Price one transported warp-0 frame's entrance, terminal, and caller b…

[unpaidmoon]

Change and mathematical scope

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

The one compatible transported frame in the PR #3929 recipe (warp 0 on lender 243) has this bill:

• Entrance: one identity scale on register 243, coefficient 1/1, in the new 5-dimensional entrance, at B index 916. Its climb is +1 H1. The warp position moves from 916 to 917. The native map is unchanged.
• Caller: ports, start_extra, helper_final, target_levels, cut, precondition, compensation, centers, center_frames, initial_corrections, section A, restore, removed, and prelude_events are unchanged. The caller adds no child.
• Terminal: end-climb counts stay H1: 289, H2: 77, H3: 54. Restore is unchanged. Cleanup gains exactly one inverse scale, (scale, 243, 1, 1), and no other opcode or frame. That inverse is not a forward frame-bill child.
• Forward histogram: +28 H1 − 16 H2 − 4 H3 + 4 H4, split as the entrance scale, +11 H1 − 4 H3 + 4 H4 at the 36 edited B indices, and +16 H1 − 16 H2 on later unedited B climbs. Rank mass stays 5134. The width inventory is unchanged.

That histogram delta is strictly positive for every power tariff r^q with q ∈ [0, 1), and zero at the rank-mass tariff q = 1. The zero caller and terminal end-climb deltas cannot reverse the sign. This is not a supplier, an owner fill, or a multiplication theorem.

Task and overlap

• Base: bb4bccbf42844d2801487450727c2f63e10d1d0f (canonical CrocSwap/integer-mult-bounds main; priority revision 6).
• Predecessor head: PR Compile native-warp frame changes with exact operator and phase checks #3929 at 0c0e31cf12e8f4f07e8419a6d33ae85129fb5a01. Vendored files are inputs/BASE-WORD.json.gz, inputs/RECIPE.json, and vendor/audit_core.py from that head. SHA256 pins are checked by verify.py.
• Task: scalar-to-moment, scope changed. The card asks whether one scalar simplification improves a paid profile. This session prices the transported-frame alternative in Discussion Handoffs and requests for independent checks #1166 comment 19034220. It is not an R439 helper-star word.
• Handoff: Handoffs and requests for independent checks #1166 (reply in thread) (the alternative, not the moved-ADD pair).
• Item 9 of the chronological open-handoff list on Handoffs and requests for independent checks #1166, using the numbered-question order published with PR Review the encoded many-axis production_axis guard. #4142, after dropping tasks already delivered, matched by an open PR, or answered or refined by this round through Price the cut58 ADDRESS swap against the separable response menu. #4149.
• Nearest overlap: PR Compile native-warp frame changes with exact operator and phase checks #3929 supplies the frame and the aggregate histogram. PR Certify maximal transported warp0 entrance and distinguish least frames from price #3933 proves the least legal completion of this entrance also loses, and that the published frames cost less than that completion while still losing; it records no caller invoice. This package does not repeat the 374-superframe census. PR Raise conditional staged544 κ by filling idle owner slots #3945 fills idle owner slots on a different staged544 word; this frame does not change the width inventory.

Validation

Python 3.12.3, standard library only. Registered replay:

python3.12 -B scripts/research_package.py --package research/transported-frame-caller-price

Passed locally as PASS_REGISTERED_RESEARCH_PACKAGE research/transported-frame-caller-price outcome=negative-result.

verify.py recompiles the published recipe with the transcribed compile_frames algorithm, recomputes the vendored frame bill, and checks caller-field identity, terminal end-climbs, the one entrance scale, the one cleanup inverse, the three-way histogram split, and the integer hypotheses cited by research/transported-frame-caller-price/PROOF.md. A swapped exit frame is rejected.

Not run: native phase replay, a joint price with PR #3945, a selected cold replay, Lean, or Docker. The strict power-tariff sign is the argument in PROOF.md; the verifier checks the integer comparisons that argument uses (2^8 > 3^5, 2^3 < 3^2, and the resulting bounds), not a float sample.

Credit

Dugongue, PR #3929, for the transported-frame recipe, compiler, and base word. Sagar Thakrar for audit_core.py, following Arham Tahir's BORROW-WORD reading. The word label credits the PR #2312 lineage. dataisfire, PR #3734, is the staged544 context of the handoff. ToikY, PR #3933, for the entrance-cap obstruction this note does not re-derive. Chris R / Clear1nsight, discussion comment 19034220, for the requested three-part 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 warp other than warp 0 have a compatible transported entrance whose entrance, terminal, and caller bill lowers a power tariff? First step: one later warp's maximal legal superframe, with the identity scale and end-climbs charged before native replay. Blocker: the other 71 warps are not searched 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 an input of this package.