[unpaidmoon]

Change and mathematical scope

Scoped negative screen. No new κ and no selected-frontier change. The selected record stays κ = 781451/250000000.

After a whole B or C call returns, ordinary complex-linear use of its audited helper rows cannot raise the complete target-minus-paid moment above Ali Romman's separated capacity bill. For every 0 < t < 1,

F(t) ≤ −L_B Δ_B(t) − L_C Δ_C(t) < 0

as soon as one such call is present, with the audited paid profiles held fixed. Helper rows may be relabelled or mixed into later coordinate-Gaussian targets. Their character budget is exactly the separated helper moment H(t); it is not duplicated.

On the central-axis character the B helper block contributes 408 flipping rows and the main cut contributes 112. Retaining those jobs already fills the joint budget of 520, so one extra flipping target does not fit.

This does not price an internal native rewrite that deletes a paid Gaussian, an odd input gauge, or an address map outside the coordinate algebra. Compiler, precision and outer costs are omitted in the optimistic direction; the sign is already negative.

Task and overlap

Base: 7c49fe32c55de02c2c873655c804b16e4c3fef0a.

Task id complex-new-helper-inventory, priority revision 8, scope changed. The card asks whether a changed helper inventory earns productive credit that survives a complete bill. The ordered eligible handoff taken here is item 3: discussion #1166 comment 19133514, the shared-producer successor of the fixed-224 serial loss. Ali Romman's capacity gate (discussion #5628) closed owner-count expansion inside the separated model and left helper feedback open. This prices that feedback.

Nearest work:

• PR Construct complementary B/C cancellation and prove a serial-consumer cost ceiling (no new κ) #4848 / research/complementary-consumer-feasibility: serial fixed-224 loss. Not rerun.
• research/complementary-caller-capacity-gate: separated whole-caller theorem. Its proof is the live input. This package does not edit it.
• The Raise conditional kappa to 0.00310045 with independent helper splits #5599 helper-subspace construction is a different contract and is not used as permission to split these helpers.

No open upstream PR states this post-call feedback ceiling. κ is unchanged.

Validation

CPython 3.12, standard library, from the repository root:

python3 -B research/shared-helper-feedback-bound/verify.py
python3 -B scripts/research_package.py --package research/shared-helper-feedback-bound

Both passed. The package command printed PASS_REGISTERED_RESEARCH_PACKAGE research/shared-helper-feedback-bound outcome=negative-result. The verifier printed PASS_SHARED_HELPER_FEEDBACK_BOUND with the 256-mask cut identity, both helper-distance polynomials, residual masses 4567 and 4576, the ratio gap for denominators 1..12, and the central-axis 520-versus-521 rejection.

Failure controls: a helper row of character-rank 2 separates from the credited rank-8 charge; the profile rows are read back from the pinned predecessor proof.

Not run: native word replay, Clifford phase suite, Lean, compiler or outer admission, and make frontier6030-verify.

Credit

Separated capacity theorem and audited profiles: Ali Romman. Fixed-224 serial loss: Chris R / Clear1nsight, from Dugongue's B/C source and Cao Yifan / intqwq's audit. This package does not modify those sources.

Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0.

Open next questions

1. Can a helper read inside the native word delete a paid Gaussian and leave a positive complete moment? First step: exhibit the deleted factor and rerun the mass split. Blocked while the paid profile stays the audited one.
2. Can an odd input gauge or a noncommuting address map evade the sign-cut charge? First step: name the gauge and one character where the rank distance falls. Blocked because those maps are outside this algebra.