Triple
T38438332
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Euler–Poincaré characteristic formula |
E904009
|
entity |
| Predicate | categoryTheoreticFormulation |
P78878
|
FINISHED |
| Object | alternating sum of dimensions of objects in a finite cochain complex equals alternating sum of dimensions of its cohomology |
—
|
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 of dimensions of objects in a finite cochain complex equals alternating sum of dimensions of its cohomology | Statement: [Euler–Poincaré characteristic formula, categoryTheoreticFormulation, alternating sum of dimensions of objects in a finite cochain complex equals alternating sum of dimensions of its cohomology]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: categoryTheoreticFormulation Context triple: [Euler–Poincaré characteristic formula, categoryTheoreticFormulation, alternating sum of dimensions of objects in a finite cochain complex equals alternating sum of dimensions of its cohomology]
-
A.
categoryOfSheavesOn
Indicates that one entity is the category whose objects are sheaves defined on the other entity (typically a space or site).
-
B.
categorifies
Indicates that one entity provides a higher-level, category-theoretic abstraction or refinement of the structure or behavior of another entity.
-
C.
categorifiedBy
Indicates that something is assigned to or placed within a specific category by another entity.
-
D.
formulatedInTermsOf
chosen
Indicates that one concept, statement, or representation is expressed, defined, or described using the language, framework, or components of another.
-
E.
topologicalCategory
Indicates a classification relationship where something is categorized based on its topological properties or 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_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.