Triple
T24806517
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Verdier duality |
E620670
|
entity |
| Predicate | expressesAsIsomorphism |
P29599
|
FINISHED |
| Object | H_c^i(X, F) ≅ H^{-i}(X, D_X F)^∨ under finiteness conditions |
—
|
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: H_c^i(X, F) ≅ H^{-i}(X, D_X F)^∨ under finiteness conditions | Statement: [Verdier duality, expressesAsIsomorphism, H_c^i(X, F) ≅ H^{-i}(X, D_X F)^∨ under finiteness conditions]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: expressesAsIsomorphism
Context triple: [Verdier duality, expressesAsIsomorphism, H_c^i(X, F) ≅ H^{-i}(X, D_X F)^∨ under finiteness conditions]
-
A.
isAssociativeUpToIsomorphism
Indicates that a binary operation is associative in a structural sense, meaning any two ways of parenthesizing a finite product are related by a canonical isomorphism rather than strict equality.
-
B.
isIsomorphicTo
chosen
Indicates that two structures have a one-to-one, structure-preserving correspondence between their elements, making them equivalent in form even if not identical in content.
-
C.
isQuasiIsomorphicTo
Indicates that two mathematical objects, typically chain complexes, are related by a morphism inducing isomorphisms on all their homology groups.
-
D.
isLocallyIsomorphicTo
Indicates that two structures are isomorphic within some local neighborhood or restricted region, even if they may differ globally.
-
E.
isDiffeomorphicTo
Indicates that there exists a smooth, bijective map between two spaces whose inverse is also smooth, so the spaces are equivalent in the sense of differential topology.
- F. None of above.
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_69e2fabf26bc8190b191faac8f67065b |
completed | April 18, 2026, 3:30 a.m. |
| NER | Named-entity recognition | batch_69f44a417a58819081777e18dda149fd |
completed | May 1, 2026, 6:37 a.m. |
| PD | Predicate disambiguation | batch_69f442a977b08190b44eac040cb90211 |
completed | May 1, 2026, 6:05 a.m. |
Created at: April 18, 2026, 4:50 a.m.