Research: selected m=73 complex stock shape A=0 under finite-stock-as-C (no new kappa)

[VictorLiwentao]

Change and scope

Bounded follow-up to #3113 under priority revision 6, card selected-stock-envelope. That package already bound the finite per-level stock allowance B_bits = 2642 and the halving guard, and left the shape constants A, B, and rho of

sigma <= (43/26)*(1-s)*(A+B) + rho

unbound because the pinned complex cover note stated no w-shaped per-level divisor.

Under the finite-stock-as-C reading already named by research/selected-coarse-depth-stock/PROOF.md, this package proves the selected m=73 complex per-level divisor candidate is independent of atom width w, so

log_2 C(w) <= A * w + B

holds with A = 0 and B = 2642. Ordinary BIT retains A ≥ 4096 via the digit tower; the complex Sp(72,2) cover has no such lift. Leaf reserve rho remains unbound. No new kappa. Selected κ stays 0.001672660197076918.

Result

Package: research/selected-stock-shape-a-zero/.
Tip: eb215c6418b1f60dea8f4b8fe966f39328dcbd80.
Content tip: 9b257d8e75bf205d150b4d2a6a8280f5e1d8f76a.
Base: 6f100d4bb5083f8c35d96fd95a539811c62f245c.

Validation

python3.12 -I -B research/selected-stock-shape-a-zero/verify.py
python3.12 -I -O -Werror -B research/selected-stock-shape-a-zero/verify.py
python3.12 -I -O -Werror -B research/selected-stock-shape-a-zero/independent.py
python3.12 -I -O -Werror -B research/selected-stock-shape-a-zero/test_package.py
python3.12 -B scripts/research_package.py --package research/selected-stock-shape-a-zero

Expected:

PASS_SELECTED_STOCK_SHAPE_A_ZERO A=0 B_bits=2642 rho=unbound no_digit_tower_lift no_new_kappa
PASS_SELECTED_STOCK_SHAPE_A_ZERO A=0 B_bits=2642 rho=unbound no_digit_tower_lift no_new_kappa_INDEPENDENT
PASS_SELECTED_STOCK_SHAPE_A_ZERO_TESTS groups=6
PASS_REGISTERED_RESEARCH_PACKAGE research/selected-stock-shape-a-zero outcome=completed

Default verify is read-only. Admission uses need() and still fires under -O.

Overlap and credit

Closest prior: #3113 for B_bits=2642 and the explicit missing-lemma A_B_rho_unbound. This package answers only the A obligation; it does not recompute B or the halving guard, and it does not close rho or a full sigma envelope. Does not reopen #3411, #3392, #3386, #3374, #3349, deferred V45, or the merged readout series through #2883.

Credit Aaron Wang / #3113, Sricharan Vagvala / #2105, Adam Gall / #2084, and the retained cover notes. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.

[VictorLiwentao]

OQ2 follow-up attempt (deferred; OQ2 still open)

A candidate package research/selected-stock-finite-c-packet/ @ cd6666300 tried to treat Sp(72,2)×14826 as a uniform C(w) packet via assembler stock=group*physical, a constant-2642 width probe, and a coarse residual restore fixture (divisor=5). Soft-overlap / weak-need deferred: the OQ2 question remains a maintainer admission on the already-published Sp×14826 / A=0 candidate; the width probe is tautological; the D=5 fixture does not use the real packet and cannot unlock outer ledger adoption. No separate CrocSwap PR opened. OQ2 stays open.