Triple
T34546208
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Bott periodicity |
E886930
|
entity |
| Predicate | yieldsIsomorphism |
P29599
|
FINISHED |
| Object | π_{k}(U) ≅ π_{k+2}(U) |
—
|
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: π_{k}(U) ≅ π_{k+2}(U) | Statement: [Bott periodicity, yieldsIsomorphism, π_{k}(U) ≅ π_{k+2}(U)]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: yieldsIsomorphism
Context triple: [Bott periodicity, yieldsIsomorphism, π_{k}(U) ≅ π_{k+2}(U)]
-
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.
hasHomomorphism
Indicates that there exists a structure-preserving map (homomorphism) from one mathematical structure to another.
-
C.
isLocallyIsomorphicTo
Indicates that two structures are isomorphic within some local neighborhood or restricted region, even if they may differ globally.
-
D.
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.
-
E.
hasAutomorphism
Indicates that there exists a structure-preserving bijection from an entity to itself that maintains all relevant relations and operations.
- 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_69f349cff89081908f91e0b064f4833e |
completed | April 30, 2026, 12:23 p.m. |
| NER | Named-entity recognition | batch_69f72020d0088190b143dc17763907dc |
completed | May 3, 2026, 10:14 a.m. |
| PD | Predicate disambiguation | batch_69f71cc8074c81909ae09bea2acf1a09 |
completed | May 3, 2026, 10 a.m. |
Created at: May 1, 2026, 2:02 a.m.