Triple

T4996544
Position Surface form Disambiguated ID Type / Status
Subject Weierstrass preparation theorem E112259 entity
Predicate relatedTo P37 FINISHED
Object Oka coherence theorem
The Oka coherence theorem is a fundamental result in complex analytic geometry stating that the sheaf of germs of holomorphic functions on a complex manifold is coherent, providing a powerful bridge between analytic and algebraic methods.
E484522 NE FINISHED

How this triple was built (4 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: Oka coherence theorem | Statement: [Weierstrass preparation theorem, relatedTo, Oka coherence theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Oka coherence theorem
Context triple: [Weierstrass preparation theorem, relatedTo, Oka coherence theorem]
  • A. Szekeres–Lindström theorem
    The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
  • B. Bogoliubov–Parasyuk theorem
    The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
  • C. Faddeev’s axioms
    Faddeev’s axioms are a set of conditions characterizing Shannon entropy in information theory, providing an alternative but equivalent axiomatization to the Shannon–Khinchin framework.
  • D. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • E. Noether’s theorem in algebraic geometry (Noether’s AF+BG theorem)
    Noether’s AF+BG theorem is a foundational result in algebraic geometry that provides conditions under which a polynomial vanishing on the intersection of two plane curves can be expressed as a linear combination of their defining equations.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Oka coherence theorem
Triple: [Weierstrass preparation theorem, relatedTo, Oka coherence theorem]
Generated description
The Oka coherence theorem is a fundamental result in complex analytic geometry stating that the sheaf of germs of holomorphic functions on a complex manifold is coherent, providing a powerful bridge between analytic and algebraic methods.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Oka coherence theorem
Target entity description: The Oka coherence theorem is a fundamental result in complex analytic geometry stating that the sheaf of germs of holomorphic functions on a complex manifold is coherent, providing a powerful bridge between analytic and algebraic methods.
  • A. Szekeres–Lindström theorem
    The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
  • B. Bogoliubov–Parasyuk theorem
    The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
  • C. Faddeev’s axioms
    Faddeev’s axioms are a set of conditions characterizing Shannon entropy in information theory, providing an alternative but equivalent axiomatization to the Shannon–Khinchin framework.
  • D. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • E. Noether’s theorem in algebraic geometry (Noether’s AF+BG theorem)
    Noether’s AF+BG theorem is a foundational result in algebraic geometry that provides conditions under which a polynomial vanishing on the intersection of two plane curves can be expressed as a linear combination of their defining equations.
  • F. None of above. chosen

Provenance (5 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_69bd4432b32c81909f3b3c6bd10f0653 completed March 20, 2026, 12:57 p.m.
NER Named-entity recognition batch_69bd72a130708190b9bc1393ba78bfb1 completed March 20, 2026, 4:15 p.m.
NED1 Entity disambiguation (via context triple) batch_69be8a3489f08190a338de8d8be09813 completed March 21, 2026, 12:08 p.m.
NEDg Description generation batch_69be8ac1336c8190a3b6f5b83543dfcf completed March 21, 2026, 12:10 p.m.
NED2 Entity disambiguation (via description) batch_69be8b57411c819082fe711485fe2821 completed March 21, 2026, 12:13 p.m.
Created at: March 20, 2026, 1:34 p.m.