Moving visuals on this page — measured at 0.26% brightness change per frame and zero flashes per second; your reduce motion setting stops them. What moves, and how it was measured

Mathematical plates that draw themselves — prime counts, orbits and lattices rendered live rather than shipped as pictures. It runs continuously while on screen, and it pauses on its own whenever it scrolls out of view.

We measured it rather than guessing: the largest frame-to-frame change in average brightness is 0.26%, and it produces zero flashes per second against the threshold of three set by WCAG 2.3.1. That is well under the limit, and it is not a promise about any individual: if moving images are a problem for you, you should not have to assess ours.

Everything animated on this site honours your system’s reduce motion setting — turn it on in your operating system or browser and these pages stop moving, with nothing else lost. All the mathematics is in the text and the still figures.

Provenance

This page audits itself while you watch.

You can copy this site. Every byte of it is served to your browser and can be saved. The scripts are minified and several are obfuscated, so they are harder to read than we would like; the checks below do not depend on reading them — they compare what the page computes against constants published where we cannot edit them.

What a copy cannot do is make a DOI resolve to it, or a company register list it, or the OEIS agree with it. So instead of defending the pixels, this page checks the things underneath them: four computations run in your own browser, right now, against constants published where we have no ability to edit them.

If one of these ever fails on the real site, it is telling you something true and we would want to know. The failures are shown as plainly as the passes.

Four checks, no assertions

Run the audit

?

Math: a SHA-384 over 524,288 shipped bytes compared against a digest printed in a deposited paper; the Mertens function summed to 100,000 and checked against ten published OEIS values; a full iterated-prisoner’s-dilemma round-robin re-deriving Axelrod & Hamilton’s structural result. Dev: about 200 lines of plain JavaScript, no dependencies, running under a nonce-based CSP that forbids every third-party origin. The hashing is crypto.subtle; everything else is integer arithmetic. Why in the browser: a server telling you it verified itself is a server asking to be trusted. This asks you to trust nothing — the bytes are fetched in your tab and the arithmetic happens on your machine.

Nothing runs until you press the button. It takes about a second, most of which is the 512 KB tablebase.

How the ledgers are kept

A hash chain, tampered with in front of you

Three ledgers on this site — API registrations, bug reports, the factory’s discoveries — are hash-chained: each row stores the hash of the row before it, and its own hash is SHA-256 over a canonical encoding of that previous hash and its fields. Below, a made-up ledger of ten entries is chained with crypto.subtle, then one byte of one entry is edited and the chain recomputed. The edited entry and every entry after it stop matching the stored hashes; the entries before it still verify. That is the whole guarantee: not who edited, but that something was, and from where on — and it binds us as much as anyone else.

The encoding is JSON.stringify([prev, fields…]), not concatenation: with concatenation, text could move between two fields without the hash noticing. Recomputed in the build with an independent SHA-256.

Being precise about it

What this proves, and what it does not

ClaimDoes this page establish it?
The chess data here is the data that was depositedYes The digest is in a paper with a DOI, which is a record we cannot revise.
The mathematics on this site is realYes Two of the checks re-derive published results from scratch in your browser and would fail loudly if the arithmetic were decorative.
This work belongs to KodamaSECExternally Not by this page. By Companies House, the ICO register and ORCID, which you can check independently in a minute.
Nobody can copy this siteNo Of course they can, and this page will run perfectly well on their copy — because the constants it checks against belong to us, and a copy running it is quoting our references.
A copy would be detectableNot by us We cannot see someone else’s server. What we can do is make the original checkable, so that anyone comparing the two has something exact to compare.

That last pair of rows is the honest bottom of this page. A site cannot prove it is not being copied. It can be built so that its claims are anchored outside itself, and then the question stops mattering: a copy inherits the pixels and none of the evidence, and the evidence was always the point.

Credits, fonts & licences

Whose work this is built on

Everything third-party here is self-hosted — no CDN, nothing fetched from anyone else’s origin at runtime — so this is where we name who made it and under what licence. If we have used something and credited it poorly, or missed it entirely, that is a mistake we want to fix: tell us at @KodamaSecLabs. The mathematical attributions are gathered on Challenges.

WhatWhere it is usedByLicence
InterThe body & interface typeface, on every pageThe Inter Project Authors (Rasmus Andersson)SIL OFL 1.1
JetBrains MonoThe monospaced typeface — code, figures, numbersThe JetBrains Mono Project AuthorsSIL OFL 1.1
Oklab colour spaceThe gradients between sections, and the colour of the homepage fieldBjörn Ottosson (2020)public method
Gray–Scott reaction–diffusionThe homepage fieldP. Gray & S. Scott; parameter regimes after J. E. Pearson (1993)public method
three.jsThe 3D endgame landscape and mascot geometrythe three.js authorsMIT
Paper.jsVector drawing for some exhibitsJürg Lehni & Jonathan PuckeyMIT
KaTeXMathematics typesettingKhan Academy & contributorsMIT
Lean 4 & MathlibMachine-checking the proofs (the P-Lean findings)the Lean FRO & the Mathlib communityApache-2.0

The mathematics itself — the ideas, theorems and prior results these build on — is credited at its point of use and gathered on Challenges, where we also keep a standing, open request for the references we may still be missing. Data sources (the OEIS, LMFDB, IBM Quantum) are named where they are used.