Planning result: exact overhead budgets for centre-path sharing on the actual selected profiles (no new kappa)

[rtyu193-rgb]

Planning result: exact ΔH overhead budgets for centre-path sharing on the actual selected profiles (no new kappa)

Card: centre-path-sharing (recursive-interfaces track, seed 8daf9514…), scope refined. PR1708 and PR1748 construct the two-call shared centre phases, and PR1708 screened the ideal relaxation (+3.4536% cap). Their open blocker is the overhead ΔH.

This package prices the lever on the actual #1094 complex and PR589 bit histograms: real idle remainder, no ideal packing. Every budget is a sharp integer: that many extra paid children pass the exact moment test, and one more fails. CLAIM. Base 0b1cccf8. Adds only research/centre-sharing-overhead-budget/ (6 files, stdlib, about 60 s).

Results

• With any sharing, the complex side stops binding. For two-call sharing, f(c) − 1 = −4.25·10⁻³ at the bit endpoint. κ becomes bit-limited at 0.001730427469823602 (+3.4536%), reproducing PR1708 on the actual histogram.

  k calls sharing	overhead keeping the full +3.45% (paid mass per call, of 64(1−1/k) saved)
  2	30.66 (rank-1 overhead) / 30.72 (rank-8)
  4	46.60 / 46.72
  8	54.57 / 54.72
  144	62.10 / 62.28

• ΔH budget for two calls. The budget is about 30.5–30.8 units per call at any overhead rank from 1 to 72, for example 4,415 rank-1, 553 rank-8 or 92 rank-48 children in total. Any gain at all requires ΔH below about 32 units per call. Break-even control: re-adding 575 rank-8 children still gains; 576, which recreates the selected histogram, does not.

• The complex side binds by only 1.23–1.33 paid-mass units per call. Removing 177 rank-1, 23 rank-8 or 4 rank-48 children hands the binding role to the bit side.

• The card's stop rule triggers on its own (ideal gain under 10%). For +10% the bit endpoint must reach 0.0018433 (×1.0634). That needs a net bit-side reduction of ≥ 649 paid-mass units (deficit 10,272 → ≥ 10,921; about 20.3 per replica of 32), with the surcharge recomputed. Centre sharing pays off for the headline only jointly with a bit mechanism of that size.

• Scalar overhead is not the constraint. Each extra macro adds 16 adapters at the compiler constant. The binding finite guard (local_primitive_bound < 2⁴⁸) leaves room for ≤ 654,144 extra macros per call; PR1748's two-call reverse phase is 384 macros.

Method and checks

• Reused code: Navinor's exact moment enclosure (selected-suppliers-de-diagnostic) and Wronskode's seed81 bootstrap and 47-slack outer formulas. Both are loaded unchanged as Git blobs at the base.
• Pins: the certificate, PR589 record and invoice receipt are hash-pinned.
• Controls: both selected endpoints are accepted and their next grid points rejected; the selected κ is recomputed; the bit surcharge reconstruction matches; every budget's sharpness is checked; the break-even control above; the script refuses -O.
• Runs: --check-only and the research tests pass.

Limits

• Not established: a selected call pair with common post-A sinks, charts or ownership (PR1748's first blocker), native μ+1 precision, hosting or admission.
• Overhead model: ΔH is modeled as paid children of one rank. Overhead that changes the idle histogram, coverage identity or outer recipe is outside the model.
• Bit side: the bit numbers are removals from the PR589 histogram, not a construction.
• Environment: Windows, CPython 3.14; the registered 3.12 replay was not run locally.

Credit

• Sharing constructions: 1337isnot1337 (PR1708) and ToikY (PR1748); priced here, not admitted.
• Reused code: Navinor and Wronskode.
• Lever framing and coverage identity: Douglas Colkitt (complex-local-word-ceiling) and PR1012.
• Selected construction: Rohan Arun (Conditional kappa 0.001672660197076918: rare-pattern T16 exchanges #1094) and its lineage.

Claude Code (Claude Opus 5.5), one donated session, no subagents, no independent human review. Apache-2.0.

🤖 Generated with Claude Code

[woklerx]

Independent audit of PR#1791 at 00d05a64898571cf57a14310fbcd3507ca99c5ec from main 0b1cccf86e2f5132ed286a26ef0a681a495740ea.

• Sharp limits corroborated: 4415 extra rank1 children or 553 extra rank8 children for two-call sharing at bit threshold.
• Independent numerical method imports neither predecessor logarithm nor Taylor engine.

Validation:

• 73 exact sign checks via independently implemented dyadic powers.
• 11 sharp-overbudget failures and 72 square-root calibrations.
• Original PR1791 registered Python3.12 replay also passes.
• Standalone registered replay on Python 3.12.7 with the unchanged main runner passes.

Limits: Independent code covers complex budget tables; supplied checker covers outer bootstrap and bit surcharge separately; No eligible selected call pair, hosting, precision, native or cold replay established.

Reproduce: python3.12 scripts/research_package.py --package research/centre-budget-independent-audit. Exact sources, original task, controls and Open next questions are in the package.

Credit: Navinor exact pricing and Wronskode outer arithmetic as used by rtyu193-rgb in PR1791; Rohan Arun selected PR1094 and predecessor lineage. Prepared for woklerx with substantial OpenAI Codex assistance; no independent human review claimed. Apache-2.0. No new selected kappa.

Exact committed audit artifact. Commit 82f75445f9a0363595a9ada410ea0d54f77624ca; base 0b1cccf86e2f5132ed286a26ef0a681a495740ea. Coordinated batch, round 01.

[Mister-Meeseeks]

Batch review at 00d05a64898571cf57a14310fbcd3507ca99c5ec.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Actual selected-profile hypothetical centre-sharing budgets are sharp integer single-rank overhead thresholds, checked by exact moments and outer slacks. k2 can retain the bit-limited3.4536% gain only under the missing shared-caller/native/hosting contract; macro headroom and required bit reductions remain planning figures.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.