Triple

T29565549

Position	Surface form	Disambiguated ID	Type / Status
Subject	Witt group of quadratic forms	`E753152`	entity
Predicate	hasHomomorphismTo	`P69858`	FINISHED
Object	Grothendieck–Witt group The Grothendieck–Witt group is an algebraic invariant formed from isomorphism classes of nondegenerate symmetric bilinear or quadratic forms under orthogonal sum, encoding both their additive and multiplicative structure.	`E753152`	NE FINISHED

How this triple was built (3 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: Grothendieck–Witt group | Statement: [Witt group of quadratic forms, hasHomomorphismTo, Grothendieck–Witt group]

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: Grothendieck–Witt group
Triple: [Witt group of quadratic forms, hasHomomorphismTo, Grothendieck–Witt group]

Generated description

The Grothendieck–Witt group is an algebraic invariant formed from isomorphism classes of nondegenerate symmetric bilinear or quadratic forms under orthogonal sum, encoding both their additive and multiplicative structure.

PD Predicate disambiguation gpt-5-mini-2025-08-07

Target predicate: hasHomomorphismTo
Context triple: [Witt group of quadratic forms, hasHomomorphismTo, Grothendieck–Witt group]

A. hasHomomorphism chosen
Indicates that there exists a structure-preserving map (homomorphism) from one mathematical structure to another.
B. hasSubgroupIsomorphicTo
Indicates that one group contains a subgroup that is structurally identical (isomorphic) to another specified group.
C. hasAutomorphismGroupContaining
Indicates that the automorphism group of one mathematical structure includes the other group as a subgroup or component.
D. isIsomorphicTo
Indicates that two structures have a one-to-one, structure-preserving correspondence between their elements, making them equivalent in form even if not identical in content.
E. hasAutomorphism
Indicates that there exists a structure-preserving bijection from an entity to itself that maintains all relevant relations and operations.
F. None of above.

Provenance (6 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_69f0ef7fcb4881908a933110adb9bda1`	completed	April 28, 2026, 5:33 p.m.
NER	Named-entity recognition	`batch_69f7be53890081909b1d93f30a8f31c6`	completed	May 3, 2026, 9:29 p.m.
NED1	Entity disambiguation (via context triple)	`batch_6a262d68eff88190bbdbcb569e590116`	completed	June 8, 2026, 2:48 a.m.
NEDg	Description generation	`batch_6a26317def3881908eb2e11b7754e1ac`	completed	June 8, 2026, 3:05 a.m.
NED2	Entity disambiguation (via description)	`batch_6a2635ad095481909c2fbed70b7a5f4c`	completed	June 8, 2026, 3:23 a.m.
PD	Predicate disambiguation	`batch_69f7bccacbac8190978976324c67db28`	completed	May 3, 2026, 9:23 p.m.

Created at: April 28, 2026, 5:52 p.m.