Triple

T5634008
Position Surface form Disambiguated ID Type / Status
Subject Fermat polygonal number theorem E147900 entity
Predicate orderDependentBound P64706 FINISHED
Object for each s ≥ 3 there exists a minimal r(s) such that every positive integer is a sum of r(s) s-gonal numbers 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: for each s ≥ 3 there exists a minimal r(s) such that every positive integer is a sum of r(s) s-gonal numbers | Statement: [Fermat polygonal number theorem, orderDependentBound, for each s ≥ 3 there exists a minimal r(s) such that every positive integer is a sum of r(s) s-gonal numbers]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: orderDependentBound
Context triple: [Fermat polygonal number theorem, orderDependentBound, for each s ≥ 3 there exists a minimal r(s) such that every positive integer is a sum of r(s) s-gonal numbers]
  • A. positionDependsOn
    Indicates that the spatial or ordered position of one entity is determined or constrained by the position of another entity.
  • B. observerDependent
    Indicates that the truth, value, or manifestation of something varies depending on which observer is considering or measuring it.
  • C. orderOf
    Indicates that one entity is arranged, ranked, or sequenced before or after another according to a specified ordering criterion.
  • D. boundFor
    Indicates that something is destined, directed, or scheduled to go toward a particular destination or target.
  • E. orderedBy
    Indicates that one entity has placed a request or purchase for another entity, typically specifying who initiated the order.
  • F. None of above. chosen

Provenance (4 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_69c00907bc8881909ed760d3ed73ef35 completed March 22, 2026, 3:21 p.m.
NER Named-entity recognition batch_69c0226118548190877793dadf6cacba completed March 22, 2026, 5:09 p.m.
PD Predicate disambiguation batch_69c01b1f12ec8190b4b9d9ee31cabe19 completed March 22, 2026, 4:38 p.m.
PDg Predicate description generation batch_69c01f0684908190ae2d14f0bd2ab892 completed March 22, 2026, 4:55 p.m.
Created at: March 22, 2026, 3:41 p.m.