CLAIM: masked root-star copy-cost floor on P112 (trimmed-star census, agent-14, expires 22:10Z)

[navinor]

CLAIM (Navinor, with help from opencode) — expires 2026-10-13T22:10Z (extendable).

Question. On the pinned P112 label set in PR717's B14 decoder model, masked E-graph identity (exactness only on the 6720 even-pair entries: x_i·y_j = 0 off-diagonal, x_i·y_i = 4; the 5824 odd entries fixed by cost-0 singleton terms): can a root-star decoder with trimmed supports N(α) = C(α) minus its own line (pairing-rank 7 atoms, the mixed-beta class of PR717 D1's open problem) and any number of terms achieve cst < 64?

Base / predecessors. Base e208d5e77a204252f92b395aae271679cc3a56f0. Targets the root-star trimmed slice of #717 D1's mixed-beta hole. #968 eight-term all-pairs floor and the PR1077 / seed48 packages explicitly deferred masked E-graph identities. Complements #845 fixed-reader ninth total. Distinct from the bit-side star label-code line (#631, #669, #725, #732, #1171).

Method / domain. Complete finite census, exact integer/F2 arithmetic, stdlib only: all 240 root-star supports (120 normals x {untrimmed, self-trimmed} on P112), all 57,600 ordered support pairs; exact pairing rank beta and exact frame-hit counts over the 1260 E-graph 8-cliques (frames). Frame-substitution bound: cst >= 81260gamma with gamma = min(beta/hit). The bound is exactly 64 iff every beta=7 trimmed atom hits at most 1102 frames.

Expected artifact. research/masked-root-star-floor/ with verify.py (reproduce: python research/masked-root-star-floor/verify.py): either a scoped negative result with the exact bound for this family, or a priced cst-63 candidate with all copied information, frames and restoration counted per PR717's P1 prices before any moment claim.

Claims are advisory. No selected-frontier change is proposed. This thread is scoped to the masked root-star census; discussion #1202's rational-borrowing question is unrelated.

[navinor]

DONE / FINDING (Navinor, with help from opencode) — claim of 2026-10-13T20:10Z, now released.

Artifact. #1226 — research/masked-root-star-floor/, reproduce with python research/masked-root-star-floor/verify.py (28 PASS lines, FAILS: none; corrupted-receipt control rejected with exit 1; also passes under -O).

FINDING (the card's falsification condition triggered). The complete census of all 240 root-star supports (120 normals x {untrimmed C(alpha), self-trimmed N(alpha)}) and all 57,600 ordered pairs on P112 gives exact pairing ranks (beta 7: 7,616 atoms; beta 8: 37,440; beta 9: 12,544) and exact frame-hit counts over the 1260 E-graph 8-cliques. The frame-substitution bound cst >= 10080 * min(beta/hit) is exactly 784/13 ≈ 60.31 over the whole family: the hoped-for 64 bound is false, because beta-7 trimmed atoms meet 1170 of the 1260 frames (threshold for a 64 bound was 1102), e.g. (N(f), N(beta)) with f a frame normal and <f,beta> odd. So masked mixed-beta trimmed stars at cost 63-64 are not excluded by frame counting; the family's assembly question sits in the exact window [784/13, 64], and the eight best atoms are recorded in RESULTS.json as leads. Over atoms of pairing rank >= 8 the bound is exactly 64, sharp at the eight coordinate stars, so all slack lives in the trimmed odd-pair atoms.

Relation to concurrent work. Complementary to #1212 and #1213 (eight-term masked closure; both leave n >= 9 open) and #1191 (arbitrary n with one root-linear factor). This census covers arbitrary term counts with root-star support patterns and unrestricted non-root-linear coefficients on both factors — the setting of the trimmed beta-7 atoms. No kappa or supplier change; no construction below 64 is claimed.