[zxv]

Result

A declared single-cut application of PR #6064 cannot fund separately paid coordinate delivery on the selected PR #6030 P104 bill. If each added coordinate enables at most two additional binary helper splits per LOCAL and costs at least one positive-rank paid job globally, the best extra target credit is less than 0.773 per coordinate, even granting all 18 LOCALs and making every other added fee free. The complete raw moment is negative throughout κ ∈ [.003125804, .0034], so this contract cannot retain the selected saving.

The two-splits-per-coordinate realization contract is explicit: PR #6064's capacity theorem alone does not bound every changed supplier's target count. Productive carriers, multiple coordinates per transport, reused coordinates across cuts, changed prefixes/boundaries, and new BIT budgets remain open.

Separately, Matarener's unmodified PR #5994 full-subspace engine finds no pure helper split on the selected word: 8,734 evaluations, 69 groups, 562 helpers; both exact group and relaxed boundary supports fail. Since that census already grants all roles at each chart, selecting another role from an existing chart bank cannot supply a free escape within that pure split contract. This is a credited application of the original engine, not an independent engine audit.

Significance for researchers

The sharp two-for-one algebraic gain needs a changed delivery or credit contract before a larger native construction is justified. Exact rational logarithm/Taylor certificates cover the whole κ interval and account for the selected claim's small raw slack, avoiding the finite-grid failure identified in PR #6049. The result refines a concrete opportunity in zxv's recent work; it does not establish a global P104 ceiling.

Validation

CPython 3.12 normal and optimized registered replays pass the rational interval budget, both complete current-word cut screens, synthetic legal/orthogonal/mismatched cuts, 36 split controls, and rejection of four changed source contracts. Exact committed-byte preflight passes at 74c353a2df322ffc0273d538450f6505b76c76e7.

python3.12 -B scripts/research_package.py --package research/dyadic-cut-delivery-budget
python3.12 -B scripts/check_research_commit.py --package research/dyadic-cut-delivery-budget

The PR adds only its isolated research package. The pending predecessor statement is retained verbatim with its exact head/hash; executable dependencies are source-pinned files on the canonical base. No native, compiler, selected cold replay, new κ, independent human review or proof-kernel acceptance is claimed. All five framework assumptions remain. The unchanged base has the research-navigation issue tracked by PR #6050; no frozen consumer pin is changed here.

Open next questions

Can one paid job deliver at least two newly eligible coordinates, or can an existing trajectory supply a coordinate for no extra recursive cost? First provide the exact native chart, timing, lifetime and signed invoice. Alternatively, give an independently productive carrier or changed multi-cut continuation with all restoration fees; capacity alone does not supply that credit.

Prepared by zxv with substantial OpenAI Codex assistance. Credit Ali Romman's dyadic/P104 lineage, DreamingOfClouds's word and complete bill, Matarener's census, Nick Petalas's related PR #6033, and retained predecessor attribution. Apache-2.0.

Hosted run 40636933560 at the exact submitted head stops during shared planning on the two unchanged base navigation tests addressed by PR #6050; it never launches this package's scientific replay. The local normal/optimized registered replay and a clean committed export replay pass. This is a base navigation blocker, not a scientific CI pass.