Triple

T36469502

Position	Surface form	Disambiguated ID	Type / Status
Subject	Green’s conjecture	`E898503`	entity
Predicate	relatedConjecture	`P38188`	FINISHED
Object	Green–Lazarsfeld conjecture on syzygies of line bundles The Green–Lazarsfeld conjecture on syzygies of line bundles is a central statement in algebraic geometry predicting precise patterns in the minimal free resolutions of line bundles on algebraic curves, linking these syzygies to geometric properties such as gonality.	`E2186208`	NE FINISHED

How this triple was built (2 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: Green–Lazarsfeld conjecture on syzygies of line bundles | Statement: [Green’s conjecture, relatedConjecture, Green–Lazarsfeld conjecture on syzygies of line bundles]

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: Green–Lazarsfeld conjecture on syzygies of line bundles
Triple: [Green’s conjecture, relatedConjecture, Green–Lazarsfeld conjecture on syzygies of line bundles]

Generated description

The Green–Lazarsfeld conjecture on syzygies of line bundles is a central statement in algebraic geometry predicting precise patterns in the minimal free resolutions of line bundles on algebraic curves, linking these syzygies to geometric properties such as gonality.

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_69f76e58ebd88190b75d9b169b59d793`	completed	May 3, 2026, 3:48 p.m.
NER	Named-entity recognition	`batch_69f7bdd2146881908ac02711aea34f04`	completed	May 3, 2026, 9:27 p.m.
NED1	Entity disambiguation (via context triple)	`batch_6a39cfd308d08190abcc9238d2060a78`	completed	June 23, 2026, 12:14 a.m.
NEDg	Description generation	`batch_6a39d3ea5e4481909db900a655c387cd`	completed	June 23, 2026, 12:31 a.m.
NED2	Entity disambiguation (via description)	`batch_6a39d46e171c8190bf55f47096200625`	completed	June 23, 2026, 12:33 a.m.

Created at: May 3, 2026, 4:10 p.m.