Triple
T10512061
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Enrico Betti |
E247938
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object | Betti numbers |
E790522
|
NE 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: Betti numbers | Statement: [Enrico Betti, notableWork, Betti numbers]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Betti numbers Context triple: [Enrico Betti, notableWork, Betti numbers]
-
A.
Betti numbers
chosen
Betti numbers are topological invariants that count the number of independent cycles or holes in each dimension of a topological space, reflecting its underlying shape and structure.
-
B.
Poincaré duality
Poincaré duality is a fundamental theorem in algebraic topology that relates the homology and cohomology groups of an oriented closed manifold in complementary dimensions.
-
C.
Milnor number
The Milnor number is an invariant in singularity theory that measures the complexity of an isolated critical point of a complex hypersurface or function.
-
D.
Lusternik–Schnirelmann category
The Lusternik–Schnirelmann category is a numerical homotopy invariant of a topological space that measures the minimal number of contractible open sets needed to cover it, playing a key role in critical point theory and algebraic topology.
-
E.
Alexander–Spanier cohomology
Alexander–Spanier cohomology is a cohomology theory in algebraic topology defined using cochains on all finite subsets of a space, notable for its generality and close relationship to Čech and singular cohomology.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
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_69d381c4aa948190942e1d803143fb0e |
completed | April 6, 2026, 9:49 a.m. |
| NER | Named-entity recognition | batch_69d509b5fcb8819087a23a2b26aecd70 |
completed | April 7, 2026, 1:42 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d8dcf65f808190993dbacde2df20eb |
completed | April 10, 2026, 11:20 a.m. |
Created at: April 6, 2026, 12:27 p.m.