d6g8k5htny-coder · Sep 28, 2026 · Sep 28, 2026 · Sep 28, 2026
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+# D5 collar first moment and scaled-ball synthesis — review record
+
+Scientific effect: NONE. This directory is a dated nonauthor review record.
+It does not edit author sources, STATUS, GRAPH, lemma_closed, prizes, or PROOF_INDEX.
+
+Read REVIEW.md.
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+{
+  "scientific_effect": "NONE",
+  "review_status": "RECORD_ONLY",
+  "objects": ["collar_C1", "scaled_ball_C2"],
+  "collar_C1": "ACCEPT_EXISTENTIAL",
+  "scaled_ball_C2": "ACCEPT_COROLLARY",
+  "continuum_verified": false
+}
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+# Nonauthor review: compact collar first moment and scaled-ball synthesis
+
+Scientific effect: **NONE**. This file does not change `lemma_closed`, prizes,
+premises, `STATUS`, `PROOF_INDEX`, `GRAPH`, or any author source.
+
+Math- `main` after #117: review files `reviews/d5_i5_planar_f_20260928/` already consume scaled-ball (C2) as a companion bound. This record is the source-bound review of that companion.
+
+## Objects
+
+| Object | Path |
+|---|---|
+| Collar | `reviews/d5_local_collar_20260928/COLLAR_PROOF.md` |
+| Punctured pin | `reviews/d5_local_collar_20260928/PUNCTURED_PIN_PROOF.md` |
+
+## Verdicts
+
+| ID | Statement | Verdict |
+|---|---|---|
+| Interpolation | degree-five three-site value/gradient map has rank 9 on the compact collar, including the midpoint axis | ACCEPT |
+| Gram | `det(BB^T)=u^2 v^4 + v^6/4`; `sigma_min(B) >= c v^2` | ACCEPT |
+| Coarse floor | `Cov_{Q_r}(grad f(X)) >= c r^{10} I_2` after deleting the auxiliary witness value | ACCEPT existential |
+| Collar first moment | `E_{Q^W} N_j(r E) <= C r^3 |E|` on `C(eta, R)` | ACCEPT existential |
+| Scaled-ball synthesis | same bound on `{|x|<=R} minus two pins` at `eta=1/4` | ACCEPT corollary of punctured-pin + collar |
+
+## Intensity split used
+
+Axis split at `C_* r^{1/2}`.
+
+- `|v| <= C_* r^{1/2}`: coarse `r^{10}` floor; intensity `r^{-72} exp(-c/r) <= C r`.
+- `C_* r^{1/2} <= |v| <= v_0`: B-frame floor; intensity `r |v|^{-34} exp(-c/v^2) <= C r`.
+- `|v| >= v_0`: uniform; intensity `O(r)`.
+
+Weighted Kac-Rice: Armentano-Azais-Leon arXiv:2304.07424v3 Theorems 2.2 and 7.1, Remark 8. One witness determinant. `F_j` continuous on all symmetric matrices.
+
+## Not claimed
+
+Numerical `C`, `r_*`. Uniformity in `R` up, `eta` down, `T`, or `k` down to 0. Elder pairing. Any STATUS / GRAPH / lemma_closed / prize change.
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+# Off-pin second factorial moment — review record
+
+Scientific effect: NONE. Dated nonauthor review record.
+Does not edit author sources, STATUS, GRAPH, lemma_closed, prizes, or PROOF_INDEX.
+
+Read REVIEW.md.
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+{
+  "scientific_effect": "NONE",
+  "review_status": "RECORD_ONLY",
+  "P_eta": "ACCEPT",
+  "planar_F": "ACCEPT_THETA_R3",
+  "torus_wide_second_moment": "CANDIDATE_PENDING_REVIEW_AND_TEST",
+  "thin_tube_first_moment": "SUPERSEDED_BY_SCALED_BALL_C2",
+  "continuum_verified": false
+}
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+# Nonauthor review: off-pin second factorial moment
+
+Scientific effect: **NONE**. This file does not change `lemma_closed`, prizes,
+premises, `STATUS`, `PROOF_INDEX`, `GRAPH`, or any author source.
+
+## Verdicts
+
+| ID | Statement | Verdict |
+|---|---|---|
+| P_eta | `E N_eta(N_eta-1) <= C_eta r^5` for window points in `{|X|>=eta}` minus pins, fixed `eta>0` | ACCEPT |
+| Planar matching event | `c r^3 <= P(A_r) <= C r^3` in `d=2` | ACCEPT (same as #117) |
+| Torus-wide `E N(N-1)` | pair intensity with a witness near a pin | CANDIDATE pending review and test (catalog C6) |
+| Thin-tube first moment | tube inside a fixed scaled ball | superseded by scaled-ball synthesis |
+
+## P_eta
+
+`frontiers/remote_collision_20260928/PROOF.md` Lemma 1 uses only that both witnesses stay a fixed positive distance from the pins. Replacing the remote radius `rho` by `eta` does not change the divided-difference Jacobian or the ledger `delta min(1, r^3/delta^3)`.
+
+## Candidate C6
+
+Write `N = N_eta + N_<eta`. P_eta bounds the first summand. The remaining object is pair Kac-Rice with a witness in `{|X|<eta}`. A first-moment bound does not produce this second moment. Catalog C2, if later proved, would obstruct a global `O(r^5)` upper bound via `N(N-1) >= 2 1_{N>=2}`. That obstruction is conditional on C2 and is not recorded as a theorem here.
+
+## Not claimed
+
+Numerical constants. `k` down to 0. `d>2` first moment. Elder selection. Any STATUS / GRAPH / lemma_closed / prize change.