Triple
T38438254
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Grothendieck–Lefschetz trace formula |
E904007
|
entity |
| Predicate | cohomologicalDegree |
P161781
|
FINISHED |
| Object | alternating sum over all i ≥ 0 |
—
|
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: alternating sum over all i ≥ 0 | Statement: [Grothendieck–Lefschetz trace formula, cohomologicalDegree, alternating sum over all i ≥ 0]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: cohomologicalDegree Context triple: [Grothendieck–Lefschetz trace formula, cohomologicalDegree, alternating sum over all i ≥ 0]
-
A.
cohomologyDegree
chosen
Indicates the specific degree in which a cohomology group or cohomological class is taken within a graded cohomological structure.
-
B.
cohomologyType
Indicates the type or classification of a cohomology theory or cohomological structure associated with an object or context.
-
C.
cohomologyRing
Indicates that one entity is the cohomology ring associated to another, encoding its cohomological structure and cup-product operations.
-
D.
definesCohomologyClass
Indicates that one mathematical object (such as a cocycle, form, or map) specifies or determines a particular cohomology class in a given cohomology group.
-
E.
hasCohomologyIsomorphicTo
Indicates that the cohomology groups (with their algebraic structure) of one object are isomorphic to those of another object.
- 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_69f76e6a2024819081aa04f4932f89d2 |
completed | May 3, 2026, 3:48 p.m. |
| NER | Named-entity recognition | batch_69fcce7afcd08190906cc3801152656a |
completed | May 7, 2026, 5:40 p.m. |
| PD | Predicate disambiguation | batch_69fcccf140ec8190862d53388a5f40d7 |
completed | May 7, 2026, 5:33 p.m. |
Created at: May 3, 2026, 4:31 p.m.