PR draft: the p=19 coded-reverse supplier (draft, verification open)

Status: draft. Not proposed for merge. Several links are exact, but the items in
"Still needs verification" are unresolved and a reviewer should not read this as a
completed supplier.

Title:

Certify conditional kappa 0.0033999964 via the physical p=19 coded-reverse word (complex 0.007578535, BIT 0.0034)

The title follows the repository's own forms: Construct conditional kappa 0.00302015 with joint helper boundaries and Certify conditional multiplication kappa 0.003020165 via critical-root transfer for conditional kappa claims, and
Quotient the complex ambient by span{511}: complex kappa 0.01209185 (outer capped at 0.0034) for a high complex supplier whose outer value is capped. This one is both:
complex 0.007578535, outer conditional kappa 0.0033999964. Shorter alternative if
maintainers prefer the older style:

The physical p=19 coded-reverse word: complex supplier 0.007578535, conditional kappa 0.0033999964 (BIT-capped)

Summary

research/coded-reverse-word-p19/ materialises the p=19 coded-reverse controller
word and prices it. The complex side reaches 0.007578535, the BIT supplier is the
admitted 0.0034, and the strict outer ledger passes at
kappa = 951999/280000000 = 0.0033999964 (+12.58 % over 60403/20000000), failing at
exactly 0.0034 only on actual_bit_above_effective.

What is exact and replayed

Reproduce (about six minutes):

python3 -B research/coded-reverse-word-p19/p19_word.py
python3 -B research/coded-reverse-word-p19/p19_claim.py
python3 -B research/coded-reverse-word-p19/verify.py
python3.12 -B scripts/research_package.py --package research/coded-reverse-word-p19

Still needs verification (why this is a draft)

1. Compiler majorant applicability. The claim rests on the retained PR4433
   power majorant, applied after setting the source module's C to this unit's
   tested saving. Its inequalities are verified and the source states the majorant
   concerns normalised rank-one leaf counts and applies it to a new unit's ranks —
   but no machine-checked proof is supplied that the coded-reverse structure
   (77 recodings, gauge, idles) is immaterial to it. The logarithmic majorant at
   ambient rank 153 caps the tested saving at 611329/200000000, and the endpoint it
   would force (1194/390625, ≈ +1.21 %) is recorded in the receipt.
2. Tail limit. The source certificates are written with δ < 19/20; this word has
   δ = 0.9515606085. The package substitutes 0.97 and shows the decay-block
   argument still closes (0.97¹²⁸ < 1/16). That is a re-derivation argument, not
   a citation.
3. Helper block. The 7,752 helper units of the invoice's T side are inherited,
   not materialised. The counter check shows they are additive, separate mass, and
   PHYSICAL.md declares them autonomous, but no helper gate is replayed.
4. Field-bill admission. The bill is exact and rank-free; its admission under
   the caller's fixed-tape/precision ABI is still a premise.
5. Single implementation. The listing is replayed by one interpreter and one
   data representation. The NumPy cross-check in the companion package cannot run
   here (no NumPy, and the package declares no dependencies).
6. Kernel review, hosted CI, precision/tape/hosting. Untouched by this package.

Audit history

Three adversarial rounds. The first refuted the endpoint (compiler majorant,
completeness, guard convention); the second conceded the repairs but kept the
compiler and guard items conditional; the third is the prompt still outstanding. The
fixes it forced are in the package: the closing swap with its sign placed after the
gauge unload, the tested saving re-derived on the integer grid, the inherited
helper block declared, the compiler receipt calling the source function, and the 36
retained idle calls materialised.

Reviewer's checklist

• Does the power majorant's scope statement license reuse for a structurally
  changed unit, or only for changed ranks?
• Is 0.97 an admissible tail limit for this family, or is 19/20 required by an
  inequality the package has not read?
• Is the helper block genuinely disjoint from the coded roles?
• Does the 396 role-rank from the idles agree with the invoice's role ranks?

Credit retained from PR4940/PR4933/PR4929/PR4433/PR4440/PR4470 as credited in the
package README.