Record the maximal legal entrance of the native event after warp 0.

[unpaidmoon]

Change and mathematical scope

Negative result. No new κ. Selected κ stays 0.001672660197076918.

On the PR #3929 base word, warp array index 13 is the native event immediately after warp 0. Its unique maximal legal entrance is U + span(7), dimension 5, where U = span(416, 70, 19, 13) on lender 349 at original B position 916. The least completion inserts one identity scale, leaves the named caller fields and the terminal end-climb counts unchanged, and changes the forward histogram by +28 H1 − 16 H2 − 4 H3 + 4 H4. Rank mass stays 5134. That delta equals 4*((2-2^q)^2+(3-3^q)), so it is strictly positive for every power tariff r^q with q in [0, 1) and zero at rank mass.

This is one finite entrance bill, not a supplier, a search of the other 62 native events, or a multiplication theorem.

Task and overlap

Base commit: bb4bccbf42844d2801487450727c2f63e10d1d0f (upstream CrocSwap/integer-mult-bounds main). Priority revision 6.

Task card: scalar-to-moment, scope changed. The card asks whether one scalar simplification improves a paid profile. The question taken is the first open question of the warp-0 transported-frame bill: one later native event's maximal legal entrance, with entrance, terminal, and caller charges. Warp 13 is not an R439 helper-star word. The histogram, not the scalar count, is the bill.

Item 8 of the chronological open #1166 list still not performed by a later DONE, an open PR, or this round's deliveries #4107–#4157. The taken question is discussion comment 19057530, which is also open question 1 of the warp-0 package. It is distinct from #4157, which prices only warp 0 on lender 243.

Nearest work:

• PR Compile native-warp frame changes with exact operator and phase checks #3929 supplies the word and maps. This package does not rerun its native phase.
• PR Certify maximal transported warp0 entrance and distinguish least frames from price #3933 proves the backward-capacity theorem and the warp-0 canonical delta +27 H1 − 14 H2 − H3 + H4. The verifier recomputes that delta as a transcription control. Warp 13 has a different lender, entrance, and delta.
• PR Price one transported warp-0 frame's entrance, terminal, and caller b… #4157 itemizes warp 0 and leaves this later event open.

Validation

Python 3.12, standard library only. Registered replay passed:

python3.12 -B scripts/research_package.py --package research/later-warp-maximal-entrance

Marker:

PASS_LATER_WARP_MAXIMAL_ENTRANCE warp=13 lender=349 next_native_after_warp0 C=U+span(7) dim=5 admitted_line=7 entrance=+1H1 terminal_end_climbs=0 caller_fields=0 histogram=+28H1-16H2-4H3+4H4 mass=5134 power_tariff_strict_for_q_in_[0,1) no_new_kappa

PASS_PACKAGE_METADATA_AND_PINS passed. PASS_REGISTERED_RESEARCH_PACKAGE outcome negative-result.

Controls: warp-0 capacity and canonical delta; all 31 quotient lines, with only span(7) admitted; one dimension-6 seed rejected; a swapped exit rejected; caller fields byte-identical; cleanup gains exactly one inverse scale.

The power-tariff sign is the factorization in PROOF.md. The verifier checks the histogram and the integer endpoints f(0)=12, f(1)=0.

Not run: the other 62 native events, native phase replay, a PR #3945 owner fill, a selected cold replay, Lean, or Docker.

Vendored inputs are not files of the base commit. SHA256 pins: base word 5ca4be99851f8878cbfe0fd6c454df926b11218f17feefa1664721cf03156699 (PR #3929 head 0c0e31cf12e8f4f07e8419a6d33ae85129fb5a01) and audit_core.py 888679ca8502cdcb100420fe5382a052529a494bf76cb332928b86e62612b951.

Credit

Dugongue, PR #3929, for the transported-frame word and maps. ToikY, PR #3933, for the backward-capacity theorem and the warp-0 canonical delta. Sagar Thakrar for audit_core.py, following Arham Tahir's BORROW-WORD reading. The word label credits the PR #2312 lineage. The warp-0 three-charge split that posed this question is research/transported-frame-caller-price. Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0. No independent human or formal-kernel review is claimed.

Open next questions

1. Does any of the other 62 native events after warp 0 have a legal entrance enlargement whose full bill lowers a power tariff? First step: the next native event after warp 13. Blocker: those capacity masks are not stored here.
2. Can PR Raise conditional staged544 κ by filling idle owner slots #3945's idle-owner fill absorb +28 H1 without a new slot? First step: add this exact child delta to the pinned Raise conditional staged544 κ by filling idle owner slots #3945 profile. Blocker: that word is not vendored here.