Triple

T9809597
Position Surface form Disambiguated ID Type / Status
Subject Herbrand's theorem E238234 entity
Predicate relatedTo P37 FINISHED
Object compactness theorem E100620 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: compactness theorem | Statement: [Herbrand's theorem, relatedTo, compactness theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: compactness theorem
Context triple: [Herbrand's theorem, relatedTo, compactness theorem]
  • A. completeness theorem for first-order logic chosen
    The completeness theorem for first-order logic is a fundamental result in mathematical logic, proved by Kurt Gödel, which states that every logically valid first-order formula is provable from the axioms of first-order logic.
  • B. Hamilton’s compactness theorem
    Hamilton’s compactness theorem is a fundamental result in geometric analysis that provides conditions under which a sequence of Riemannian manifolds with controlled curvature and injectivity radius admits a smoothly convergent subsequence.
  • C. Tarski–Mostowski–Robinson theorem
    The Tarski–Mostowski–Robinson theorem is a fundamental result in model theory that characterizes when a class of structures is first-order axiomatizable, linking definability properties with closure under ultraproducts and isomorphisms.
  • D. Herbrand's theorem
    Herbrand's theorem is a fundamental result in mathematical logic and proof theory that characterizes the validity of first-order formulas via finite sets of ground instances, forming a basis for automated theorem proving.
  • E. Löwenheim–Skolem theorem (via additional arguments)
    The Löwenheim–Skolem theorem is a fundamental result in model theory stating that any first-order theory with an infinite model has models of all infinite cardinalities, leading to the so-called Skolem paradox about the existence of countable models of set theory.
  • 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_69ca84defac48190abc1148804f184c1 completed March 30, 2026, 2:12 p.m.
NER Named-entity recognition batch_69cdb220310c8190a16ca0b746f0ef7a completed April 2, 2026, 12:02 a.m.
NED1 Entity disambiguation (via context triple) batch_69d1cc5b4dd8819088c86946b4eb8a39 completed April 5, 2026, 2:43 a.m.
Created at: March 30, 2026, 8:29 p.m.