Triple

T22329092
Position Surface form Disambiguated ID Type / Status
Subject de Rham cohomology E551975 entity
Predicate isomorphismType P29599 FINISHED
Object H^k_{dR}(M) ≅ H^k_{sing}(M;ℝ) LITERAL 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: H^k_{dR}(M) ≅ H^k_{sing}(M;ℝ) | Statement: [de Rham cohomology, isomorphismType, H^k_{dR}(M) ≅ H^k_{sing}(M;ℝ)]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: isomorphismType
Context triple: [de Rham cohomology, isomorphismType, H^k_{dR}(M) ≅ H^k_{sing}(M;ℝ)]
  • A. isIsomorphicTo chosen
    Indicates that two structures have a one-to-one, structure-preserving correspondence between their elements, making them equivalent in form even if not identical in content.
  • B. isAssociativeUpToIsomorphism
    Indicates that a binary operation is associative in a structural sense, meaning any two ways of parenthesizing a finite product are related by a canonical isomorphism rather than strict equality.
  • C. isAutomorphismGroupOf
    Indicates that a group is the full automorphism group consisting of all structure-preserving bijections (automorphisms) of a given mathematical object.
  • D. automorphismGroupIsomorphicTo
    Indicates that the automorphism group of one structure is isomorphic, as a group, to the automorphism group of another structure.
  • E. isDiffeomorphicTo
    Indicates that there exists a smooth, bijective map between two spaces whose inverse is also smooth, so the spaces are equivalent in the sense of differential topology.
  • F. None of above.

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_69e11e482f788190b78d1588fc26d606 completed April 16, 2026, 5:37 p.m.
NER Named-entity recognition batch_69f1576ab52c819087563cd778d6bc5e completed April 29, 2026, 12:57 a.m.
PD Predicate disambiguation batch_69e73004d9e88190bb862319a5aea06b completed April 21, 2026, 8:06 a.m.
Created at: April 16, 2026, 8:43 p.m.