Semantic Research Engine

Every discipline writes the same idea differently. What one textbook calls a rate, another calls a growth constant and a third writes as a single Greek letter. The formula pipeline turns textbook formulas into structure; this engine worked on what the symbols in them mean. It collected the variables, folded the ones that stand for the same thing onto a single concept, and where a variable had no definition at all, it went and found one.

That search is the part worth describing. The engine wrote itself a request for each missing definition and worked through a cascade of sources, each with a standing level of trust: its own graph first, then Wikidata, then Wikipedia, then Semantic Scholar, and arXiv last. The answer carries the trust of the source it came from, so a definition is never just present or absent, it is present on some footing. Between March and 1 August 2026 the engine filed 5,476 such requests for itself and closed every one of them. It has filed none since.

There is a ladder above that, and this is where the honest part begins. A concept counts as labeled when it has a name, defined when it has a definition, connected when it sits next to at least two semantic primitives, and grounded when a trusted source stands behind it. In the archived graph, 122,446 of 169,907 variables are defined, which is 72 per cent. Above that, even the measurement is in doubt: a count in early September found not a single edge between a variable and a primitive, while the archive taken later that month holds about three thousand, and where they came from is not yet settled. The top rung holds nothing either way: no variable is grounded. The code for the decomposition step still exists; nothing runs it. It had not run since the primitive inventory was rebuilt from scratch: the 13,104 machine-generated entries of March were discarded that same month in favour of 63 hand-picked ones, that set grew to 167 over the spring, and in May it was pruned back to the 75 that stand today. Nothing has been decomposed against them since.

What did grow is the folding itself. 81,708 links tie individual symbols to 12,558 shared concepts, up from 6,940 when the register was first seeded from Wikidata. That register is the working part of this engine, and it is the number at the top of this page. Its original promise has only half arrived: structural identity across fields turns up mostly repetition rather than genuine analogy, and the 2,059 cross-domain matches the engine has found rest on the shape of the expressions, not yet on their meaning.

The last full formula signing run was on 26 July 2026. The re-extraction timer that fed this engine is switched off, and since 25 September 2026 the service that carried it is too; the graph it worked in is kept as an archive. None of that is hidden here because a page about an instrument that measures things should be able to say when the instrument stopped.