Triple

T1057180
Position Surface form Disambiguated ID Type / Status
Subject local existence and uniqueness theorem E22820 entity
Predicate category P87 FINISHED
Object existence and uniqueness theorem E22820 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: existence and uniqueness theorem | Statement: [local existence and uniqueness theorem, category, existence and uniqueness theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: existence and uniqueness theorem
Context triple: [local existence and uniqueness theorem, category, existence and uniqueness theorem]
  • A. local existence and uniqueness theorem chosen
    The local existence and uniqueness theorem is a fundamental result in differential equations that guarantees, under suitable conditions, a single solution passing through a given initial point, valid in some neighborhood of that point.
  • B. Peano existence theorem
    The Peano existence theorem is a fundamental result in the theory of ordinary differential equations that guarantees the existence (but not necessarily uniqueness) of solutions under mild continuity conditions on the right-hand side.
  • C. Banach fixed-point theorem
    The Banach fixed-point theorem is a fundamental result in metric space theory that guarantees the existence and uniqueness of a fixed point for any contraction mapping and provides a method for finding it via iterative approximation.
  • D. implicit function theorem
    The implicit function theorem is a fundamental result in calculus and differential geometry that guarantees, under suitable smoothness and nondegeneracy conditions, the local solvability of equations for some variables as differentiable functions of others.
  • E. Lax equivalence theorem
    The Lax equivalence theorem is a fundamental result in numerical analysis stating that for a well-posed linear initial value problem, consistency and stability of a finite difference scheme together imply its convergence.
  • 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_69a493dada0481909c43649f9843ea91 completed March 1, 2026, 7:30 p.m.
NER Named-entity recognition batch_69a4b8da80dc8190b79beaf509910725 completed March 1, 2026, 10:08 p.m.
NED1 Entity disambiguation (via context triple) batch_69ac5ea233ec819081d81164e540fe71 completed March 7, 2026, 5:21 p.m.
Created at: March 1, 2026, 7:42 p.m.