Authorship and edition

GitHub contributors: 0x-chad, 0xjohnnydev, 1337isnot1337, 24kHandsome1201, 3xcalibur-tech, 4RchYMing, 6ojo, AAAmirinu, aakashthakkar, adamgall, AdemVessell, AgoraPluribusMichael, ahoy-cmyk, ai-nanachi, akiva8201-dotcom, aladh, alejandrozu, alephnan, AlexS-scale, aliromman, AllStars101-sudo, alluri-ritual, Ambassators, AmnonTamsut, an664, androolloyd, anthonylei, antunishdPursuit, anudeepadi, applebees2, applecrusher, Arham-Tahir64, arhamgarg, arkfx, ArnavSwiggy, artuskg, AryanSudhirDev, at1as, avirazza, azide0x37, BagMan9, bbMisk, bg-grillo-alan, BigCactusLabs, bitplane, Bortlesboat, brianross93, Brodee042, burntout76, cbarber1, cbethin, chafreaky, ChaloupeMusic, cheesegrader, chinmayarvind23, Chrisbryan17, claude, Clear1nsight, codex, columbia-git, commdata2338, conorholds, CubeJerry, cursoragent, Curtis-D, cxnmai, DanieleCorso, dataisfire, DavidAriasC, davidawad, davidgovea, davidNbreslauer, DaysSky, dcharb78, dd-hemant, deftsalt, Deftsalt-debug, digitalis-p, dillona, DLamdata, dleen, DominikScholz, DreamingOfClouds, Dugongue, EdDiboi, ellipsi2, erebos-labs, eumemic, FabrikonManufacturing, FanPUYen, faw01, flyingviper, franciscoyne001-svg, g-guthrie, gaboroa14, gabriele-nespoli, GamingPuzzled, geckods, Gonzalo-Mier, gupt1156, gvconly, hemantjoestar, hevlyo, hexapode, higherbeing, hikaru0706, hipotures, Hope7Happiness, hpst3r, huxint, ianlibanio, icekylinx, ich123, ikeboy, ineffyble, ishan-1729, jacklightChen, jackmgaller, jacobalansussman, jamesyc, jeremydiviney, jeremykothe, jeremykothe2, jerrylin-23, jgilfoil, jmbarrancoidener, jmbarrancoml, joaqcoo, jon314159, jonathanlam, josecarlosgonzalezroque-design, JosieElliston, JoyboyBrian, jp3isme, jsnider3, juper997, just-mn, jwr404, Kairos-Ess, Koroffstrogov, krzysztofwojt, kumagi, Kyu, kyzer1023, littleBro, ljste, lukemansoor, lydakis, Lyy-iiis, M6LI, Mainzu, martinxxx9, mason-hale, Matarener, maxime-fleury, Maximooch, maximussthegreat, mdumitrean, merramil, midhatn, mightyOil, mihir-s-05, mikey1201, mikhailramalho, Mister-Meeseeks, MrPink604, mtpsl, muatfannajm-dot, mythrilium, namredips, navinor, nedveder, NeoKazuya, NicholasStone, nightangelflowerwin-ops, ntedvs, ofennell-quipex, p-romeo, pai-scaffolde, PatatePatatePatate, Paureel, PellaML, petalas, PeterCarp320, philippeVV, pir0u, platypii, princezuda, Pseudoataraxia, RaphaelFakhri, rcfc-jreed, rfu08, RichardHoekstra, roger-sato, rohanarun, rohangar1, Rohansguliani, roife, romainhedouin, RossRichardson, rosswaycaster, ROTl24, rseligm2, rtyu193-rgb, Ryan-Haines, sandersdavid90-droid, Scratch-net, secoussesmusic-coder, sennemmi, seslly, sethburkart-9932, SethBurkart123, shhxera, shiftybitshiftr, SHIN09-git, sk1-j, SovereignSteak, Srikrishnabalaji, ssteeper, starship-s, steph4n-gh, Sudarsh3301, swbiggart, Tairitsu-Aya, taizaki69, tekuuu, TennisBowling, thakrarsagar, the-missionary-company, themilkman216, theon199, ThiagoCAltoe, TMM2009, ToikY, tomdif, Tuafo, unpaidmoon, Varun-Mittal-1001, vectorsss, VibeCodyH, VictorLiwentao, Vlado-V, waynenilsen, WeberChen8128, WilliamLawyer, williamreidrichards, woklerx, Wronskode, x0hu, yonghaozheng64-commits, yongjae321, yssite, ywz65, yzhouwang, zeusinsight, zewelor, ZK-Snarky, zxv.

Authorship is attributed automatically to non-bot GitHub repository contributors and PR authors in the included corpus. Handles are preserved rather than guessing names. This is a draft attribution policy, not evidence that contributors approved this manuscript. Individual contribution sections retain their PR authors. Commit coauthors, reviewers, and non-GitHub antecedents may require additional credit; the pinned CONTRIBUTORS record is retained in the source snapshot.

Edition abcc8bdc8cb1fcd0; repository CrocSwap/integer-mult-bounds; main commit 12fa8c5c844be21bfefb38a19503fbd867a11244.

Abstract

We organize a collaborative investigation of the exponent saving in integer multiplication into a versioned research survey. This edition includes all 3379 merged and open pull requests observed in the source collection: 3073 merged contributions and 306 open proposals. The mathematical setting is the conditional bound \(T(n)=O(n(\log n)^{1-\kappa})\). The selected repository record reports \(\kappa=836330098538459/500000000000000000\). This value is an exponent saving, not a runtime measurement. Each contribution has a stable identifier, source revision, publication status, and its complete available PR description. The paper distinguishes repository selection, experimental evidence, and proposed claims. Its source-derived contribution record is complete for this snapshot; mathematical editorial synthesis remains a separate, explicitly tracked layer.

What a living research paper asserts

A research paper is an argument supported by evidence. In an automated research programme, submissions arrive faster than that argument can safely be rewritten. We therefore separate the current mathematical account from the history of contributions. A change to a PR updates its evidence record; it does not silently promote a claimed result into a theorem. A merged archive may remain only partially reviewed. Failed searches and scoped obstructions belong in the account because they explain which avenues remain plausible and which hypotheses matter.

The unit of explanation is a contribution: the question it addresses, the mechanism it changes, the evidence it offers, its scope, and its relationship to earlier work. Source text supplies the first draft of this explanation. Editorial notes can provide a fuller mathematical account without overwriting contributor testimony. Every editorial note is bound to a source fingerprint and marked stale if that source changes. Frozen editions make the evolving account citable.

Mathematical setting and selected result

The project studies how finite bit and complex primitives support a recursive integer multiplication algorithm under retained framework assumptions. Primitive cost, scheduling, workspace restoration, and transfer to the outer algorithm are separate obligations. A better local construction need not improve the final exponent when a different primitive or transfer condition is limiting.

The following is the repository’s selected record at the pinned main revision, not the largest number found in a PR title:

{
  "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status",
  "kappa": "836330098538459/500000000000000000",
  "decimal": "0.001672660197076918",
  "proof": "docs/research/community-batch1099-review.md",
  "reproduce": "make frontier1094-verify"
}

Selection is reported from the repository; this paper generator does not replay certificates or independently prove the multiplication bound.

How to read the contribution record

Every merged or open PR receives a section below, ordered by PR number within broad navigational themes. Theme assignment is a title-based heuristic, not a scientific classification or ranking. The complete available body is included, with headings normalized and figures linked rather than fetched. Equations and code are preserved through Pandoc. An empty body is disclosed as an explanation gap. An attributed opening passage provides orientation where available; it is not presented as an independently verified summary.

Open contributions remain proposals. Merged contributions remain subject to the pinned review ledger and their stated assumptions. Neither status alone establishes correctness. Source references within a PR retain the contributor’s attribution. This edition does not fetch discussion comments, reviews, diffs, or linked artifacts; claims depending on those sources need further editorial investigation.

PR pages were collected over an interval, not an atomic GitHub transaction. Collection metadata: Live paginated REST pull requests; 2026-10-20T11:46:20+00:00 to 2026-10-20T11:46:55+00:00. Closed, unmerged PRs are retained in the snapshot but excluded from this edition’s requested merged/open corpus. Earlier editions retain contributions that subsequently leave that corpus.

Research programme at this edition

• Additional mathematical investigations: 1415 contributions (1330 merged, 85 open).
• Constructions and quantitative improvements: 901 contributions (777 merged, 124 open).
• Obstructions and negative results: 151 contributions (136 merged, 15 open).
• Research infrastructure and coordination: 68 contributions (55 merged, 13 open).
• Verification, corrections, and reproducibility: 844 contributions (775 merged, 69 open).

Editorial synthesis

Historical editorial narrative: its source bindings require review. Use the selected record above for the current result.

Why the frontier has more than one coordinate

The repository illustrates a central problem for automated research: the newest numerical claim and the selected reviewed result can move at different speeds. At this edition, the selected record still attributes the conditional exponent saving \(0.001672660197076918\) to PR 1094. Meanwhile, PR 3743 examines a moment bracket near \(0.001730418899766071163804\) for a T488 profile. The latter submission expressly claims no new kappa and no word replay. These numbers describe different evidence situations; replacing the former with the latter would erase that distinction.

A useful paper must consequently explain both the mathematical candidate frontier and the frontier of completed evidence. The first asks which construction might achieve a better exponent. The second asks which construction, assumptions and reproduction obligations have actually been admitted by the project’s review process. Neither can be reconstructed reliably by sorting PR titles numerically.

A construction, an arithmetic check, and a structural caution

PR 1094 changes whole-helper placement through rare full-bin patterns while retaining the scalar word and its timings. Its significance is that allocation can change the idle-rank profile even without changing the underlying word. The submission reports a finite witness and extensive local checks, while retaining all-size and transfer assumptions. This is a construction contribution with conditional consequences.

PR 3743 instead narrows the arithmetic interpretation of an existing T488 profile. It reports a sign change across adjacent decimal endpoints separated by \(10^{-24}\). That helps situate the released numerical string relative to the moment root. It does not itself construct or replay the word. This is evidence about the arithmetic of a candidate, a distinct and useful contribution.

PR 3749 supplies a different lesson: two idle histograms with equal total idle mass can fall on opposite sides of the moment threshold. Under the submission’s stated calculation, aggregation therefore loses information relevant to admission. A scalar summary of resource usage is insufficient to replace the rank distribution. This is a scoped structural warning, not a new multiplication bound.

These examples motivate a contribution-complete paper. Constructions, arithmetic checks and restrictions on valid reasoning all advance the research account, even when only some change the selected exponent. The explanations above are editorial readings of the cited submissions and the selected record, not independent replays.

Reproducibility and editorial obligations

The immutable JSON snapshot contains every fetched PR, the pinned selected result, the review ledger, contributor credits, and repository context. A deterministic build requires that snapshot, this generator, any editorial notes, and the recorded Pandoc version. The generator checks corpus coverage and detects stale editorial notes. It does not validate mathematics. Research and writing infrastructure assisted by Codex.

2 editorial explanations are stale in this edition. 0 contributions have no submitted description.

See the pinned docs/research/bottleneck-brief.md.

See the pinned docs/research/research-glossary.md.