Triple

T5570610
Position Surface form Disambiguated ID Type / Status
Subject Fermat's theorem on sums of two squares E146190 entity
Predicate hasPrimeCaseStatement P64861 FINISHED
Object An odd prime p can be written as x^2 + y^2 with integers x,y if and only if p ≡ 1 (mod 4) — 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: An odd prime p can be written as x^2 + y^2 with integers x,y if and only if p ≡ 1 (mod 4) | Statement: [Fermat's theorem on sums of two squares, hasPrimeCaseStatement, An odd prime p can be written as x^2 + y^2 with integers x,y if and only if p ≡ 1 (mod 4)]
PD Predicate disambiguation gpt-5-mini-2025-08-07 
Target predicate: hasPrimeCaseStatement
Context triple: [Fermat's theorem on sums of two squares, hasPrimeCaseStatement, An odd prime p can be written as x^2 + y^2 with integers x,y if and only if p ≡ 1 (mod 4)]
  • A. hasCase
    Indicates that one entity is involved in, associated with, or characterized by a particular case, instance, or occurrence represented by another entity.
  • B. hasUndecidableStatement
    Indicates that a formal system or theory possesses at least one statement whose truth or falsity cannot be determined within that system using its axioms and rules of inference.
  • C. primeCondition
    Indicates that a condition or requirement is primary, fundamental, or of highest priority within a given context.
  • D. hasTypeOfCase
    Indicates that an entity is associated with or classified under a particular type or category of case.
  • E. hasPrimeModulus
    Indicates that the associated entity or structure is defined over, or characterized by, a modulus that is a prime number.
  • 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_69c008ffed108190a084602227af6157 completed March 22, 2026, 3:21 p.m.
NER Named-entity recognition batch_69c020502a288190af37f9ebb88fccae completed March 22, 2026, 5:01 p.m.
PD Predicate disambiguation batch_69c01b12826c8190969a584d0f53aa44 completed March 22, 2026, 4:38 p.m.
PDg Predicate description generation batch_69c01f4032408190a4f0d2eb21ebd870 completed March 22, 2026, 4:56 p.m.
Created at: March 22, 2026, 3:37 p.m.