Conditional κ = 8.01967436473393e-4: exact integer-lifted shared donors with E8 (+0.1103% over #352)

[Dugongue]

Conditional κ = 801967436473393/10^18 ≈ 8.01967436473393e-4, +0.11032656% over #352.

This adds an own exact signed integer-lifting extension to the installed bit supplier and composes it with ten terminal sinks and one corrected early cache. The complex side remains Sussman's E8 supplier from #352. The entire actual word and stock are repriced; gains are not added.

Side	Coarse saving
Own composed bit word	c = 401305552420403 / 500000000000000000
Unchanged E8 complex input	b = 876248285600677 / 10^18

The bit side binds. This is an incremental finite improvement, not a claim to surpass every later PR or an unconditional multiplication theorem.

Own mechanism

Transport every removed helper READ through the actual signed target suffix, yielding Q_r; let T_r be its complete target response. At a common cold cut, solve explicit integer equations

Q_p = sum_d alpha[p,d] (T_d - Q_d).

Install the donor shears at a common admitted cap, delete the pivot READs, and restore the shears at the full endpoint. Exact response cancellation establishes the target map; literal frame, source, copied-lifetime, bank and finite-cost checks establish admission of this particular word.

The selected witness has 48 disjoint groups, 171 pivots, 283 distinct donors, and 560 nonzero terms. Sixteen terms have coefficient ±2. They become 576 ordinary unit setup ADDs and corresponding restore ADDs; the repeated same-frame operations require no extra rank child. This goes beyond the earlier 146-pivot unit-only witness. Every selected donor still has T_d = 0: no warm-donor compression claim is made.

The kernel removes 1184 initial READs. Its local histogram delta is {1:+165, 2:+315, 3:-315, 4:+21, 5:-21}, saving 171 rank mass. Combined with the ten sinks and the source-corrected cache, local mass falls from 169560 to 169174. Gaussian elimination and integer lifting are standard; the contribution is the exact signed shared-donor synthesis, this new witness, and its admitted composition. Prior kernel/sink/cache identities are credited.

Validation and finite invoice

Run:

python -m pip install -r research/e8-signed-lift/requirements.txt
python -B research/e8-signed-lift/verify.py /tmp/e8-signed-lift-review

Requires Python 3.11+, a GNU-compatible C++17 compiler and Boost headers. Add --cxx / --boost-include if needed. Use a fresh output directory. The replay checks:

• SHA-bound source inputs and deterministic final-word reconstruction;
• all 9148800 retained signed target entries and 9600 removed zero entries;
• every actual clean-source operand span and all 11450 five-stage F2 formal columns with arbitrary dirt;
• frame/COPY legality, both reflected ledgers, six new prime-safe frames and all changed exact projector charts;
• zero-padding-free allocation for 300 physical replicas, with 397002 banks per stage;
• ten nonvacuous omitted-category controls;
• two exact rational moment engines, the complete 10^-16 fallback, all 47 strict outer constraints and excluded adjacent κ;
• the complete finite invoice: stock 3137010 (normalized 627402), selector charge 1806132027000, 57-bit counted primitive coefficient, 92-bit payload prefix.

An additional signed control removes the two actual unit ADDs of an even term. F2 is unchanged, but four signed target entries change by two. This directly checks the reason binary verification alone is insufficient for the extension.

Final word SHA-256:

66ba5f42081c7299bd20be713500d3cce87494851baac7e16f840a3e75ba0055

The unchanged E8 supplier and underlying analytic/compiler interfaces are explicit inherited inputs. Their public mathematical verifiers were not rerun here. No new Lean verification is claimed.

Reuse and preserved research

notes/ contains sufficient transported-response and higher-rank-cap arguments, a construction proof, scoped attempted routes and the final integration record. discovery/ preserves native extraction, bounded integer synthesis and disjoint-selection sources for future extensions; it is optional for replay.

The useful extension is larger exact integer donor bases with actual shared donor charges. Preserved unsuccessful attempts include higher-rank caps, identical-first-frame cohorts, nonzero-total-response donor bases, warm one-donor matches and no-gain trace rewrites. These are restricted search outcomes, not impossibility theorems. Earlier complex retiming candidates are superseded and contribute no added gain to this κ.

Credits

#351 supplies the compact native baseline; #352 supplies the E8 interface and published complex coarse bound. Sussman's E8 source is jacobalansussman/wht-power-saving-lean, commit 9c94857. Earlier community kernel, sink, corrected-cache, frame and assembly mechanisms remain credited in NOTICE.md and the retained source notices. Prepared with OpenAI Codex assistance; Apache-2.0 with retained upstream notices.

[Mister-Meeseeks]

Thank you @Dugongue. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Signed integer lifts of shared donors with E8.

Review and limits: Fresh own-word replay includes signed restoration, exact spans and invoice. Its unchanged complex supplier is explicitly reused, not freshly reverified by this command.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: e59117a865452b4562891d80c3d2b154b60cb5cf. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.