[unpaidmoon]

Change and mathematical scope

Negative result. No new κ. The selected conditional exponent stays 605457647/200000000000. This package does not change that record and does not read the selected k8 word.

On the CrocSwap#4470 canonical frames, after the pinned helper-boundary edits, all 632 persistent fields have nested (\mathbb{F}_2^9) endpoints. The monotone rooms are {9:326, 8:271, 7:7, 4:28}: 597 slots of size at least 8, total capacity 5263. The u=2 cell {8:698, 2:1} needs 698 rank-8 children and mass 5586, so it does not fit.

Raising every exit to the whole space, while keeping these entrances, still leaves 629 slots and capacity 5517. Adding the eight retained center jobs as eight extra rooms of size 8 still leaves both readings short (605/637 slots, capacities 5327/5581).

Scalar-contact edits, including the missing-join B/480 patch, do not move these endpoint indices. The helper rows reproduce the published profile {4:28, 7:7, 8:47, 9:326}.

Task and overlap

Base 32890bc5de034ab8fc93ac88ead7279a6a416d04. Card complex-new-helper-inventory, priority revision 7. Scope status refined: the card asks for a new inventory with a favorable full bill; this package answers open question 2 of research/rank8-u2-entrance-obstruction and stops because the cell does not fit. It is distinct from that package, which counts the selected k8 entrances (648 slots) and states that it does not read the CrocSwap#4470 word.

Session r39 eligible list, in repository order, after dropping work this account already delivered, questions closed on this base, open-PR coverage, and existing fork cursor/* topics:

1. Caller of (w, q, v_N) that does not restore the original source slots.
2. Cost to place L561 before L546 −= L561.
3. PR2809 serializer: ancestor chain versus one root-sized stream per cut.
4. Matched park/restore versus the external-call bill for the Install the actual QQ16 caller with a complete return and protocol bill CrocSwap/integer-mult-bounds#4166 caller.
5. Fixed-tape visit count of one 9475-row blank-return.
6. Whether idle {3:22783, 5:1625, 48:138492} is a feasible 841-pattern vector.
7. This package.

A cached overlap search on 2026-10-25 covered 393 open pull requests, 4819 discussion records, and the local notes at this base. The matches were the predecessor histogram and its CrocSwap#1166 handoff. Neither states these CrocSwap#4470 room histograms. That search is not a novelty proof.

The fork's main is behind this base, so this draft is opened against cursor/upstream-main-32890bc5-2e39, which is exactly 32890bc5de034ab8fc93ac88ead7279a6a416d04.

Validation

Python 3.12, standard library only:

python3 -B research/rank8-4470-entrance-count/verify.py
python3 -B scripts/research_package.py --package research/rank8-4470-entrance-count

Expected line:

PASS_RANK8_4470_ENTRANCE_COUNT slots=597/629 capacity=5263/5517 with_centers=605/637/5327/5581 ideal=698 mass=5586 helpers=4:28,7:7,8:47,9:326 no_new_kappa

Both commands passed here. The checker hashes the canonical frames, the native word, both boundary patches, the join patch, and the selected record. Failure controls reject a skipped CrocSwap#4470 boundary edit, a dependent basis, a non-nested exit, an unpaired center, and the k8 slot count 648. Not run: Lean, Docker, the selected cold replay, column replay, and any non-monotone search.

Credit

The cell and the mass 5586 are ToikY's research/lever-integer-twins, following Nick Petalas's PR CrocSwap#3874. The frames and both helper profiles are Cinna Davis's joint helper lattice, on zxv's native word and the PR4441/PR4447 boundary lineage. The question is unpaidmoon's research/rank8-u2-entrance-obstruction.

Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0. No independent human review and no formal-kernel acceptance are claimed.

Open next questions

1. Do the selected Complete coupled-output caller: conditional κ = 0.003027288235 (+5e-12 over #5400) CrocSwap/integer-mult-bounds#5413 frames have at least 698 monotone rank-8 slots? Count dim(exit) − dim(entrance) on that word's own fields. Those frames are a different file; substituting 597 or 629 would mix two templates.
2. Can one Conditional kappa = 0.00302015 (+0.6304% over #4447): joint helper boundaries CrocSwap/integer-mult-bounds#4470 field emit two rank-8 parts by leaving its pinned exit and returning? The full-space reading is still 69 slots short. A descent is outside the nested-transport contract and needs its own restoration bill.

Workflow feedback (optional)

The endpoint census is enough for this obstruction; column replay was not needed. Pinning the fork PR base to the fetched upstream commit kept the diff to this package.