QUINCUNX: A Discovery Engine for the World's Sparse Domains, & Where They Join — Ars Inquirendi

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QUINCUNX: A Discovery Engine for the World's Sparse Domains, & Where They Join

Blueprint and First Registered Test on Historical Pre-Print-Era Evidence

Stephen Pink, ChatGPT (5.6 Sol, OpenAI), Grok (4.5, xAI) and Claude (Fable 5, Anthropic) · This version: 12 August 2026, 19:15 UTC

Edoardo Tresoldi, Basilica di Siponto (2016) — the lost early-Christian basilica partly reconstructed in wire mesh above its own ruins. Photo: mauritius images GmbH / Alamy.

Abstract

For fifty years, machines have generated conjectures and killed them against evidence one domain at a time: Graffiti in graph theory, BACON and Eureqa in physical law, Robot Scientist in yeast genetics, FunSearch and its successors in problems a program can score. Each required a hand-built hypothesis language and evaluator. QUINCUNX instead attempts a general loop that has not previously been implemented as a whole: Mint conjectures; Select them against evidence; Grade the mechanisms behind the survivors; Promote the strongest into reusable, explicitly scoped inference instruments; and apply those instruments to incomplete records to Infer what the surviving record does not contain.

What makes such an assembly newly possible is the conjunction of large language models, modern computation and extensive machine-accessible data. Language models provide something approaching a general conjecture language: they can generate hypotheses in volume, operationalize prose claims against documented datasets, write machinery to test them, and move ideas across domains that previously required separate specialist systems. QUINCUNX consequently moves the principal bottleneck from conjecture generation towards severe selection. A possible further product follows from that generality: at sufficient scale, the engine may reveal where apparently separate domains of knowledge actually join, as mechanisms or inference instruments generated in one body of evidence prove testable in another.

Its intended scope is broad, but particularly important are fields in which decisive experimental or computational oracles are unavailable. These are domains of found data : evidence accumulated for other purposes, often unrepeatable, incomplete, survivorship-shaped, unevenly measured and mutually dependent. Historical evidence provides an extreme case. QUINCUNX’s first registered masked-ground-truth test therefore created an artificial historical lacuna in the Epigraphic Database Heidelberg (EDH), a completed scholarly corpus of roughly 82,000 Roman inscriptions. Thirty-three of its sixty-six provincial files were left unfetched while the engine froze twenty-five conjectures and sixteen quantitative predictions derived from the half available to it; the concealed files were then fetched, reconciled against the source and mechanically scored.

The first registered run demonstrated inference into a deliberately concealed part of a known historical dataset: information extracted from the visible part had measurable predictive purchase on pre-specified properties of the hidden part. Several estimates landed close to their targets, including an overall non-Latin share predicted at 2.42% and observed at 2.42%. More importantly, a subsequently registered comparison with structure-blind baselines showed substantial positive predictive skill for the two linguistic-geography differentiations, while the corresponding marble differentiations performed worse than the naive baseline. The same procedure therefore rewarded structural inference where it travelled and penalized it where it did not. Of twenty-five registered conjectures, nineteen survived their first tests, five were killed and one became undecidable.

The run also demonstrated why inference over found data requires more than successful prediction. Defects were encountered in statistical construction and data instruments; these were preserved in the record, diagnosed, repaired under registered rules where the correction was mechanically determined, and separated from subsequent questions of independent certification. More generally, dataset integrity and construction-path independence must be demonstrated rather than assumed; model memory is a possible contamination route; model-coded variables require provenance and independent validation; mechanisms must survive adversarial rivals rather than merely accompany correlations with plausible stories; and promotion must account for statistical power, multiplicity, calibration and the effective number of independent evidential paths. Data cleaning, reconciliation and instrument repair are therefore part of the engine itself rather than preliminary housekeeping.

Above all, inferred quantities must never harden into evidence for later rounds. QUINCUNX therefore builds breadth, not height : its inferences may direct the search for new evidence, but they may not...