Price the plane-port u=2 screen against the rank-8 cell's 16-child sl…

[unpaidmoon]

Change and mathematical scope

Negative pricing result. No new κ. Selected conditional κ stays 836330098538459/500000000000000000 (0.001672660197076918).

The ideal cell selected centre + local mass at rank ≤ 8 + two unpaid coordinates passes a = 1/98 after 16 added rank-1 children on the nine-call uniform pool and fails at 17. That cell is not a producer. The recorded u=2 endpoint is the plane-port contract. Its source-bound copy invoice C = 224 overspends the two unpaid coordinates (293/292). The decoder-free shrink screen still has relaxation moment above 1 at a = 1/98, by at least 68 rank-1 children, which is past the cell's whole 16-child allowance.

This is not a rank-8 delivery of mass 5586, not a new coverage law, and not a supplier admission.

Task and overlap

• Base: bb4bccbf42844d2801487450727c2f63e10d1d0f (canonical CrocSwap/integer-mult-bounds main). Priority revision 6.
• Head: ec150978dfc52df7755ac52c6caaf501366a00db.
• Task: complex-new-helper-inventory, scope changed. The card asks for a new physically realizable inventory. This session stops on the handoff's pricing test instead of synthesizing one.
• Handoff: Discussion Handoffs and requests for independent checks #1166 comment 19029639, which points at the next task in Discussion FINDING / HANDOFF: the complex budget is a* ≈ ν/Λ — a lever map for step changes #2278 comment 19029577 (PR Certify integer-count budgets for three ideal lever combinations (no new kappa) #3889).
• Ordered eligible list, chronological on Handoffs and requests for independent checks #1166 from comment 19016211, after dropping this round's delivered work (Price flag 9's head-step co-host at exactly +2 rank mass #4107–Price the cut58 ADDRESS swap against the separable response menu. #4149 and the two fork-only duplicates), later DONE notes, and tasks already performed by an open PR:
  1. (7, 18) / (7, 20) functional census (comment 19021170, question 1).
  2. Largest child rank a physical local word on the selected template can emit (comment 19021222).
  3. Invoice-level ownership audit of the composed T488 profile (comment 19022532, question 1).
  4. Priced physical rank-8/u2 contract against the 16 extra rank-1 children (comment 19029639). This session.
• Nearest predecessors: PR Certify integer-count budgets for three ideal lever combinations (no new kappa) #3889 (integer slack; not a producer), PR Certify the ideal combined-lever budget grid of the selected complex local word (screening; no new kappa) #3874 (ideal grid), research/plane-port-copy-budgets (the shrink screen), research/paired-plane-native-payload (the C = 224 invoice). None of those prices the screen against the 16-child boundary.

Validation

CPython 3.12.3, standard library only.

python3.12 -I -B research/rank8-u2-plane-port-slack/verify.py
python3.12 -B scripts/research_package.py --package research/rank8-u2-plane-port-slack

Observed:

PASS_RANK8_U2_PLANE_PORT_SLACK extra_pass=16 shrink_deficit=68 unchanged_deficit=147 above_saturated_cell=true native=293/292 no_new_kappa=true
PASS_REGISTERED_RESEARCH_PACKAGE research/rank8-u2-plane-port-slack outcome=completed

The same verifier passed under python3 -O -B. Controls recompute the {8:698, 2:1} optimum, the 16/17 boundary, the line-port idle 1646, the native ratio 293/292, and reject a moved selected κ. A near-empty u=2 word passes a = 1/98, so the plane-port failure is not a dead cost engine.

Not run: Lean, Docker, the selected cold replay, the plane-port bit screen, and discussion 1587's exactness check.

Credit

Nick Petalas (PR #3874) and ToikY (PR #3889) for the integer cell and the 16-child question. ctoth and discussion 1587 for the plane-port contract. JosieElliston for research/plane-port-copy-budgets. Jeremy Diviney and the PR #2203 lineage for the native payload account. Douglas Colkitt for research/complex-local-word-ceiling. Sagar Thakrar for the PR #1012 coverage identity.

Prepared by unpaidmoon with substantial Cursor Grok assistance. No independent human or formal-kernel review is claimed. New work is Apache-2.0.

Open next questions

Linked from research/rank8-u2-plane-port-slack/TASK.json:

1. Is there a u=2 producer whose paid children have rank at most 8 and whose additive bill is at most 16 rank-1 children on this nine-call cell? First step: one literal histogram at a = 1/98. Blocker: the selected line-port word pays the unpaid=1 identity.
2. Can the 112 rank-2 drops be replaced by a charge of at most 1792/9 per call without losing the I_2 endpoint? First step: one native word with C ≤ 199. Blocker: the one-array interface needs two totals per block.

Workflow feedback (optional)

#1200

The ordered #1166 list is recoverable, but later DONE comments leave several numbered next tasks, so two careful readings can differ by a slot. A single current-status line on each handoff, naming the one remaining question, would make item selection stable.