Bit word R480: totals on dead registers, c = 0.001574753352953808650916 (+0.595% over #493)

[DreamingOfClouds]

One change to #493's E8 bit word. In R489, the nine decoder totals each get a fresh register. Here each total is
formed on a register that is already dead, and the host is the last eligible register of the total's combination.
#493's generator already supported dead hosts but took the first register, and that word fails the official finite
prefix bill. Everything else is #493's word, gate for gate. The result is R = 480, the R ≥ 480 bound #493's
README argues for its family (an analysis under its stated hypotheses: this partition, three branches per source,
totals in phase A; not machine-checked).

	R	five-stage payload (limit: < 2^104)	bit c (#472 eleven-stage whole-residual pipeline, as in #493)
#493 (fresh totals)	489	100 bits	0.001565442026981656908596
#493's generator, dead hosts, first register	480	129 bits, refused by columns_h	–
this PR: dead hosts, last register	480	102 bits, PASS	393688338238452162729/250000000000000000000000 = 0.001574753352953808650916 (+0.5948%)

κ does not change, because the side that binds is the complex side. With #484's complex b (Lemmas A and G) κ =
662515748707749/500000000000000000 = 0.001325031497415498. With #471's it is 0.001303530097714685, and with #458's
0.001295523322678044. The bit gain is headroom for any complex supplier above #493's c.

Exploration outside the package (not run by verify.py): over needer swaps and first, last and random total hosts at
R = 480, every variant we priced gave the same c.

What is in research/e8-r480-dead-totals/

• code/adapt.py: derives the three files this package runs from Conditional κ = 0.001303530097714685: an E8 bit word with 489 helpers, sources as carriers (0.001325 with #484's draft complex supplier) #493's files, using 8 listed string edits (each
  anchor found exactly once). The generator change is sorted(combo) → sorted(combo, reverse=True) in the dead-host
  choice. The audit and local audit get R = 480 and the R480 word path. Every other script is Conditional κ = 0.001303530097714685: an E8 bit word with 489 helpers, sources as carriers (0.001325 with #484's draft complex supplier) #493's, unchanged.
• data/bitE8mut-r480.json.gz: rebuilt byte for byte from Conditional κ = 0.001303530097714685: an E8 bit word with 489 helpers, sources as carriers (0.001325 with #484's draft complex supplier) #493's frozen plan. data/hosting-r480.json: Conditional κ ≈ 1.2375517e-3: idle-axis hosting of helper residuals (+9.2% over #434) #442's
  hosting programme, as run by Conditional κ = 0.001303530097714685: an E8 bit word with 489 helpers, sources as carriers (0.001325 with #484's draft complex supplier) #493's host_select.py, rediscovered exactly by the verifier.
• verify.py: (full) Conditional κ = 0.001303530097714685: an E8 bit word with 489 helpers, sources as carriers (0.001325 with #484's draft complex supplier) #493's verify.sh unchanged as parent. Then, for R480:
  • κ = 8.75481145306751e-4: first E8 bit word (complex-bound; +9.29% over #352) #370's stock checker refuses source destinations, as for Conditional κ = 0.001303530097714685: an E8 bit word with 489 helpers, sources as carriers (0.001325 with #484's draft complex supplier) #493; the relaxed copy passes, with exact F2 replay.
  • κ = 1.048005508028206e-3: mutable-basis Hamming packets (≈2^-9.89814; conditional; complex +4.97%) #425 interface checks (literal cleanup), plus 11 word mutants and 2 hypothesis controls.
  • Legality, five- and eleven-stage formal columns (payload 102 bits), record and mutable-source mutants.
  • Gram on 672 frames.
  • Conditional κ = 0.001263365464781156: eleven-stage R740 hosting with complete row bound #445 geometry, Conditional κ = 0.001292099559442278: R715 shared kernel, target mixing and whole hosting #472 emitter, R = 480 hosted audit (42,240 whole residuals, all template mutations rejected), and
    the invoice, both moment engines and the 47 strict outer inequalities with Complex supplier b ≈ 1.327·10⁻³ (+4.7%) on whole-residual hosting: shared-donor kernel and entrance gauges with paid residual wrappers (conditional on two lemmas) #484, Conditional kappa = 0.001274548075945587: full-nine-axis kernel normalization and same-owner spectator borrowing #471 and Conditional κ = 0.001274032589159993: complex kernel with paid residual adapters #458.
  • Controls: Conditional κ = 0.001303530097714685: an E8 bit word with 489 helpers, sources as carriers (0.001325 with #484's draft complex supplier) #493's own first-register variant is refused (129 bits), and Conditional κ = 0.001303530097714685: an E8 bit word with 489 helpers, sources as carriers (0.001325 with #484's draft complex supplier) #493's R489 c is reproduced exactly through
    its unmodified files.
• Finite invoice: the dead-hosted totals lengthen the cancellation-free chains. The physical prefix becomes 5,479 bits
  (charged 5,504), and the three-level coefficient 16,491 bits (charged 16,512). These enter only the finite cutoffs,
  and every invoice assertion passes.

BOOST_INCLUDE=/path/to/boost python research/e8-r480-dead-totals/verify.py /absolute/new/output --light   # skips #493's verify.sh
BOOST_INCLUDE=/path/to/boost python research/e8-r480-dead-totals/verify.py /absolute/new/output

Scope

The scope is #493's, unchanged: all of #472's eleven-stage composition interfaces and #425's mutable-source interface
(checked by #493's interface.py). Complex savings are cited from their receipts, not rebuilt. No unconditional
theorem is claimed.

Credits

eumemic (#493: the R489 carrier-skeleton word, the generator with its dead-register option, the relaxed checker, the
interface checks and the R ≥ 480 family argument). Through #493: Zhihao Chen (#425, #386), DreamingOfClouds (#463, #315,
#484), DaysSky (#442, #381), chafreaky (#445, #451, #472, #458), Dylan Crow (#370), icekylinx (#433), Dugongue (#471,
#483), Jacob Sussman (the E8 unit).

Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.

🤖 Generated with Claude Code

[Mister-Meeseeks]

Integrated on main in 9449300, with original commit history and individual credit retained.

Your R480 dead-register totals are integrated and used by the selected #535/#510 composition. The changed word and eleven-stage pipeline were replayed. A maintainer portability correction checks exact feasibility and residual histogram when HiGHS chooses a different tied allocation; the frozen physical witness still passes the unchanged owner audit.

Maintainer review and exact scope · Contributor record. The multiplication claim remains conditional on the inherited all-size/realization/analytic interfaces; these checks do not establish a complete unconditional theorem.

Thank you for contributing this work.