[aliromman]

This adds two scoped negative results for historical centre-information interfaces. They exclude helper savings from specified packet-basis changes and rank savings from specified delayed centre injections. They supply no changed supplier, native fee improvement, or complete kappa improvement.

The joint-basis proof, delayed-injection argument, independent agent review, and source manifest state the proof and its limits.

• Joint packet bases: the minimum inventory is 36 helper slots per Hamming block, or 504 over fourteen blocks. This fixes the 16-helper factory, twelve second face copies, four independent existing two-source partial directions per tetrahedron at the forty-operation factory cut, ordinary late pair deliveries, and the stated early retired-donor centre interface. Every early query must fit the common final cap of its whole output component. That common-cap condition is a premise; an arbitrary ordered restoration is not covered. The exact enumeration checks 13,860 subsets, 8,820 independent bases, and 126 paired centre cases. The fresh joint receipt records the minimum in this inventory relaxation.
• Delayed centre injection: for each pinned zero-, four-, and eight-cold word, one unchanged held copy per centre requires private canonical rank at least 64. The tested cuts are before B, after each scalar event, and after each full annotated TARGET-frame change before its scalar: 2,438 cuts per word. They do not include injection inside a frame-transition implementation. A separate favorable productive model has extra rank at least 128: it uses one distinct carrier per centre, grants free exchange at its original rank-eight frame, requires a FULL9 exit, and credits only the old rank-one completion. The fresh reverse receipt records both bounds and binds the forward receipts.

These results give exact tests for proposed changes to those interfaces. A smaller construction must leave at least one stated restriction. New packet factories, arbitrary rational query directions, different restoration schedules, split injections, shared carriers, changed B words, and new source/target operators remain outside the results. The rank bounds are not bounds for every native fee or every centre encoding.

The base is cef4b52f2a59009865bf8eabde1be3f159063703. The existing fixed-word gauge limits use a different scalar graph and vary its gauges. The existing packet-factory bounds count 224 helpers, or 392 with second copies, without the paired-centre inventory proved here. No global novelty claim is made.

From the repository root, use Python 3.10 or later with SymPy, assertions enabled, and a new output directory:

python3 -B research/legacy-packet-limits/verify.py --work /tmp/packet-limits-replay

Expected final line:

PASS_LEGACY_PACKET_LIMITS checks=5

The independent replay passed all five top-level checks on CPython 3.14.7 with SymPy 1.14.0, with one subprocess at a time. The joint checks use Fraction and SymPy engines. The delayed checks use forward transport with Prim's algorithm and reverse transport with literal subspace point sets and Kruskal's algorithm. Controls reject a free-centre-direction claim, a false common cap, and reduced private/productive rank claims. Omitting the first cut term changes the terminal decoder in all three words. The review receipt records the exact commands and outcomes.

The wrapper rejects optimized parent execution, changed source bytes, and an existing output directory. It clears inherited PYTHONOPTIMIZE for children. The environment validation records a fresh full replay with PYTHONOPTIMIZE=1 and parent -I; independent probes confirm that child and grandchild assertions remain active. Historical delayed receipts retain their earlier checker hash. Fresh receipts bind the preserved checker and agree on all mathematical fields.

The consumed sources and their credit are:

• @icekylinx supplied the literal factory in PR #531, pinned at e07a8a3f9f79c22113398a0c5dbbc7601f489b3e. The retained sources credit its ancestry in PR #514, PR #507, PR #425, and PR #433.
• @DominikScholz supplied the 504-helper reference provider in PR #569, pinned at 1424da81263a5305b35e4cf74ef686c275f03f3f.
• @eumemic supplied the construction behind the three delayed-injection words in PR #564, pinned at c18417b02b80594b2ca1c8c21185d28befafc935. The frozen words are historical replay outputs, not direct Git blobs; their replay provenance is retained.
• @DreamingOfClouds supplied the labelled-stream framework in PR #509, pinned at 7b9c720ecc9f483c383e7cd9c2ab81f06ee5df59, with its original predecessor credits.

Original notices and Apache-2.0 licensing remain. Substantial OpenAI Codex assistance was used for proofs, checks, review, and packaging. Independent agent review is not human review. No current selected-supplier replay, full historical supplier replay, new arbitrary-dirt construction, phase proof, hosting proof, complete invoice, outer recurrence, Lean run, or hosted CI result is claimed. The broader centre-encoding objective remains unresolved.