Triple

T14859942
Position Surface form Disambiguated ID Type / Status
Subject Proofs and Refutations E349460 entity
Predicate usesExample P1259 FINISHED
Object Euler’s polyhedron formula E54784 NE FINISHED

How this triple was built (2 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Euler’s polyhedron formula | Statement: [Proofs and Refutations, usesExample, Euler’s polyhedron formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Euler’s polyhedron formula
Context triple: [Proofs and Refutations, usesExample, Euler’s polyhedron formula]
  • A. Euler’s polyhedron formula chosen
    Euler’s polyhedron formula is a fundamental result in topology and geometry that relates the numbers of vertices, edges, and faces of a convex polyhedron through the equation V − E + F = 2.
  • B. Kepler–Poinsot polyhedra
    The Kepler–Poinsot polyhedra are the four regular star polyhedra that extend the concept of Platonic solids into non-convex, self-intersecting forms.
  • C. The Fifty-Nine Icosahedra
    The Fifty-Nine Icosahedra is a classic mathematical monograph by H. S. M. Coxeter that systematically classifies and analyzes the distinct stellations of the regular icosahedron.
  • D. Euler–Poincaré characteristic formula
    The Euler–Poincaré characteristic formula is a fundamental relation in topology and algebraic geometry that expresses a space’s Euler characteristic in terms of alternating sums of dimensions of its cohomology groups.
  • E. “Solutio problematis ad geometriam situs pertinentis”
    “Solutio problematis ad geometriam situs pertinentis” is Leonhard Euler’s 1736 Latin paper that founded graph theory and topology by solving the Seven Bridges of Königsberg problem.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69d822ed7e1881909b90fca143ad7e34 completed April 9, 2026, 10:06 p.m.
NER Named-entity recognition batch_69ded44598e48190b759a05ed2d9ecaf completed April 14, 2026, 11:56 p.m.
NED1 Entity disambiguation (via context triple) batch_69fe650a43bc8190b836fe690d2a3c71 completed May 8, 2026, 10:34 p.m.
Created at: April 10, 2026, 1:54 a.m.