This is Peer Review Round 4 of the frozen Paper 3 source bundle.

### 1. Typographic Claim Verification
I have cross-checked the updated wording in Table 1 against the exact wording in the foundation snapshot of the `research/claim-register.md`.

*   **P3-C02:**
    *   *Claim register:* "The reconstructed symmetry data act on a declared observable algebra/interface compatible with context composition."
    *   *Table 1:* "The reconstructed symmetry data act on a declared observable algebra/interface compatible with context composition."
    *   **Result:** Exact match.
*   **P3-C04:**
    *   *Claim register:* "Monoidal composition produces typed pre-geometric outcome objects while probability remains an independent interface."
    *   *Table 1:* "Monoidal composition produces typed pre-geometric outcome objects while probability remains an independent interface."
    *   **Result:** Exact match.
*   **P3-C05:**
    *   *Claim register:* "A realization map cleanly separates pre-geometric outcome data from ordinary measurements localized in a realized spacetime."
    *   *Table 1:* "A realization map cleanly separates pre-geometric outcome data from ordinary measurements localized in a realized spacetime."
    *   **Result:** Exact match.

The requested literal corrections have been successfully applied.

### 2. Scientific and Audit Checks
I have reaudited the document content to ensure no unauthorized scientific or executable drifts occurred and that all rigorous demarcations remain fully intact:

*   **Exact Claim/Assumption Statuses:** Table 1 correctly identifies P3-C03 as `OBSTRUCTED` and all others as `OPEN`. Table 2 correctly identifies all nine assumptions as `UNVALIDATED`.
*   **Lean Executable Scope and Obstruction IDs:** Section 11.1 perfectly cites the exact repository metrics: thirty-four total claims, exactly one `OBSTRUCTED` claim (`P3-C03`), exactly one evidence path (`research/counterexample-register.md`), and the two exact counterexample IDs attached to it (`CE-P3-05` and `CE-P3-06`).
*   **Branch Typing:** Table 3 successfully keeps Doplicher-Roberts (compact group, no fibre functor), Neutral Tannakian (affine group scheme, exact fibre functor), Nonneutral Tannakian (affine gerbe), and Super-Tannakian (affine supergroup scheme) in mathematically disjoint, typed rows.
*   **Observable/Action Separation:** Section 4 cleanly introduces the observable functor `A: Ctx -> uCStar` and action `alpha` as distinct interface inputs, recognizing that a generic representation category cannot logically select them.
*   **State Averaging and Nonamenable Obstruction:** Section 5 accurately deploys compact Haar averaging for invariant states and cites the nonamenable `F_2` counterexample to prove invariant states cannot be inferred unconditionally.
*   **State-Family Naturality:** Section 5.5 correctly cites BFV as an exact comparator blocking the free assumption of a natural, distinguished state family.
*   **Dynamics and Conservation:** Section 6 distinguishes symmetry invariance from dynamically conserved quantities, rigorously requiring a separate one-parameter dynamics `tau` and generator domain `D(delta)` for conservation laws.
*   **Probability-Free Outcomes:** Section 7 declares the outcome label functor `O: Ctx -> FinSet` and separates it entirely from evaluations, effects, and operational probability rules.
*   **Algebraic Frame Data:** Section 8 keeps Tannakian fibre-functor torsors appropriately scoped as algebraic datum rather than operational reference frames with calibrated measurements.
*   **Spacetime Comparators:** Section 9 correctly places Haag-Kastler and BFV explicitly on the post-realization side, acknowledging that they presuppose spacetime and causal geometry.

### 3. Corrections Needed
None. The text perfectly reflects the required precision, dependency isolation, and claim-register vocabulary. 

VERDICT: ACCEPT