Triple

T25457154
Position Surface form Disambiguated ID Type / Status
Subject Birkhoff’s representation theorem for finite distributive lattices E637942 entity
Predicate describesAsIsomorphic P29599 FINISHED
Object lattice of lower ideals of a finite poset 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: lattice of lower ideals of a finite poset | Statement: [Birkhoff’s representation theorem for finite distributive lattices, describesAsIsomorphic, lattice of lower ideals of a finite poset]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: describesAsIsomorphic
Context triple: [Birkhoff’s representation theorem for finite distributive lattices, describesAsIsomorphic, lattice of lower ideals of a finite poset]
  • 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. isLocallyIsomorphicTo
    Indicates that two structures are isomorphic within some local neighborhood or restricted region, even if they may differ globally.
  • C. 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.
  • D. isQuasiIsomorphicTo
    Indicates that two mathematical objects, typically chain complexes, are related by a morphism inducing isomorphisms on all their homology groups.
  • E. 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.
  • 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_69e75db8bab08190baca80b4a8c315fd completed April 21, 2026, 11:21 a.m.
NER Named-entity recognition batch_69f606c79ad081908369605f72e65ca6 completed May 2, 2026, 2:14 p.m.
PD Predicate disambiguation batch_69f602ce79ec8190b8336c2b9de18ac7 completed May 2, 2026, 1:57 p.m.
Created at: April 21, 2026, 2:10 p.m.