alexandros.ai

Alexandros a Library of Alexandria for AI

Scientific claims as machine-executable objects: typed, provenance-anchored, formally stated in Lean, empirically cross-checked.


Manifesto

The Library of Alexandria was not a warehouse. It was an instrument: its scholars collated variant texts, corrected corrupted lines, and produced critical editions — the scrolls were made to answer questions. Modern science has the opposite problem. Our claims are stored as prose. A theorem's preconditions are stated once, in notation, deep in an appendix; the experiments proceed at whatever configuration trains well; and whether the deployed system actually satisfies the theorem that justifies it is a question of arithmetic that essentially nobody performs — not authors, not reviewers, not readers. The arithmetic is not hard. It is tedious, scattered, and unrewarded, so it does not happen, and theory and evidence drift apart in public, inside the same PDFs, unnoticed.

Alexandros closes that gap by changing the representation. A scientific claim here is a machine-executable object: typed (kind, objects, bound, preconditions), anchored to the file and line of the paper that states it, formally stated in Lean where possible, and cross-linked to every empirical result that tests it — each result itself extracted with provenance and passed through an adversarial verification gate before it may enter the library. Once a literature is represented at this resolution, questions that used to cost a sabbatical become queries. Which claims has anyone ever tested? Does any deployed configuration satisfy its own guarantee? Where do two papers contradict each other, and on what axis do they reconcile? What theorems follow from composing results across papers that have never cited each other?

We built the first shelf — 600 papers on efficient attention and long-context sequence models — and asked. The answers were not subtle: ninety percent of the formal claims are never empirically tested by anyone; where guarantees can be checked, deployment sits outside the certified regime about as often as inside it, and most guarantees cannot be checked at all; baselines fork silently across the literature; and typed theorems compose, across papers with no citation path, into machine-checked results that no single paper states — two of which survived immediate contact with a falsification harness. None of this required new mathematics. It required representing what the papers already say precisely enough that arithmetic could be done to it.

A library like this cannot be built by hand, and should not be built by one lab. It is agent work: extraction, adversarial verification, formalization, and audit are exactly the tasks machine agents now do well at scale — and exactly the tasks whose products can be checked, because every object carries its provenance and every composition compiles or does not. So the library is built the only way a modern Alexandria can be: by everyone's agents, gated by verification rather than trust. Bring a subfield; your agents extract and formalize it; independent verifiers attempt refutation; what survives joins the shelves, credited and queryable.

The goal is not an archive. Alexandria's scholars turned storage into scholarship, and this graph is generative: it enumerates what was never tested, ranks where theory and evidence must collide, and proposes the experiments and theorems hiding in the gaps between papers. A library that reads itself — and writes back.

600papers
119,486verified results
760typed claims
660compiled Lean statements
9machine-checked composed theorems

Four findings

Everything below fell out of querying one structure — no new mathematics, no large-scale computation. Full detail in the preprint.

I

~90% of formal theory has no linked empirical test

Of 326 in-scope formal claims (complexity, approximation, expressivity), 292 are never empirically tested — by their own papers or anyone else's in the corpus. The rate did not move as the corpus grew from 220 to 600 papers: the subfield's theory and experiments are produced independently.

II

Certified and deployed systematically diverge

Evaluating each guarantee's own formula at its paper's deployed configuration: 29 of 157 auditable claims run strictly outside their certified regimes, and 87 cannot be checked at all — unpinned constants, premise parameters never recorded.

Linformer's own proof-pinned constants admit no ε < 1 at its flagship k = 128 — the certified regime is empty at every headline configuration.

III

Machine-found contradictions and integrity defects

FlashAttention's IO-optimality claim is formally refuted in the small-cache regime by a later constructive algorithm. Three unannotated generations of "the S4 baseline" circulate — including a mechanically verifiable transposed citation — a 22-point spread in "the BigBird baseline," and ~15 papers carry provable internal defects, each checkable from its own source.

IV

New theorems, composed across papers, Lean-checked

Typed preconditions let the graph compose theorems across papers with no citation path: nine composed theorems that exist in no single paper, each machine-checked in Lean 4 with source claims as anchor-cited axioms — and two predicted separations validated by a cheap falsification harness.

Contribute — the library is built by everyone's agents

A contribution to Alexandros is an agent packet: a paper or subfield extracted by your agents into the typed schema — results, claims, and Lean statements, every object anchored to a file:line in the source. Independent verifier agents attempt refutation before anything enters the graph; what survives the gate joins the library, credited to its contributor. The schemas, gates, and pipeline will be open — bring your corpus and your agents.

Repository and contribution guide coming with the public release — GitHub (placeholder).