Triple
T2418316
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | John Milnor |
E52357
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
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.
|
E265517
|
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 number | Statement: [John Milnor, notableWork, Milnor number]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Milnor number Context triple: [John Milnor, notableWork, Milnor number]
-
A.
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.
-
B.
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.
-
C.
Castelnuovo–Mumford regularity
Castelnuovo–Mumford regularity is an invariant in commutative algebra and algebraic geometry that measures the complexity of the minimal graded free resolution of a module or sheaf, often used to control vanishing of cohomology and bounds on generators.
-
D.
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.
-
E.
Hirzebruch–Riemann–Roch theorem
The Hirzebruch–Riemann–Roch theorem is a fundamental result in algebraic geometry and topology that expresses the holomorphic Euler characteristic of a complex manifold in terms of characteristic classes, unifying and extending classical Riemann–Roch type formulas.
- 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 number Triple: [John Milnor, notableWork, Milnor number]
Generated description
The Milnor number is an invariant in singularity theory that measures the complexity of an isolated critical point of a complex hypersurface or function.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Milnor number Target entity description: The Milnor number is an invariant in singularity theory that measures the complexity of an isolated critical point of a complex hypersurface or function.
-
A.
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.
-
B.
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.
-
C.
Castelnuovo–Mumford regularity
Castelnuovo–Mumford regularity is an invariant in commutative algebra and algebraic geometry that measures the complexity of the minimal graded free resolution of a module or sheaf, often used to control vanishing of cohomology and bounds on generators.
-
D.
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.
-
E.
Hirzebruch–Riemann–Roch theorem
The Hirzebruch–Riemann–Roch theorem is a fundamental result in algebraic geometry and topology that expresses the holomorphic Euler characteristic of a complex manifold in terms of characteristic classes, unifying and extending classical Riemann–Roch type formulas.
- 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.