[unpaidmoon]

Change and mathematical scope

Scoped obstruction. No new κ and no selected-frontier change. The selected record stays κ = 781451/250000000.

The 40 degree-at-least-2 monomials charged by open PR #7031 are not primitives of the selected #6030 invoice, under the constructors that invoice uses. A recursive primitive there is a pair (side, rank) built from frame-dimension gaps, eighteen local copies, fifteen query shears, idle lengths 7 and 8, and one rank-145 target. Ordinary names on the same word are the opcodes ADD, CLEAR, COPY, INIT, MOVE, and SCALE. Those constructors do not read a chart monomial.

Replaying the selected word reproduces the invoice histograms. Against that alphabet:

• 32 of the 40 exponent integers are keys of neither histogram. All six degree-4 masks, 99, 101, 113, 163, 165, 177, are among them.
• Masks 3 and 5 are keys of both sides, so an integer collision is not a unique name.
• No printed monomial equals an opcode.
• 14 exponent integers occur in the selected port list; 26 do not.
• Degrees 2, 3, and 4 are histogram keys, but rank is not defined to be degree. That tariff is not adopted.

The simple-root labels of the hosting ports 11, 21, 38, 140 are 282, 284, 270, 454. The chart is not the port-space coordinate system of the invoice, so an integer shared with a port or a frame vector is not an identification.

The missing obligation is a total map from these 40 exponents to that primitive alphabet which one of the inherited constructors determines. This is not a proof that no other contract could name them, and it is not a thirteen-row profile comparison.

Evidence class: exhaustive 48-term expansion, exhaustive replay of the finite word, and exhaustive checks of the 40 exponents against the finite key sets, plus the written observation that the constructor texts do not read a degree. Not a heuristic.

Task and overlap

Base: 17469fff78c22941280f04d39dc5a1faee09c840. Task card complex-rank-shape-decoder, priority revision 8. Scope is changed: the card asks whether a decoder or coframe change improves the signed moment; this package answers only open question 3 of #7031.

Nearest overlap is #7031 itself (head 531ecca652dde63c6010cd6097cb55a994367ce7) and discussion comment 19514167, which charge the 40 monomials and leave the naming open. This package does not redo that hosting, does not host frame 1, and does not consider sums of letters. Open conditional-κ pull requests are not the selected record.

Validation

Python 3.12, standard library only. From the repository root:

python3 -B research/p104-frame0-invoice-primitive-names/verify.py
python3 -I -O -B research/p104-frame0-invoice-primitive-names/verify.py
python3 -B scripts/research_package.py --package research/p104-frame0-invoice-primitive-names
python3 -B scripts/check_research_commit.py --package research/p104-frame0-invoice-primitive-names --check-source-history

Observed: PASS_P104_FRAME0_INVOICE_NAMES monomials=40 outside_both_histograms=32 degree4_outside=6 paid_collisions=3 target_collisions=7 opcode_hits=0 port_collisions=14 kappa=781451/250000000, PASS_REGISTERED_RESEARCH_PACKAGE ... outcome=negative-result, and PASS_RESEARCH_COMMIT_BYTES at 19eac371b963b5dd4a3bf2902bca6e3e009758a1. Failure controls drop the factor x0, accept mask 99 as a paid rank, and replace the 18 local copies by 17.

Not run: make frontier6030-verify, the native Clifford replay, Lean, and any expansion of frames 1–12.

Credit

The 40 monomials: unpaidmoon, PR #7031. The selected invoice and word: DreamingOfClouds, PR #6030, on the PR #5827 verifier chain. Ports and the line map: PR #6933. Prepared by unpaidmoon with substantial Cursor Grok assistance. New work is Apache-2.0.

Open next questions

Give a total map from these 40 exponents to the inherited primitive alphabet that one of the selected constructors determines. The thirteen-row comparison stays blocked until that map exists. First step: make one constructor read one of these exponents, or show that a constructor already does, and check the image of all 40. The present constructors read frame dimensions, idle lengths, and a diagonal popcount only.

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