Triple
T11219330
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Milnor number |
E265517
|
entity |
| Predicate | usedIn |
P98
|
FINISHED |
| Object |
ADE singularity theory
ADE singularity theory is a classification framework in singularity theory and Lie theory that organizes certain simple surface singularities and related algebraic structures into three families labeled A, D, and E.
|
E911352
|
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: ADE singularity theory | Statement: [Milnor number, usedIn, ADE singularity theory]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: ADE singularity theory Context triple: [Milnor number, usedIn, ADE singularity theory]
-
A.
Singular Points of Complex Hypersurfaces
"Singular Points of Complex Hypersurfaces" is a foundational monograph in singularity theory that systematically studies the local and topological properties of singularities arising in complex algebraic and analytic hypersurfaces.
-
B.
Thom–Mather stratification
Thom–Mather stratification is a refined notion of stratification in differential topology that imposes strong regularity and control conditions on how smooth strata fit together, generalizing and strengthening Whitney stratifications.
-
C.
Clebsch–Aronhold invariants
The Clebsch–Aronhold invariants are classical algebraic invariants associated with binary forms, particularly quartic forms, that play a key role in invariant theory and the classification of algebraic curves.
-
D.
Topological Methods in Algebraic Geometry
Topological Methods in Algebraic Geometry is a foundational mathematical monograph by Friedrich Hirzebruch that applies topological techniques, particularly characteristic classes and cobordism theory, to problems in algebraic geometry.
-
E.
Hilbert’s sixteenth problem
Hilbert’s sixteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the topology and arrangement of algebraic curves and surfaces, particularly the number and position of their ovals.
- 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: ADE singularity theory Triple: [Milnor number, usedIn, ADE singularity theory]
Generated description
ADE singularity theory is a classification framework in singularity theory and Lie theory that organizes certain simple surface singularities and related algebraic structures into three families labeled A, D, and E.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: ADE singularity theory Target entity description: ADE singularity theory is a classification framework in singularity theory and Lie theory that organizes certain simple surface singularities and related algebraic structures into three families labeled A, D, and E.
-
A.
Singular Points of Complex Hypersurfaces
"Singular Points of Complex Hypersurfaces" is a foundational monograph in singularity theory that systematically studies the local and topological properties of singularities arising in complex algebraic and analytic hypersurfaces.
-
B.
Thom–Mather stratification
Thom–Mather stratification is a refined notion of stratification in differential topology that imposes strong regularity and control conditions on how smooth strata fit together, generalizing and strengthening Whitney stratifications.
-
C.
Clebsch–Aronhold invariants
The Clebsch–Aronhold invariants are classical algebraic invariants associated with binary forms, particularly quartic forms, that play a key role in invariant theory and the classification of algebraic curves.
-
D.
Topological Methods in Algebraic Geometry
Topological Methods in Algebraic Geometry is a foundational mathematical monograph by Friedrich Hirzebruch that applies topological techniques, particularly characteristic classes and cobordism theory, to problems in algebraic geometry.
-
E.
Hilbert’s sixteenth problem
Hilbert’s sixteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the topology and arrangement of algebraic curves and surfaces, particularly the number and position of their ovals.
- 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_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. |
| NEDg | Description generation | batch_69e49d37989881909c7e75ddfff06726 |
completed | April 19, 2026, 9:15 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69e49f41a1f8819087cc15527dc7ff63 |
completed | April 19, 2026, 9:24 a.m. |
Created at: April 8, 2026, 9:30 p.m.