Triple
T11219204
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | John Milnor |
E265514
|
entity |
| Predicate | notableConcept |
P201
|
FINISHED |
| Object | Milnor–Wood inequality |
E265520
|
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: Milnor–Wood inequality | Statement: [John Milnor, notableConcept, Milnor–Wood inequality]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Milnor–Wood inequality Context triple: [John Milnor, notableConcept, Milnor–Wood inequality]
-
A.
Milnor–Wood inequality
chosen
The Milnor–Wood inequality is a result in differential geometry and topology that bounds the Euler class of flat circle bundles over surfaces, with important implications for foliations and group actions on the circle.
-
B.
Thurston hyperbolization theorem
The Thurston hyperbolization theorem is a fundamental result in 3-manifold topology that characterizes when certain 3-manifolds admit complete hyperbolic structures, forming a cornerstone of Thurston’s geometrization program.
-
C.
Mostow rigidity theorem
The Mostow rigidity theorem is a fundamental result in geometry and topology stating that, in dimensions greater than two, the large-scale geometry of a complete finite-volume hyperbolic manifold is uniquely determined by its fundamental group, implying strong rigidity for such structures.
-
D.
Hyperbolic Manifolds and Discrete Groups
"Hyperbolic Manifolds and Discrete Groups" is a foundational mathematical monograph that develops the theory of hyperbolic geometry and its deep connections with discrete group actions and low-dimensional topology.
-
E.
Fenchel–Nielsen coordinates
Fenchel–Nielsen coordinates are a system of parameters that describe hyperbolic structures on surfaces by recording lengths and twist angles along a collection of simple closed geodesics.
- 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_69d6aac59460819089b9848b27f57848 |
completed | April 8, 2026, 7:21 p.m. |
| NER | Named-entity recognition | batch_69d7e8eb84c48190b4f3bede254afde2 |
completed | April 9, 2026, 5:59 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e4976f38788190855aed6338d819b7 |
completed | April 19, 2026, 8:50 a.m. |
Created at: April 8, 2026, 9:30 p.m.