Triple

T21494130
Position Surface form Disambiguated ID Type / Status
Subject abc conjecture E530309 entity
Predicate relatedTo P37 FINISHED
Object Mason–Stothers theorem
The Mason–Stothers theorem is a result in algebraic function theory that gives a sharp relation between the degrees of three coprime polynomials satisfying A + B = C and the number of distinct roots of their product, and serves as a polynomial analogue of the abc conjecture.
E1487644 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: Mason–Stothers theorem | Statement: [abc conjecture, relatedTo, Mason–Stothers theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Mason–Stothers theorem
Context triple: [abc conjecture, relatedTo, Mason–Stothers theorem]
  • A. Faltings' theorem
    Faltings' theorem is a landmark result in arithmetic geometry that proves every algebraic curve of genus greater than one over a number field has only finitely many rational points.
  • B. Pillai’s conjecture
    Pillai’s conjecture is an unproven statement in number theory asserting that the difference between perfect powers takes each positive integer value only finitely many times.
  • C. Bombieri–Lang conjecture
    The Bombieri–Lang conjecture is a major unsolved conjecture in number theory and arithmetic geometry predicting that varieties of general type over number fields have only finitely many rational points.
  • D. Baker theorem on linear forms in logarithms
    The Baker theorem on linear forms in logarithms is a fundamental result in transcendental number theory that provides explicit lower bounds for nonzero linear combinations of logarithms of algebraic numbers, with powerful applications to Diophantine equations and Diophantine approximation.
  • E. Mordell–Weil theorem
    The Mordell–Weil theorem is a fundamental result in number theory stating that the group of rational points on an abelian variety (in particular, an elliptic curve) over a number field is finitely generated.
  • 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: Mason–Stothers theorem
Triple: [abc conjecture, relatedTo, Mason–Stothers theorem]
Generated description
The Mason–Stothers theorem is a result in algebraic function theory that gives a sharp relation between the degrees of three coprime polynomials satisfying A + B = C and the number of distinct roots of their product, and serves as a polynomial analogue of the abc conjecture.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Mason–Stothers theorem
Target entity description: The Mason–Stothers theorem is a result in algebraic function theory that gives a sharp relation between the degrees of three coprime polynomials satisfying A + B = C and the number of distinct roots of their product, and serves as a polynomial analogue of the abc conjecture.
  • A. Faltings' theorem
    Faltings' theorem is a landmark result in arithmetic geometry that proves every algebraic curve of genus greater than one over a number field has only finitely many rational points.
  • B. Pillai’s conjecture
    Pillai’s conjecture is an unproven statement in number theory asserting that the difference between perfect powers takes each positive integer value only finitely many times.
  • C. Bombieri–Lang conjecture
    The Bombieri–Lang conjecture is a major unsolved conjecture in number theory and arithmetic geometry predicting that varieties of general type over number fields have only finitely many rational points.
  • D. Baker theorem on linear forms in logarithms
    The Baker theorem on linear forms in logarithms is a fundamental result in transcendental number theory that provides explicit lower bounds for nonzero linear combinations of logarithms of algebraic numbers, with powerful applications to Diophantine equations and Diophantine approximation.
  • E. Mordell–Weil theorem
    The Mordell–Weil theorem is a fundamental result in number theory stating that the group of rational points on an abelian variety (in particular, an elliptic curve) over a number field is finitely generated.
  • 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_69e0c45bd15481909fba5910765cdda2 completed April 16, 2026, 11:13 a.m.
NER Named-entity recognition batch_69e9ea567244819091863350fedae3ae completed April 23, 2026, 9:45 a.m.
NED1 Entity disambiguation (via context triple) batch_6a09e1398efc8190a6465defb1715c2b completed May 17, 2026, 3:39 p.m.
NEDg Description generation batch_6a09e24c7da48190b7e19f709b3c0d79 completed May 17, 2026, 3:44 p.m.
NED2 Entity disambiguation (via description) batch_6a09e2c86858819092216c12d8aa3348 completed May 17, 2026, 3:46 p.m.
Created at: April 16, 2026, 6:23 p.m.