Triple
T10389330
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Weil representation |
E244847
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Maslov index
The Maslov index is a topological invariant that assigns an integer to loops or paths of Lagrangian subspaces in symplectic geometry, capturing their phase change or winding behavior.
|
E860126
|
NE FINISHED |
How this triple was built (4 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: Maslov index | Statement: [Weil representation, relatedTo, Maslov index]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Maslov index Context triple: [Weil representation, relatedTo, Maslov index]
-
A.
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.
-
B.
Poincaré–Hopf theorem
The Poincaré–Hopf theorem is a fundamental result in differential topology that relates the sum of the indices of a vector field’s isolated zeros on a compact manifold to the manifold’s Euler characteristic.
-
C.
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.
-
D.
Atiyah–Bott fixed-point theorem
The Atiyah–Bott fixed-point theorem is a fundamental result in equivariant cohomology that expresses global invariants, such as indices of elliptic operators, in terms of local data at the fixed points of a group action.
-
E.
Lefschetz
Lefschetz is a surname most notably associated with Solomon Lefschetz, a pioneering mathematician in algebraic topology and geometry.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Maslov index Triple: [Weil representation, relatedTo, Maslov index]
Generated description
The Maslov index is a topological invariant that assigns an integer to loops or paths of Lagrangian subspaces in symplectic geometry, capturing their phase change or winding behavior.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Maslov index Target entity description: The Maslov index is a topological invariant that assigns an integer to loops or paths of Lagrangian subspaces in symplectic geometry, capturing their phase change or winding behavior.
-
A.
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.
-
B.
Poincaré–Hopf theorem
The Poincaré–Hopf theorem is a fundamental result in differential topology that relates the sum of the indices of a vector field’s isolated zeros on a compact manifold to the manifold’s Euler characteristic.
-
C.
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.
-
D.
Atiyah–Bott fixed-point theorem
The Atiyah–Bott fixed-point theorem is a fundamental result in equivariant cohomology that expresses global invariants, such as indices of elliptic operators, in terms of local data at the fixed points of a group action.
-
E.
Lefschetz
Lefschetz is a surname most notably associated with Solomon Lefschetz, a pioneering mathematician in algebraic topology and geometry.
- F. None of above. chosen
Provenance (5 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_69d381b5116081908d85227bab6d3c0c |
completed | April 6, 2026, 9:49 a.m. |
| NER | Named-entity recognition | batch_69d4e9b40dd8819080ac839487020a44 |
completed | April 7, 2026, 11:25 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d795b2423c8190a7c0e9b6fcbcc6db |
completed | April 9, 2026, 12:04 p.m. |
| NEDg | Description generation | batch_69d7998acbf881909b6f063c4bf2d0a6 |
completed | April 9, 2026, 12:20 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69d79aa0cc5481908bc14cda8fb6e8b1 |
completed | April 9, 2026, 12:25 p.m. |
Created at: April 6, 2026, 12:05 p.m.