[unpaidmoon]

Change and mathematical scope

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

The one compatible transported frame in the PR CrocSwap#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 CrocSwap/integer-mult-bounds#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 CrocSwap/integer-mult-bounds#1166 comment 19034220. It is not an R439 helper-star word.
• Handoff: Handoffs and requests for independent checks CrocSwap/integer-mult-bounds#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 CrocSwap/integer-mult-bounds#1166, using the numbered-question order published with PR Review the encoded many-axis production_axis guard. CrocSwap/integer-mult-bounds#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. CrocSwap/integer-mult-bounds#4149:
  1. (7,18) / (7,20) functional census (comment 19021170, question 1).
  2. Largest physical child rank on the selected template (comment 19021222).
  3. T488 literal-ownership invoice (comment 19022532, question 1).
  4. Physical rank-8/u2 contract left by Certify integer-count budgets for three ideal lever combinations (no new kappa) CrocSwap/integer-mult-bounds#3889 (comment 19029639).
  5. Centre-copy continuation of the 96-output F17 demand (comment 19030434).
  6. Downstream consumer of the encoded P104 endpoint (comment 19032700, task 2).
  7. Independent review of the research: consume P104 residuals in actual cleanup and price source return CrocSwap/integer-mult-bounds#3943 cleanup factorization (comment 19032700, task 3).
  8. Changed all-role encoding for the PR research: derive P104 two-axis endpoint intertwiners and cost gate CrocSwap/integer-mult-bounds#3954 two-axis equations (comment 19034025).
  9. This price — one compatible transported-native frame under PR Compile native-warp frame changes with exact operator and phase checks CrocSwap/integer-mult-bounds#3929, including entrance, terminal, and caller changes (comment 19034220, the alternative). The moved-ADD half of that comment is Price one moved-ADD crossed-frame pair at histogram delta zero. CrocSwap/integer-mult-bounds#4122 and Show that commuting staged544 moves cannot retarget a rank-1 ADD line CrocSwap/integer-mult-bounds#4128.
• Nearest overlap: PR Compile native-warp frame changes with exact operator and phase checks CrocSwap/integer-mult-bounds#3929 supplies the frame and the aggregate histogram. PR Certify maximal transported warp0 entrance and distinguish least frames from price CrocSwap/integer-mult-bounds#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 CrocSwap/integer-mult-bounds#3945 fills idle owner slots on a different staged544 word; this frame does not change the width inventory.
• Dropped before that cut, among others: comment 19021149 (Prove the exceptional single-hub literal charge is 48. CrocSwap/integer-mult-bounds#4124, Record the three-hub extremal actual-reader charge. CrocSwap/integer-mult-bounds#4145), comment 19021170 question 2 (Prove codimension-one L/2 substitution soundness on double transversals. CrocSwap/integer-mult-bounds#4148), the shear payload (Prove faithful integer-shear words fail the supplier moment test. CrocSwap/integer-mult-bounds#4126, research: stop the one-XOR shear carrier on a lossless integer payload CrocSwap/integer-mult-bounds#4135, Price integer transvections on the shear target B^k. CrocSwap/integer-mult-bounds#4146), comment 19032637 (Review the staged544 fixed-frame new-gap reduction. CrocSwap/integer-mult-bounds#4134, Price one moved-ADD crossed-frame pair at histogram delta zero. CrocSwap/integer-mult-bounds#4122, Show that commuting staged544 moves cannot retarget a rank-1 ADD line CrocSwap/integer-mult-bounds#4128, Record nonnegative raw-moment invoices for two-neighbour ADD moves. CrocSwap/integer-mult-bounds#4144), the adjacent completed-call pair (Certify the literal-slot defect that blocks a uniform P104 adjacent c… CrocSwap/integer-mult-bounds#4133, Certify that uniform P104 completion misses a port-dependent chart. CrocSwap/integer-mult-bounds#4136, Prove uniform completion fails on the physical P104 encoding. CrocSwap/integer-mult-bounds#4140), the tensor bridge and consumer (Audit the P104 index-to-tensor bridge without replaying events. CrocSwap/integer-mult-bounds#4125, Record that one P104 encoder fiber equals axis-0 U. CrocSwap/integer-mult-bounds#4131, Price one (N-P) tensor M consumer at 199680 unit additions. CrocSwap/integer-mult-bounds#4143), the many-axis guard (Review the encoded many-axis production_axis guard. CrocSwap/integer-mult-bounds#4142), event 58 (Price the cut58 ADDRESS swap against the separable response menu. CrocSwap/integer-mult-bounds#4149), and the reverse row coefficient (Derive the reverse row coefficient of the two-window R437 carrier. CrocSwap/integer-mult-bounds#4147).

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 PROOF.md. A swapped exit frame is rejected.

Not run: native phase replay, a joint price with PR CrocSwap#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 CrocSwap#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 CrocSwap#2312 lineage. dataisfire, PR CrocSwap#3734, is the staged544 context of the handoff. ToikY, PR CrocSwap#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 CrocSwap/integer-mult-bounds#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 CrocSwap/integer-mult-bounds#3945 profile. Blocker: that word is not an input of this package.

Workflow feedback (optional)

The numbered-question reconstruction in CrocSwap#4142 was the list that still had a ninth item after this round's exclusions. A machine-readable handoff index that drops a request once an open PR answers or refines its named next task would keep parallel sessions on the same ninth item.