unless an independent verifier result is explicitly `VALID`.

## 2. Frozen result

- content corpus: 61 source-backed artifacts inherited from v0.3
- candidates: 1,726
- structural reviews: 1,726
- structural promotions: 727
- curated authority audits: 20
- authority promotions: 13
  - `PROOF_ASSET`: 12
  - `OBSTRUCTION`: 1
- deferred authority audits: 3
- canonical ledger events: 5,127
- root formal NS: `OPEN`
- C1: `OPEN`
- C2: `OPEN`
- scope: `observed-relative`
- cross-series automatic quotient: none introduced
- state/replay SHA-256: `7b04d50d8fcf7c13c6d9f381bf1562fba368ea3ffe2dad9bb094c17fdee030b3`
- authority conformance: 13/13 PASS

## 3. Core curated batch

### ETN-X

- Proposition 8.1 Critical UV Necessity: existing bounded source-internal result re-audited; no new duplicate proof asset.
- C1 Chain Necessity: `DEFER`; remains an open proof obligation.
- C2 Finite Obstruction: `DEFER`; remains an open proof obligation.

### DCRP103

Five bounded local algebraic results were promoted as `CLOSED_POSITIVE / AUDIT` proof assets:

1. D103.1 Eigen-lock commutator equation
2. D103.2 Shear resonance condition
3. D103.3 Single-shear theorem
4. D103.4 Five-Ray Spectrum
5. D103.5 Riesz-loaded coaxial response

These assets do not imply global/nonlocal self-consistency or Navier-Stokes regularity.

### DCRP104

The two already-native no-go claims were re-audited without duplicate promotion:

- frozen coaxial L2 no-go;
- fixed-positive-viscosity globally frozen L2 eigen-lock no-go.

The latter remains explicitly non-uniform in the vanishing-viscosity limit; v0.4 does not transfer it to epsilon -> 0.

### DCRP105

Four bounded source-internal results were promoted as `CLOSED_POSITIVE / AUDIT` proof assets:

1. D105.1 Simple-shear TR angular scalar
2. D105.2 Local Kelvin/TR compatibility witness
3. D105.3 Exact viscosity residual on the inviscid kernel
4. D105.4 Fixed-band viscosity matching

The existing D105 nonuniformity claim was re-audited. The viscosity-matched survivor and first-order solvability/spectral-drift frontier remain `OPEN`.

## 4. Selected RFP batch

Promoted at `AUDIT` authority:

- RFP-05 Theorem 32.1 — conditional Infinite Path Extraction theorem;
- RFP-10 Theorem 42.1 — Current Finite-Obstruction Incompleteness theorem;
- RFP-12 Theorem 12.1 — Exact Spectral-Variance Identity;
- RFP-12 Theorem 19.1 — Frequency-Norm Synchronization No-Go, represented as an `OPEN / AUDIT` obstruction asset.

Deferred:

- RFP-10 Theorem 39.1 — Finite Coercive-Cover Closure Theorem, because its H1 formation-completeness and H3 finite-coercive-cover premises are not established as root closure facts.

## 5. Authority firewall

v0.4 enforces:

```text
source theorem label
!= source-internal proof asset
!= independently verified proof authority
!= parent theorem closure
```

and:

```text
source NO-GO
!= obstruction asset
!= route BLOCKED
!= parent CLOSED_NEGATIVE
```

All v0.4-created assets are capped at `AUDIT` authority.

## 6. Replay and idempotency

Both curated authority batches are event-sourced and checkpointed. Re-applying either batch produces `IDEMPOTENT_NOOP`. Replaying the complete 5,127-event ledger reconstructs the exact frozen state hash.

## 7. What remains open

- formal Navier-Stokes root target;
- C1 Chain Necessity;
- C2 Finite Obstruction;
- route / representation completeness;
- D105 viscosity-matched shear/polarization survivor;
- D105 first-order solvability / spectral-drift frontier;
- independent verification of source-internal proof assets;
- all unreviewed/deferred proof-authority candidates outside the curated v0.4 batch.

## 8. Next phase

A natural v0.5 is **Independent Verification + Authority Upgrade**, not bulk automatic theorem promotion. It should attach independent symbolic/human/theorem-prover verifier records to selected `AUDIT` assets and allow `AUDIT -> PROOF` only where the verifier contract is satisfied.