Triple
T6801424
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Poincaré duality |
E156194
|
entity |
| Predicate | characterizes |
P662
|
FINISHED |
| Object | Poincaré duality spaces |
E156194
|
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: Poincaré duality spaces | Statement: [Poincaré duality, characterizes, Poincaré duality spaces]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Poincaré duality spaces Context triple: [Poincaré duality, characterizes, Poincaré duality spaces]
-
A.
Poincaré duality
chosen
Poincaré duality is a fundamental theorem in algebraic topology that relates the homology and cohomology groups of an oriented closed manifold in complementary dimensions.
-
B.
L’Analysis Situs et la Géométrie Algébrique
L’Analysis Situs et la Géométrie Algébrique is a foundational mathematical treatise that helped establish modern algebraic topology and its connections with algebraic geometry.
-
C.
"Algebraic Topology"
"Algebraic Topology" is a foundational mathematical text that develops topological concepts using algebraic methods such as homology and cohomology theories.
-
D.
Alexandrov–Čech cohomology
Alexandrov–Čech cohomology is a topological cohomology theory that computes invariants of spaces using inverse limits over open covers, closely related to and often coinciding with sheaf cohomology.
-
E.
Whitney approximation theorem
The Whitney approximation theorem is a fundamental result in differential topology stating that any continuous function between smooth manifolds can be uniformly approximated by smooth functions.
- 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_69c68826e6a48190a3d220b541e639de |
completed | March 27, 2026, 1:37 p.m. |
| NER | Named-entity recognition | batch_69c6d2e595188190a0bb4b595df3adb2 |
completed | March 27, 2026, 6:56 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c71a9b0cc48190819380aeaf0228e7 |
completed | March 28, 2026, 12:02 a.m. |
Created at: March 27, 2026, 2:16 p.m.