Triple
T27133869
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Pontryagin duality |
E681628
|
entity |
| Predicate | assertsIsomorphism |
P29599
|
FINISHED |
| Object | canonical evaluation map from a group to its double dual is an isomorphism |
—
|
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: canonical evaluation map from a group to its double dual is an isomorphism | Statement: [Pontryagin duality, assertsIsomorphism, canonical evaluation map from a group to its double dual is an isomorphism]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: assertsIsomorphism Context triple: [Pontryagin duality, assertsIsomorphism, canonical evaluation map from a group to its double dual is an isomorphism]
-
A.
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.
-
B.
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.
-
C.
isLocallyIsomorphicTo
Indicates that two structures are isomorphic within some local neighborhood or restricted region, even if they may differ globally.
-
D.
isIsometricTo
Indicates that two structures or spaces are related by a distance-preserving mapping, making them geometrically identical in shape and size.
-
E.
isIsogenousTo
Indicates that two mathematical structures, typically elliptic curves or abelian varieties, are related by an isogeny, i.e., a non-constant morphism with finite kernel that preserves their group structure.
- 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_69eefacbcc2081909ebf00daa23f1981 |
completed | April 27, 2026, 5:57 a.m. |
| NER | Named-entity recognition | batch_69f62478fd0c81909b7de1d72aa0e2c0 |
completed | May 2, 2026, 4:21 p.m. |
| PD | Predicate disambiguation | batch_69f61b40f02081909bd9c3ea73249163 |
completed | May 2, 2026, 3:41 p.m. |
Created at: April 27, 2026, 9:06 a.m.