Triple
T8733410
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hasse invariant |
E207312
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Witt group of quadratic forms
The Witt group of quadratic forms is an algebraic structure that classifies nondegenerate quadratic forms over a field up to stable equivalence, with addition given by orthogonal sum and inverses given by taking opposite forms.
|
E753152
|
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: Witt group of quadratic forms | Statement: [Hasse invariant, relatedTo, Witt group of quadratic forms]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Witt group of quadratic forms Context triple: [Hasse invariant, relatedTo, Witt group of quadratic forms]
-
A.
Rational Quadratic Forms
Rational Quadratic Forms is a classic monograph in number theory that systematically develops the arithmetic theory of quadratic forms over the rational numbers.
-
B.
Hermitian forms (work on quadratic forms)
Hermitian forms (work on quadratic forms) are a class of complex-valued quadratic forms that are linear in one variable and conjugate-linear in the other, generalizing real symmetric quadratic forms and playing a central role in linear algebra and functional analysis.
-
C.
Milnor K-theory
Milnor K-theory is an algebraic K-theory constructed from fields using tensor powers of their multiplicative groups modulo Steinberg relations, playing a central role in modern algebraic geometry and number theory.
-
D.
Über die Bildung des Formensystems der ternären biquadratischen Form
"Über die Bildung des Formensystems der ternären biquadratischen Form" is the 1907 doctoral dissertation of mathematician Emmy Noether, in which she investigates the invariant theory of certain higher-degree algebraic forms.
-
E.
Algebraic Groups and Class Fields
"Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
- 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: Witt group of quadratic forms Triple: [Hasse invariant, relatedTo, Witt group of quadratic forms]
Generated description
The Witt group of quadratic forms is an algebraic structure that classifies nondegenerate quadratic forms over a field up to stable equivalence, with addition given by orthogonal sum and inverses given by taking opposite forms.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Witt group of quadratic forms Target entity description: The Witt group of quadratic forms is an algebraic structure that classifies nondegenerate quadratic forms over a field up to stable equivalence, with addition given by orthogonal sum and inverses given by taking opposite forms.
-
A.
Rational Quadratic Forms
Rational Quadratic Forms is a classic monograph in number theory that systematically develops the arithmetic theory of quadratic forms over the rational numbers.
-
B.
Hermitian forms (work on quadratic forms)
Hermitian forms (work on quadratic forms) are a class of complex-valued quadratic forms that are linear in one variable and conjugate-linear in the other, generalizing real symmetric quadratic forms and playing a central role in linear algebra and functional analysis.
-
C.
Milnor K-theory
Milnor K-theory is an algebraic K-theory constructed from fields using tensor powers of their multiplicative groups modulo Steinberg relations, playing a central role in modern algebraic geometry and number theory.
-
D.
Über die Bildung des Formensystems der ternären biquadratischen Form
"Über die Bildung des Formensystems der ternären biquadratischen Form" is the 1907 doctoral dissertation of mathematician Emmy Noether, in which she investigates the invariant theory of certain higher-degree algebraic forms.
-
E.
Algebraic Groups and Class Fields
"Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
- 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_69ca8358e4008190898471a59b96c301 |
completed | March 30, 2026, 2:06 p.m. |
| NER | Named-entity recognition | batch_69cc5d2a26988190acfda17f232e610a |
completed | March 31, 2026, 11:47 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69cf292d71ec819082095cb7b8b2d39c |
completed | April 3, 2026, 2:42 a.m. |
| NEDg | Description generation | batch_69cf2bd4f50c8190bad328e82d299ae0 |
completed | April 3, 2026, 2:54 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69cf2cbf60808190a006ee4fb26cde41 |
completed | April 3, 2026, 2:58 a.m. |
Created at: March 30, 2026, 6:37 p.m.