Triple
T2418320
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | John Milnor |
E52357
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Milnor–Wood inequality
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.
|
E265520
|
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: Milnor–Wood inequality | Statement: [John Milnor, notableWork, Milnor–Wood inequality]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Milnor–Wood inequality Context triple: [John Milnor, notableWork, Milnor–Wood inequality]
-
A.
Teichmüller curve
A Teichmüller curve is a complex geodesic in the moduli space of Riemann surfaces that arises from flat surface structures and has rich connections to dynamics, geometry, and number theory.
-
B.
Grothendieck–Ogg–Shafarevich formula
The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
-
C.
Hurwitz bound on automorphism groups of curves
The Hurwitz bound on automorphism groups of curves is a classical result in algebraic geometry stating that a compact Riemann surface of genus at least 2 has at most 84(g − 1) automorphisms.
-
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.
Riemann–Hurwitz formula
The Riemann–Hurwitz formula is a fundamental result in algebraic geometry and complex analysis that relates the genera of two Riemann surfaces connected by a branched covering map, accounting for the ramification data.
- 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: Milnor–Wood inequality Triple: [John Milnor, notableWork, Milnor–Wood inequality]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Milnor–Wood inequality Target entity description: 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.
-
A.
Teichmüller curve
A Teichmüller curve is a complex geodesic in the moduli space of Riemann surfaces that arises from flat surface structures and has rich connections to dynamics, geometry, and number theory.
-
B.
Grothendieck–Ogg–Shafarevich formula
The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
-
C.
Hurwitz bound on automorphism groups of curves
The Hurwitz bound on automorphism groups of curves is a classical result in algebraic geometry stating that a compact Riemann surface of genus at least 2 has at most 84(g − 1) automorphisms.
-
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.
Riemann–Hurwitz formula
The Riemann–Hurwitz formula is a fundamental result in algebraic geometry and complex analysis that relates the genera of two Riemann surfaces connected by a branched covering map, accounting for the ramification data.
- 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_69ab495622948190bc6bc6e4cddaf645 |
completed | March 6, 2026, 9:38 p.m. |
| NER | Named-entity recognition | batch_69abc950516c8190989591673de6b1f7 |
completed | March 7, 2026, 6:44 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69aebf4dcf6c8190a51f26af7e7a9b9c |
completed | March 9, 2026, 12:38 p.m. |
| NEDg | Description generation | batch_69aec2b3291c8190966344cd20963660 |
completed | March 9, 2026, 12:53 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69aec30f9ef481909b83f3cf9fd6e998 |
completed | March 9, 2026, 12:54 p.m. |
Created at: March 6, 2026, 9:42 p.m.