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Research // what we found, and what we helped others find

Research

Our founding members’ own research, the work Aska Digital contributed to, and every repository behind them. Each piece says whose it is, what the people and the AI agents did, and how far the evidence goes. None of it has been through peer review yet, and each piece says so.

Not peer reviewed 7 projects · 5 founding members data/projects.json · 18 Oct 2026

How we workFounding members’ researchWork we contributed toEvery repository

Propose, check, decide: one project at a time

How to read: each project’s own numbers at the three steps every result here goes through: AI agents propose, checkers verify, people decide and sign. Choose a project, or press play to go through all six.

Ctrl //

  1. Agents propose

    7,459,491

    repeating dips found by the first full-sky search in NASA’s public TESS data

    src: eumemic/exoplanets README.md, full-sky search table

  2. Checkers verify

    13,986

    of them matched no known planet or TESS Object of Interest and passed all 17 automated tests of LEO-Vetter, a published vetting tool

    src: README.md, full-sky search table

  3. People decide and sign

    665

    counted as planet candidates on 14 Oct 2026, each with predicted transit times anyone can test; none confirmed yet

    src: README.md, note of 14 Oct 2026 (58c6318)

Exoplanets · eumemic, with AskaCandidates · not confirmedNot peer reviewedOpen Exoplanets

Sources: each station’s own line; numbers from data/projects.json and the project dossiers, checked 13–14 Oct 2026.
Show all six as a table
Each project at the three steps
ProjectAgents proposeCheckers verifyPeople decide and sign
Exoplanets7,459,491 repeating dips found by the first full-sky search in NASA’s public TESS data (eumemic/exoplanets README.md, full-sky search table)13,986 of them matched no known planet or TESS Object of Interest and passed all 17 automated tests of LEO-Vetter, a published vetting tool (README.md, full-sky search table)665 counted as planet candidates on 14 Oct 2026, each with predicted transit times anyone can test; none confirmed yet (README.md, note of 14 Oct 2026 (58c6318))
Integer multiplication below n log n1,334 pull requests opened by people and their agents in the first week (git ls-remote refs/pull/*/head, 13 Oct 2026)47 assembly inequalities the current record passes in exact arithmetic, with independent owner and pricing audits (CrocSwap/integer-mult-bounds README, PR #1094 review)17 reviewed records selected by maintainer Doug Colkitt, 9 to 13 Oct; all conditional on the unreviewed manuscript (certificates/selected-result.json history (20 commits, 17 distinct values))
Incentre lattice5 runs an AI search loop went from density 0.4686 to the Kepler bound 0.7405 in about 11 minutes (autoresearch-fold/results.tsv)16,240 exact numbers, every one ≥ 0, that rule out a collision anywhere along the fold (3,248 pair tests) (results/fold-continuous-fcc/certificate.json)v2 preprint published and signed by Ahraz Arifuddin on Zenodo, 13 Oct 2026; no person other than the author has checked the proofs yet (doi.org/10.5281/zenodo.23340326)
After the 722722 manuscripts written by one OpenAI model, with about three hours of computing per result on average (openai/math README @ adc7f12 and fd4aeeb)300 / 719 top-line results formalized in Lean by OpenAI’s own count on 7 Oct; its catalogue marks them unreviewed (openai/math history.md @ fd4aeeb)3 manuscripts withdrawn by OpenAI on 7 Oct after a sign error; none refereed by people so far (openai/math history.md @ fd4aeeb)
mobius-x13 versions of the claimed theorem, researched and drafted with Claude (mobius-x1 README.md, NOTICE)0 / 3,456,000 failures in Aska’s full-network check of Theorem 2; Lean checks the arithmetic core (certificates/run_e1_rep_h10_bad0.txt)0 human referees so far; it was refereed only by AI agents, and says so (mobius-x1 README.md)
gf2m-circuits112 gates for an AES-field multiplier at depth 6, found by a search that scores every candidate wiring by total gates (2010 record: 117) (papers/Jain_GF2m_multipliers_2026.pdf, Table 1)65,536 input pairs every AES-field multiplier is tested on, all of them; 30 Lean proofs that circuits compute the right answer (their gate counts are not Lean-checked) (multipliers/tools/verify.py; multipliers/lean, sbox/lean)2 papers posted in the repository by Swapnil Jain, who signs them; not peer reviewed (papers/ in the repository)

00//How we work

The same rule for people and machines

Agents propose. Checkers verify. People decide.

Every result on these pages went through the same three steps, and each one tells you which step it has reached.

AI agents propose, freely. An agent is an AI model set loose on a task: it reads, writes code, runs it, looks at what happened and tries again. Agents are cheap and do not tire, so we let them try far more ideas than a person could, and most of those ideas fail. A proposal costs almost nothing, so on its own it proves nothing.

Checkers verify, strictly. A checker is a program that accepts a claim only if it passes a test with no room for opinion: arithmetic done exactly, with no rounding; every case of a finite search, run to the end; or a proof checker such as Lean, which accepts a proof only if every single step follows from the rules. A checker does not care who, or what, made the claim.

People decide, and sign. A person picks the question, reads what the checker actually confirmed, decides whether that is the thing we meant, and puts their name to it. When something turns out to be wrong, a person answers for it.

Every claim carries its status. Each result wears a plain label saying how far it has climbed, such as CLAIMED, PREPRINT, CONDITIONAL, PEER REVIEWED or LEAN-VERIFIED. A claim is never dressed up as a proof, and a check of one step is never sold as a check of the whole.

Where each project stands

How to read: five rungs of evidence, weakest at the bottom. Each project sits on the rung of its headline claim, the weakest part of its status line; point at or focus a project for its full status.

  1. Formally verified

    A proof checker such as Lean accepted every step.

    none of our projects yet

  2. Independently replicated

    Someone else did it again and got the same answer.

    none of our projects yet

  3. Peer reviewed, or deployed

    Checked by outside experts, or in daily use.

    none of our projects yet

  4. Preprint, or conditional

    Written out in public; or true if an earlier, unreviewed result is.

    Incentre lattice Integer multiplication below n log n After the 722 gf2m-circuits

  5. Claimed, or candidate

    Someone says so, with evidence still to come.

    Exoplanets Maxwell's point charges mobius-x1
Source: each project’s status in data/projects.json. A project can have parts on higher rungs: the Fourier record inside “After the 722” is Lean-verified, and every gf2m-circuits circuit is Lean-proved to compute the right answer, though its gate counts and the comparisons with earlier records are not.

01//Founding members’ research

Point at or focus a card to run its figure

Five lines of work by founding members and Foundation0, all in the open.

Each card says whose work it is and exactly what Aska Digital, or an AI agent working for Foundation0, added. Every number has its source beside it.

GeometryAhraz Arifuddin · Aska Digital

Incentre lattice

From a doodle to the densest packing of balls.

PreprintNot peer reviewed

Aska Digital’s own work. Founding member Ahraz Arifuddin chose the questions and signs the claims; AI models from Anthropic and OpenAI drafted most of the proofs, code and checks, and the paper records which model did what.

THE DOODLE, DRAWN EXACTLYr = (√2−1)/2 ≈ 0.2071

A square, its diagonals, one dot per triangle at its incentre (the centre of the circle that fits inside it). Neighbouring dots end up √2 − 1 apart.

On Foundation0SiteRepositoryPreprint v2 (Zenodo)

Astronomyeumemic, with Aska

Exoplanets

Faint shadows in old starlight: 665 small-planet candidates in public NASA data, as of 14 Oct 2026.

Candidates · not confirmedNot peer reviewed

Founding member eumemic’s project, built with Claude Code. Aska sent ten merged pull requests, one of which built the first version of its website; one fix, restoring light curves the data reader had dropped (PR #6), led to a re-search that added 120 counted candidates.

SCHEMATIC · STACKING PASSES64 passes stacked

Why stacking works: noise shrinks like 1/√N as passes are added, until a dip too small to see once stands out. The dip is TIC 4206066’s published 398 ppm, 1.7 h signal; the noise is simulated.

On Foundation0SiteRepository

AlgorithmsDoug Colkitt + crowd

Integer multiplication below n log n

A public race of people and AI agents to multiply huge numbers in fewer than n log n steps.

Conditional · maintainer-reviewedNot peer reviewed

Founding member Doug Colkitt’s race (CrocSwap). Founding member Rohan Arun held the reviewed record on 14 Oct (PR #1094), and eumemic sent 80 pull requests. Aska built the live race tracker that grew into this site, and submitted two small claims that were never reviewed and were soon overtaken.

LOG₂ κ · DATED 23 SEP → 13 OCTlog₂κ −9.22

Every reviewed record on a halvings scale, from the machine-written paper’s 2−182 to 2−9.22. All of them rest on that unreviewed paper.

On Foundation0RepositoryRace tracker (feed of 11 Oct)The story

MathematicsMembers + crowd

After the 722

OpenAI published 722 machine-written maths papers. Here is what people and their agents did next.

Mostly conditionalNot peer reviewed

Starts from OpenAI’s 722 machine-written manuscripts. Founding members Rohan Arun and Ryan Shea took six of its families further within a week, and Doug Colkitt’s race a seventh; eumemic and many others joined in.

TIMES BETTER, LOG SCALE6 results

How many times better six numbers got in a week, on a log scale. Long bars mean loose first proofs, not important results.

On Foundation0openai/mathMath, faster (essay)

Physicspoint-charges · Claude, asked by Ahraz Arifuddin

Maxwell's point charges

How many points of balance can a few electric charges have? Exact, computer-checked counts for four, five and six charges.

ClaimedComputer-checked counts · not reviewed by a person

Foundation0’s own point-charges repository, a project of its physics0 hub. Asked by founding member Ahraz Arifuddin to find new areas for Foundation0, Claude (Anthropic) chose this question and wrote the code, certificates and note in one session. No person has reviewed it yet.

SIX CHARGES · DISTANCE ON A LOG SCALE29 equilibria · Maxwell: 25

Every certified equilibrium of the six-charge configuration, seen down the axis, with distance from the centre on a log scale from 0.0001 to 1 (the rim): the inner clusters are 50 to 5,000 times smaller than the triangle. Filled: 1-saddles; rings: 2-saddles.

On Foundation0StudyNoteCertificates

02//Work we contributed to

Swapnil Jain’s repositories

Two repositories by Swapnil Jain, with a part from us.

These are Swapnil Jain’s results. Aska’s agentic team sent one pull request to each, and each card says exactly what that pull request did.

CircuitsSwapnil Jain + Aska

mobius-x1

A claimed way to compute a basic transform on bits (the GF(2) Möbius transform) with fewer one-bit XOR steps than Yates’ 1937 recipe, for astronomically large inputs.

Not peer reviewed · AI-refereed only

Swapnil Jain’s repository. Aska wrote and ran the full-network check behind Theorem 2, its strongest version: 3,456,000 bank swaps tested in a network of size h = 10, with zero failures (merged PR #1).

PASCAL MOD 2 · 32 INPUTSrow 31 · 32 odd

The matrix the transform computes, made here from Pascal’s triangle with the odd entries filled. The claimed saving only appears when the input has billions of digits.

On Foundation0RepositoryAska PR #1

CryptographySwapnil Jain + Aska

gf2m-circuits

Fewer logic gates (the tiny on/off circuits chips are built from) for the arithmetic inside AES, the cipher that protects most web traffic.

Lean-verifiedTested on every inputNot peer reviewed

Swapnil Jain’s repository. Aska contributed verified multipliers for four more binary fields, built with the papers’ method (merged PR #1); they are not records.

GATES vs DEPTH · AES FIELD−5 gates at depth 6

Each new multiplier is checked on all 65,536 input pairs and proved in Lean. Hollow mark: the 2010 record.

On Foundation0RepositoryAska PR #1

03//Every repository, by member

No portraits, by design

Everything each founding member has on the record.

Five people who already work this way, and the repositories behind their work. “Builds on” names the family of OpenAI’s machine-written manuscripts a repository starts from.

Show //
22 of 22 entries

M·01

Rohan Arun

@rohanarun

Builds software that lets AI coding agents work on open research problems, including Auto-research-agent, a Mac app that sends Codex or Claude Code to an open problem in one click. With those agents, the most active contributor to the integer-multiplication race, and the author of conditional refinements to four of OpenAI's machine-written papers.

Main projectAuto-research-agent

M·02

Doug Colkitt

@Mister-Meeseeks

Started and maintains the open race to multiply huge numbers in fewer than n log n steps, the best speed proven so far. People and their AI agents took a machine-written paper's saving of 2−182 and grew it to about 2−9.2 in a week, every step checked in exact arithmetic, all still resting on the unreviewed original paper.

Main projectinteger-mult-bounds

M·03

Ryan Shea

@shea256

Builds tools for AI-run experiments, such as autofoundry, which rents GPUs from four cloud providers and runs the same experiment across them. Working with Codex and Claude on OpenAI's machine-written problems, they ranked first, as of 14 Oct 2026, on a public board for exact Fourier transforms below n log n, with a Lean-verified result shared with Jeremy Kothe, whose circuit it uses.

Main projectautofoundry

M·04

eumemic

@eumemic

Builds software for long-running AI agents and puts those agents to work on open science. The main project, built with Claude Code, searched NASA's public TESS data for more than four million stars and as of 14 October 2026 counts 665 small-planet candidates too faint to see in any single month of data.

Main projectExoplanets

M·05

Ahraz Arifuddin

@ahrazzle

Runs Aska Digital's team of AI agents and points it at open questions. The main project follows a childhood doodle (a square, its diagonals, one dot per triangle) into crystal geometry, ending in an exact proof that a loose ball-and-rod scaffold folds, without stretching, into the densest stacking of equal balls.

Main projectIncentre lattice

  • Incentre lattice
    PreprintNot peer reviewed

    Exact fold from density 0.2233 to 0.7405 (the Kepler bound), with 16,240 exact certificate coefficients.

    On Foundation0Incentre lattice

  • Exoplanets: pipeline fixes and website
    Merged · credited

    Ten merged pull requests to eumemic's search: four pipeline fixes, one of which (PR #6) led to a re-search that added 120 counted candidates; an independent check; tests; documentation; and the first version of the project website.

    On Foundation0Exoplanets

  • mobius-x1: full-network check
    Merged

    The whole-network test behind Theorem 2: 0 failures in 3,456,000 checks.

    On Foundation0mobius-x1

  • gf2m-circuits: field multipliers
    Merged · not records

    Verified multiplier circuits for more binary fields, e.g. GF(29) in 136 gates against a 142 baseline.

    On Foundation0gf2m-circuits

  • Foundation0
    This site

    Began as a live tracker of the integer-multiplication race.

Source: data/members.json (names as each member shows them on GitHub or in their own published work; status lines as each repository states them). Member pronouns: they/them.

04//Sources

Report an error and we fix it in the open

Where this page comes from.

  1. Projects, statuses and numbers: data/projects.json; each number’s own source file or commit is printed beside it on its card.
  2. Founding members and their repositories: data/members.json.
  3. OpenAI’s 372 result families and our field classification: data/openai-math-families.json, from openai/math.
  4. The reviewed κ of the integer-multiplication race is fetched live from certificates/selected-result.json when you open this page; if that file cannot be reached, the card falls back to the newer of this site’s own feed.json and our dated snapshot, and says which it shows and when.
  5. Mistakes: open an issue. Corrections are made in public, in the repository history.