Research

Claims with receipts attached.

We publish the proof, the refutation, and the machine-checked artifact bundle that lets you reproduce either one. Where a result is negative, we publish that too.

Empiricalv2.0

An Empirical Study of Prompt-Cache Efficiency in Six LLM Agent Harnesses

Measures how six production agent harnesses use — and waste — provider prompt caches, and what the resulting cost delta looks like across a realistic workload.

Agents

Trophies Are Not Tools: Priming Agents With Past Success

Injecting an agent's prior successes into context is widely assumed to help. We measure when it helps, when it actively degrades performance, and why the two cases are hard to tell apart in advance.

Mathematics

A Proof of Graffiti 290

A complete, machine-checked proof of the Graffiti 290 conjecture, with the search that found it and the certificate that verifies it.

Mathematics

A Proof of Graffiti 292

Settles Graffiti 292 in the affirmative, with a reproduction bundle that re-derives every step from source.

MathematicsRefutation

Graffiti 284: A Refutation

A counterexample to Graffiti 284, together with the exhaustive search that produced it and the independent check that confirms it.

Mathematics

Anatomy of the First Jacobian Counterexample

Dissects the structure of the first counterexample found in the Jacobian programme — what generated it, and what it rules out.

Mathematics

Cyclic Rigidity and the Jacobian Conjecture in Dimension Two

A rigidity result constraining the two-dimensional case, with the full computational search that established it.

Mathematics

Sym³ Origin of the Jacobian Counterexample

Traces the counterexample back to a symmetric-cube construction, explaining why it appears exactly where it does.

Mathematics

Power-Weighted Lifts for Higher-Weight Keller Maps

Extends the lift construction to higher-weight Keller maps and reports what the extension does and does not settle.

Mathematics

Machine-Verified Corollary Mining for the Jacobian Conjecture

An automated pipeline that mines, states and verifies corollaries of the Jacobian programme without human selection in the loop.

Mathematics

Erdős 835: A Primality Sieve and Machine-Checked Small Cases

A sieve construction for Erdős 835 plus exhaustive machine-checked verification of the small cases.

Why every paper ships an artifact bundle

A result you cannot re-run is a claim, not a finding. Each bundle contains the source, the search parameters, the certificate and the exact command that regenerates the result from scratch — so disagreeing with us is a matter of running it, not of trusting us.