Triple
T5837373
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hodge theory |
E129504
|
entity |
| Predicate | studies |
P1945
|
FINISHED |
| Object | Hodge star operator |
E251240
|
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: Hodge star operator | Statement: [Hodge theory, studies, Hodge star operator]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hodge star operator Context triple: [Hodge theory, studies, Hodge star operator]
-
A.
Lefschetz operator
The Lefschetz operator is a linear operator in Kähler geometry that acts on differential forms by wedging with the Kähler form, playing a central role in the Hard Lefschetz theorem and Hodge theory.
-
B.
Dirac operator
The Dirac operator is a fundamental first-order differential operator on spinor fields that generalizes the classical Dirac equation and plays a central role in geometry, topology, and quantum field theory.
-
C.
dAlembert operator
The d'Alembert operator is a second-order differential operator used in relativistic wave equations to describe how fields propagate through spacetime.
-
D.
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.
-
E.
Levi-Civita symbol
chosen
The Levi-Civita symbol is an antisymmetric tensor used in mathematics and physics to represent orientations, cross products, and determinants in multiple dimensions.
- 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_69c0084af79c81908af128ccc29983d0 |
completed | March 22, 2026, 3:18 p.m. |
| NER | Named-entity recognition | batch_69c034a48750819099ae917ae2b54e6d |
completed | March 22, 2026, 6:27 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c0a19a6554819086cdae499f4d2247 |
completed | March 23, 2026, 2:12 a.m. |
Created at: March 22, 2026, 3:54 p.m.