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.