INTEGER MULTIPLICATION / LIVING PAPER
A research programme, continuously documented

Integer multiplication,
in motion.

A living account of the mathematics, the evidence, and the people moving the frontier.

Source collection completed 2026-10-20T11:23:49+00:00 · Edition fc9de1a2fad36725
Checks for changes every 30 minutes. GitHub scheduling can be delayed.

Read the current account →Download PDF · 5,193 pagesLaTeX sourceRead all contributions
3,375merged and open contributions
258credited GitHub contributors
1current editorial explanations

One programme. Different kinds of evidence.

The selected repository record reports conditional κ = 0.001672660197076918. Larger numbers in submissions may represent candidates or partial calculations. Selection, publication and mathematical verification are separate events.

A transparent draft. Every included PR has its submitted explanation. Deeper editorial explanations are counted separately. The automated refresh imports evidence and updates the manuscript; it does not independently prove or review results.

Progress over time

Follow the selected mathematical checkpoints and the activity around them. A merged contribution does not, by itself, establish a stronger bound.

Selected conditional κ · recent gains

Latest selected change: 2026-10-13T18:45:23Z · 6.7 days before this snapshot. No later selected change is recorded.

Latest step: Δκ = +4.72077871e-07

Last 8 changed checkpoints. Vertical axis: gain in κ relative to 0.001635183729255778. The scale adapts to these checkpoints, so small advances remain visible. Time ends at the last change; the full timeline below includes the subsequent plateau. Dates are UTC.

Recent selected kappa gains relative to baseline-3.00e-067.87e-061.87e-052.96e-054.05e-05Oct 12Oct 13Oct 13Oct 13Oct 132026-10-12T21:01:12Z: κ = 0.001635183729255778; gain from baseline +0.00000000e+002026-10-12T22:36:34Z: κ = 0.001635527380375392; gain from baseline +3.43651120e-072026-10-13T05:57:09Z: κ = 0.001661202643272239; gain from baseline +2.60189140e-052026-10-13T06:44:14Z: κ = 0.001661634653669567; gain from baseline +2.64509244e-052026-10-13T13:30:30Z: κ = 0.001661957774647029; gain from baseline +2.67740454e-052026-10-13T15:06:01Z: κ = 0.001661960547713947; gain from baseline +2.67768185e-052026-10-13T18:05:11Z: κ = 0.001672188119205421; gain from baseline +3.70043899e-052026-10-13T18:45:23Z: κ = 0.001672660197076918; gain from baseline +3.74764678e-05
Full history · absolute κ and time since last change

Selected conditional κ

Higher means a larger exponent saving, not a measured runtime improvement. Begins at the first selected-result record. Click a checkpoint to inspect its source; dates are UTC.

Selected conditional kappa over time0.00000.00050.00090.00140.0018Oct 09Oct 12Oct 14Oct 17Oct 202026-10-09T04:53:33Z: selected κ = 0.00046091692026-10-09T05:55:01Z: selected κ = 0.0004721430852026-10-09T06:01:09Z: selected κ = 0.0004721547912026-10-09T12:32:26Z: selected κ = 0.0006618855492595982026-10-10T14:08:14Z: selected κ = 0.0007235715900074642026-10-12T01:55:19Z: selected κ = 0.0015177609778203312026-10-12T13:10:36Z: selected κ = 0.0015849311117857872026-10-12T14:41:59Z: selected κ = 0.0016022789219832122026-10-12T16:59:30Z: selected κ = 0.00161272137265532026-10-12T21:01:12Z: selected κ = 0.0016351837292557782026-10-12T22:36:34Z: selected κ = 0.0016355273803753922026-10-13T05:57:09Z: selected κ = 0.0016612026432722392026-10-13T06:44:14Z: selected κ = 0.0016616346536695672026-10-13T13:30:30Z: selected κ = 0.0016619577746470292026-10-13T15:06:01Z: selected κ = 0.0016619605477139472026-10-13T18:05:11Z: selected κ = 0.0016721881192054212026-10-13T18:45:23Z: selected κ = 0.001672660197076918
Checkpoint values and source revisions
Date (UTC)Selected κSource
2026-10-090.00046091696aed8701
2026-10-090.000472143085e2a02cac
2026-10-090.00047215479186b30e03
2026-10-090.000661885549259598d697aaa7
2026-10-100.00072357159000746491e29e7b
2026-10-120.001517760977820331a1e7d848
2026-10-120.0015849311117857871c1e42f0
2026-10-120.001602278921983212270c2458
2026-10-120.00161272137265531db1fbe6
2026-10-120.0016351837292557782e9ed969
2026-10-120.0016355273803753925c5567d1
2026-10-130.0016612026432722392cdd93d0
2026-10-130.001661634653669567d6dfd8f2
2026-10-130.0016619577746470293b83e4f1
2026-10-130.0016619605477139473825dc0e
2026-10-130.00167218811920542187db776d
2026-10-130.0016726601970769180a31ad88

Contribution activity

● Submitted ● Merged

Cumulative submitted and merged contributions09281,8562,7843,713Oct 07Oct 10Oct 13Oct 17Oct 202026-10-07: 2 submitted2026-10-08: 39 submitted2026-10-09: 59 submitted2026-10-10: 70 submitted2026-10-11: 134 submitted2026-10-12: 233 submitted2026-10-13: 901 submitted2026-10-14: 1537 submitted2026-10-15: 2071 submitted2026-10-16: 2320 submitted2026-10-17: 2594 submitted2026-10-18: 3080 submitted2026-10-19: 3302 submitted2026-10-20: 3375 submitted2026-10-07: 0 merged2026-10-08: 25 merged2026-10-09: 35 merged2026-10-10: 36 merged2026-10-11: 36 merged2026-10-12: 131 merged2026-10-13: 330 merged2026-10-14: 1091 merged2026-10-15: 1385 merged2026-10-16: 2077 merged2026-10-17: 2307 merged2026-10-18: 2503 merged2026-10-19: 2504 merged2026-10-20: 3073 merged

Daily cumulative counts for the current merged/open corpus, not a reconstruction of historical review status. Download graph data.

The contribution record

Explore constructions, corrections, independent checks and negative results. Each page preserves credit and the exact submitted revision.

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Citable editions, retained evidence

Every published edition has an archived source snapshot, manuscript and build manifest. Earlier accounts remain available as the programme changes.

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