[1337isnot1337]

This adjoins one previously uncataloged contact span and carries the resulting native word through the complete conditional transfer to kappa = 0.00300123.

The increment over #4441 (0.00300105) and #4446 (0.003001053) is small. The new mathematical observation is that a missing three-dimensional span improves a four-dimensional scalar contact for every exponent 0<C<1. This is an author-checked conditional construction awaiting independent review, with the inherited all-column, owned-erasure, whole-job, compiler, tape, precision, analytic, prime and recovery premises retained. The selected record is unchanged.

At contact B/480, replace frame 732 by the span of its two incoming frames. The four incident paid ranks change from [2,2,1,3] to [1,1,2,4]. Strict concavity gives 1+4^(1-C) < 2^(1-C)+3^(1-C). Every scalar coefficient/order, warp, center, main endpoint and independent helper output is retained; all source nested-transport predicates remain intact.

• Exact new local paid profile: {1:2254,2:514,3:444,4:103,5:40,8:8}; the 408-helper target profile is unchanged.
• Both native orientations are replayed by two literal interpreters on all 632 arbitrary persistent inputs, with the owned center returned to zero. All four new transports are lowered and independently decoded in both orientations, including absolute phase.
• The complete p17 word retains 19 full calls, 16 individually paid query shears, every whole idle, 11,560 productive fields, 69,273 paid requests and rank surplus 800.
• Exact raw-root bracket: (0.0030012390168,0.0030012390174). Reprice both completion/original tails at tensor exponent 1024; retain the stronger ordinary BIT admission 0.0034; check all 54 strict outer inequalities plus four guards.
• Explicit sufficient uniform rank N=2^64215200000000. The enormous finite compiled word is specified algorithmically, not materialized.

The new author commit is scoped to research/missing-join-frame/ and retains predecessor attribution. It builds on exact #4440 head 40e22a8 and updated #4441 head 5f9d871, whose complete registered replay was audited before extension. Those pending dependencies are present in this branch unchanged. #4446 was checked during the next frontier refresh; it uses the same predecessor invoice at a slightly tighter declared endpoint, and this new certificate remains stronger.

Reproduce under Python 3.12:

python3.12 -B scripts/research_package.py --package research/missing-join-frame

PROOF.md, PATCH.json, NATIVE.json.gz, RESULT.json, SOURCES.json and VALIDATION.md give the actual contact, exact receipts, source pins, conditional limits and validation evidence. Normal replay freshly executes both parent native/query verifiers before the changed word. --write is authoring only.

Prepared for Cinna Davis / 1337isnot1337 with substantial OpenAI Codex assistance; no subagents. Apache-2.0. Retains PR4440/4441, zxv's native/controller work, PR4412/4414/4416/4433, Jacob Alan Sussman's compiler and the source BIT/transfer lineage.

Validation at author commit 322e0ec764aa7ef7801383feb1f656e460dd8bed: complete CPython 3.12.14 registered replay PASS; separate Git-free -O -B replay PASS with exact receipt equality; changed-source, wrong-plane and wrong-emitted-rank controls rejected; metadata/source pins and whitespace PASS; committed-byte/source-history preflight PASS (57 checked package/input files). Hosted CI is pending at publication. The corrected initial sparse-checkout failure is disclosed in VALIDATION.md.