Κ = 0.003 用于交叉整数乘法

Κ = 0.003 用于交叉整数乘法
Κ = 0.003 for integer multiplication crossed

原始链接: https://github.com/CrocSwap/integer-mult-bounds/pull/4441

本 PR 将已验证的新鲜辅助重定时应用于 #4440 的查询稀疏复杂控制器中的全部 19 个完整原生调用，同时保留付费剪枝、空闲调用、主算子以及更强的 BIT 供应器。它产生作者检查的条件界 T(n)=O(n(log n)^(1-0.00300105))，提高 kappa，优于 #4440、#4416 和固定值 0.0023。该构造保留 11,560 个生产字段，将付费调用从 72,902 减少到 69,273（节省 3,629），并保留 800 的秩质量盈余。精确区间将 kappa 置于约 0.003001054183，约有 4.18e-9 余量；变更后的 profile 要求 gamma<97/100。验证包括重放源验证器、原生依赖检查、C++ 优化器补丁再生、预检、最小导航修复以及通过的科学作业，但三个归档 CI 检查仍为红色。该工作不作出选定前沿、无条件、运行时、最优或形式接受主张，并等待审查。致谢归于前代构造及其贡献者。

Hacker News 最新 | 往期 | 评论 | 提问 | 展示 | 招聘 | 提交登录整数乘法的 Κ = 0.003 已被突破 ( github.com/crocswap ) 10 分由 aleph_minus_one 1 小时前 | 隐藏 | 往期 | 收藏 | 2 条评论帮助 aleph_minus_one 1 小时前 [–] 另见 https://bigospeedrun.com/integer-multiplication 回复 fwlr 1 分钟前 | 父评论 [–] 我想提名那里的图犯下某种罪行：它使用从 1e-55 到 1 的对数坐标，其中 1e-55 处有一个结果，1e-18 处有一个结果，1e-3 处有一百万个结果，omgwtfbbq 阈值画在 1……而且每个结果都画成覆盖 6 个数量级的气泡。回复考虑申请 YC 2027 年冬季批次！申请开放至 11 月 2 日。指南 | 常见问题 | 列表 | API | 安全 | 法律 | 申请 YC | 联系搜索：

原文

Apply the verified fresh-helper retiming to all 19 full native calls of #4440's p17 query-thinned complex controller. All 16 paid query shears, whole idle calls, main operators and the stronger BIT supplier are retained. The resulting author-checked conditional bound is

T(n) = O(n (log n)^(1 - 0.00300105)).

This raises κ by 0.00004105 (+1.3868%) over #4440's 0.00296, 11.7098% over #4416's 0.00268647, and 30.4804% over the pinned selected 0.0023.

Complete changed construction

Independent productive fields stay 11,560.
Paid calls fall 72,902 → 69,273, saving 3,629.
Productive/paid rank masses become 260,798 / 259,998, preserving surplus 800.
Each full native unit uses the exact 117-entrance, 42-exit, 395-scalar-frame patch. Both orientations preserve every main operator, scalar order/coefficient, warp contact and owned center.
Exact intervals give 0.0030010541830 < fixed-profile root < 0.0030010541834. An interval proof covers every real 0<C<1; the declared κ leaves about 4.18e-9 headroom.

The new moment requires a repaired paid-tail limit: gamma < 97/100; #4440's 31/32 fails on this changed profile. At tested saving 0.003001052, power 1024, cutoff 20^1024 and target floor 21^1024 pay every original and completion tail. PR4433's generalized logarithmic majorant with power 1000 specifies sufficient uniform rank 2^165315500000000. The enormous word remains algorithmic rather than materialized.

The stronger BIT construction is unchanged: ordinary admission 0.0034 with atom power 0.004. All nine outer rows, 54 current predicates and four functional guards pass. Enlarged local scalar/route constants fit the complete raw nonrecursive budget.

Start at the combined package README, proof and audit of #4440.

Source and validation boundary

The requested 20-minute frontier check found the stronger #4440 during the run. Its exact head 40e22a8 was audited and its registered replay passed before composition. That unchanged predecessor is included in actual publication ancestry. The helper unit is pinned to this PR's original ccdae89. Their source files are unchanged.

Normal combined CPython 3.12.15 registered replay passes, freshly executing both complete source verifiers before the new event-level invoice, two-engine moment check, ceiling, paid tails, compiler, scalar/route and full consumer checks. The native dependency checks both orientations and all 632 arbitrary input columns with two retained interpreters, plus 320 exact phase/boundary records and mutation controls. The published optional C++20 optimizer regenerates the helper patch exactly. Committed-byte/source-history preflight passes at 5f9d871.

The first hosted plan at ccdae89 stopped on four pre-existing selected-status navigation tests. This branch makes the minimal two-document navigation repair while retaining selected κ=0.0023; all six targeted navigation/locale tests pass. The combined 50-file Git-free export replay passes. Final-head hosted planning and the fresh-helper-thinned, fresh-helper-boundary and query-thinned-controllers scientific jobs all pass (workflow evidence). Overall CI remains red on three archived source-pin checks: historical-1042-link, test-suite-locale-reads and d8-mixed-target-seeda97c8e. Hash comparisons confirm that their expected sources already differed from upstream 2a13eb1; their frozen inputs have not been rewritten to force acceptance. The closing frontier check at 20:42 UTC found no stronger new kappa claim.

This is an author-checked conditional construction awaiting review. All-column/native, permitted physical movement and whole-job matching, owned-erasure, finite-template precision, analytic decomposition, fixed-tape, prime and recovery contracts remain premises. No selected-frontier change, unconditional theorem, practical runtime claim, global optimum or formal/independent-human acceptance is claimed.

Credit: #4440's query thinning, stronger BIT and owned-query construction; zxv's native/controller and higher-moment/logarithmic-compiler work; Jacob Alan Sussman's mixed flow; the #4416 paid-completion construction; and the retained native, Clifford, BIT, precision and outer contributors. New helper retiming and the combined construction were prepared for @1337isnot1337 with substantial OpenAI Codex assistance, Apache-2.0. All predecessor notices are retained. No subagents.