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[ 2026 ]

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beyond-dijkstra v0.1.0: the first implementation of the 2026 successor algorithm, measured and audited down to a false lemma. DOI 10.5281/zenodo.21473443.

Independent researcher · Algorithm engineering

I measure what
theory promises.

In 2025 a new shortest-path algorithm broke the sixty-year-old sorting barrier; in 2026 its authors published a faster successor. I implemented both — the successor for the first time anywhere — verified them bit-for-bit against the papers, and measured them honestly against Dijkstra. The second study went further: it found a counterexample to the completeness clause of the paper's central lemma, and proved by hand what the repaired engine actually guarantees.

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Project · 2026

Out of Time — tabular foundation models on credit default, read the way a bank reads them

The published credit benchmarks find tabular foundation models such as TabPFN and TabICL generally best, on random folds. A bank validates a model out of time: on the loans originated after it was fitted, cohort by cohort, with calibration and population stability read beside discrimination. Out of Time does that for TabPFN-3 and TabICLv2 on the origination vintages of Lending Club and Freddie Mac, beside a weight-of-evidence scorecard and a tuned gradient-boosting model, against kill criteria written before any foundation model was fitted on each book, and deposited after the Lending Club runs and the Freddie Mac fits.

0.656–0.736both models' mean probability over the realised default rate on their own Lending Club context rows, at the shipped temperature of 0.9
2 booksLending Club and Freddie Mac, nine vintage builds on each
97.4–97.6%no-shift samples in which the published delta-method z-test on the PSI rejects, at a nominal 5% and 10 bins
3pre-registrations, every departure from them dated and listed in the paper

The verdict is mixed, and stated as registered. At the temperature the packages ship, both models under-predict default on the very Lending Club rows they were conditioned on, and the temperature alone removes the gap there. On Lending Club no discrimination, calibration or stability kill fires for TabPFN, the calibration one at the margin and only on the matrix that keeps the debt-to-income ratio; for TabICL the calibration kill fires at 0.9 and not at 1.0, on a pooling named after the result and resting on one build, and the stability kill fires on the oldest builds against its own context and inverts against an out-of-sample reference. Every number traces to a recorded run through a claim ledger. The instrument built for the stability readings is released as psi-inference.

Project · 2026

beyond-dijkstra — the successor algorithm, implemented first and audited

In February 2026 Duan, Mao, Shu and Yin sharpened their own sorting-barrier result to O(m √(log n · log log n)). Pure theory, no implementation anywhere. beyond-dijkstra is the first: a Rust port gated bit-for-bit against an audited Python reference, a fifteen-entry audit of the paper's proofs against the running code, and a hand-proved completeness theorem for the repaired engine. The audit found two pseudocode crashes on ordinary graphs and a counterexample to the completeness clause of Lemma 3.7 — the clause that licenses the most standard optimization there is, and a variant that trusts it returns a wrong distance.

1.8–2.2×best engineered variant vs optimized Dijkstra; what remains is Dijkstra carrying the paper's labels
38–182×the faithful implementation's gap across random graphs and a road network
70 verticesthe counterexample graph: a lemma-trusting variant returns 23.59375 for a true 23.546875
n < 2⁴⁰⁹⁶below this size the paper's parameter prescription violates its own validity condition

The algorithm computed exact distances on every input run; one of the proofs that it must does not hold. Both halves of that verdict, and the repair with its proof, rest on the same public verification record.

Project · 2025–2026

logtwothirds — the sorting barrier, measured

Duan, Mao, Mao, Shu and Yin's O(m log^2/3 n) algorithm (STOC 2025) computes shortest paths asymptotically faster than Dijkstra. The theory leaves one question open: does it actually run faster? logtwothirds is a Rust library with Python bindings built to answer that: a faithful implementation verified bit-for-bit against an audited reference (distances and settlement order), an engineered variant family, and a full benchmark record.

1.10–1.20×engineered BMSSP vs optimized Dijkstra at n = 10⁶–10⁷, the smallest published gap
26–128×the faithful implementation's gap, narrowing with n at the predicted rate
n ≈ 2⁴⁰⁰ ⁰⁰⁰extrapolated crossover, beyond any physically storable input
520+adversarial graphs in the bit-exact correctness gate

The verdict is a negative result, stated without spin: the asymptotic advantage is real, and no practical input size realizes it. Along the way the study caught an implementation pitfall in the paper's relax-on-equality rule: a duplicate cascade that random float-weighted tests cannot detect and a real road network triggers immediately.

About

Engineer, educator, fast learner

I teach programming (Python, AI, C#, game development), and before that I translated and proofread scientific and patent literature in physics and computer science. My background is a physics-and-math education (Peter the Great St. Petersburg Polytechnic University), and my working style is the one this research shows: read the primary source, build the thing, verify it rigorously, and report what the measurements actually say.

I'm looking for a role in AI, research or engineering. The problems that pull me are the frontier ones: new models and methods, quantum computing, computational biology.

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