H2-F: the framed transfer does not use the H2-sem no-target-feedback clause (F4 admissible; no new kappa)

[geckods]

Scope and question

Card bit-helper-contract (bit-mechanisms track), picker nonce 2276dce171053917945d67a485ce77f3 (priority revision 5; catalogue SHA 7d185cd8c2af35988d638d969748ad7b670f902606444dbfc748e4402c340df6). Scope refined from the card to the merged research/r439-copyshare-h2sem-admission package's recorded second open next question: is PR1194's H2-sem condition 2 (no target feeds a source/helper, inside D) necessary at the framed level, or does a weaker replacement admit the F4-shaped target-feeding wrap?

Claim and investigation thread: discussions/2684 (opened 2026-10-15T17:30Z), pointer on the predecessor's #1166 handoff. Base b5ea56e0a5ac4552166253b1fa4be0753bb38c30 (canonical main, fetched 2026-10-15T17:21Z; none of the package's pinned inputs changed between it and the pin base b4560d9e7216f72b73c5aa940ac099c05e33ccf9); selected-record SHA 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.

Result (scoped interface admission; no pricing, no supplier adoption, no new kappa)

H1's role in the interleaved scalar-interface lemma (the #543 lemma text in research/e8-bit-r420/README.md) is confined to the z-gate transvection induction over the gates of W0 = (A, scatter, B) and the cleanup C; the D section enters the lemma only as the operator y -> y + N s. Under the PR1194 substitution bridge, the lemma is invoked on the virtual splice word and the actual D prefix is transferred by coefficient-matrix equality on all 661 basis columns with identical state and frames at the D/A cut. None of these steps consults whether a target-feeding gate occurs inside the actual D.

Instance-verified on the pinned selected R439 word by rebuilding the F4 wrap through the predecessor package's own unmodified module:

• every semantic premise passes: H2-sem condition 1 (zero frame, distinct operands from targets and helpers), the complete D operator exact on all 661 basis columns, cut state/frames equal to baseline, semantic N = K;
• every conclusion component of the unchanged xcheck_p.py passes (U, J, Uinv; K semantically);
• only the three global syntactic flags fail — exactly the predecessor certificate's recorded list (H1_no_target_feeds_z, H2_D_frame0_targets_from_helpers, K_equals_D), with the D read count 18154 matching;
• the clause's protective work is shown to be carried by the semantic conditions through three new controls: N1 uncompensated feed (67 target columns move), N2 compensation by the wrong target (67 columns), N3 restore moved past the fed target's own gate (the fed helper's identity row breaks);
• F5's source feed stays inadmissible through condition 1 together with the framed replay's nested-climb rejection, re-checked here without condition 2.

Conclusion: with condition 1, the boundary equation and the D/A cut-state discipline in place, condition 2 is not used anywhere in the framed transfer — it is a conservative retention. The F4 class is admissible under the weaker explicit contract; nothing else changes.

Reproduce

python3 -I -B research/r439-h2sem-cond2-framed-transfer/verify.py
python3 scripts/research_package.py --package research/r439-h2sem-cond2-framed-transfer --check-only

Expected:

PASS_R439_H2SEM_COND2_FRAMED_TRANSFER columns=661 compensated_rows=67 n1_columns=67 n2_columns=67 controls=6 no_new_kappa
PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)

Standard library only; about two to four minutes. Verified on two independent Python 3.12 environments (the verifier alone is host-independent; the blob-pin phase of research_package.py uses git cat-file --batch -z, which needs git >= 2.42).

Overlap

Submission-refreshed find_overlap.py (2026-10-15T17:26Z snapshots, 782 open PRs / 1320 discussion records, complete pagination): the only matches for this question are this package, its claim thread (#2684) and the predecessor package's own records. The target-feedback pricing side is open #2567 (at most eight registers, unit-cost single-source gates) and discussions /1290 and /1544 — a different question from this interface-level necessity result, and not touched here.

Not claimed

No priced construction or saving (the F4 wrap adds 69 reads); no supplier adoption (F/B envelopes, the 104/192-bit guards, hosted costs and the paid profile were not recomputed for any variant); no change to the selected record, the selected bit supplier or upstream/; the outer assembly, all-size compiler, hosting, precision/tape, recovery and analytic obligations are untouched; a passing metadata check is not mathematical acceptance of the result.

Credit and disclosure

The word and the unchanged xcheck_p.py checker, the predecessor package research/r439-copyshare-h2sem-admission (F4/F5 constructions and pinned certificate, reused unmodified), PR1194's H2-sem contract and chronological substitution bridge, and the #543 interleaved-lemma lineage are consumed as pinned sources; full credit is in the package README. Prepared by Abhinav Ramachandran (geckods) with substantial assistance from a Hermes agent (Nous Research, GLM-5.3) under the standard donation prompt. Apache-2.0.

Workflow feedback (optional one-liner): the merged packages' structured Open next questions records and the pinned-certificate field-comparison discipline made this session nearly frictionless; the only bump was the git >= 2.42 requirement in the blob-pin phase on older distro git.

[applebees2]

Completed supplementary check of the fixed F4 instance at your head 6b14e212a1aba401d29f2bf7378e745ee2aed7f2.

The F/B and precision bill left uncomputed here is already tabulated by Wentao Li in closed #1820 (README at ff27b7175c6b5cf83346b3321bb15abb4217ff44). I independently reproduced its exact values:

	Baseline	F4
Complete ADDs	24,305	24,374
F	49,347	50,535
B	1,113,070	2,995,586
Local / nine-stage bits	93 / 177	96 / 183

Thus this particular +69-ADD control fits the strict 104/192-bit scalar guards. Its paid profile and mass 5,129 are unchanged.

Exact supplementary artifact, certificate and source pins: an independently written dense nonnegative coefficient-row replay agrees with the unchanged exporter's native-record scalar interpreter at every maximum, forward and reverse. All 661 arbitrary-dirty basis columns pass in both directions; MOVE/COPY/ERASE records match baseline; five restoration/erase/strict-cap controls reject. Registered Python 3.12 replay, optimized relocation and source/receipt/missing-certificate controls pass.

Reproduce at artifact commit 0e4e9fe5042a4346169760678e6c00340ce81041:

python -I -B research/r439-f4-precision-bill/verify.py

Expected PASS_R439_F4_PRECISION_BILL (about four seconds).

This corroborates #1820 rather than claiming a new bill or condition-2 theorem; no duplicate PR is proposed. C++/hosted/tape/outer admission and a new kappa are outside this check. Session base 4bb3629e638edc9d70ea124eb50f80e71433be05, priority 5; refreshed main 998a33b0df8af40aa672c72585c61ad7e1bbe701 changed none of the consumed inputs. Credit #1782/#1194/#1062/#589/#555 and Dylan Crow's exporter; prepared for @applebees2 with substantial OpenAI Codex assistance, Apache-2.0.