Triple

T21494058
Position Surface form Disambiguated ID Type / Status
Subject Beal conjecture E530308 entity
Predicate alsoKnownAs P39 FINISHED
Object Mauldin’s conjecture
Mauldin’s conjecture, more commonly known as the Beal conjecture, is an unsolved problem in number theory asserting that any solution in positive integers to A^x + B^y = C^z with exponents greater than 2 must have A, B, and C sharing a common prime factor.
E1487639 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: Mauldin’s conjecture | Statement: [Beal conjecture, alsoKnownAs, Mauldin’s conjecture]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Mauldin’s conjecture
Context triple: [Beal conjecture, alsoKnownAs, Mauldin’s conjecture]
  • A. Green’s conjecture
    Green’s conjecture is a central statement in algebraic geometry that predicts a precise relationship between the syzygies of the canonical embedding of a smooth projective curve and its Clifford index.
  • B. Tate Conjecture
    The Tate Conjecture is a major open problem in arithmetic geometry that predicts a deep connection between algebraic cycles on varieties over finite fields and their Galois-invariant étale cohomology classes.
  • C. Fontaine–Mazur conjecture
    The Fontaine–Mazur conjecture is a central open problem in number theory that predicts which p-adic Galois representations of number fields arise from geometry or from automorphic forms.
  • D. Mazur's torsion theorem
    Mazur's torsion theorem is a landmark result in number theory that classifies all possible torsion subgroups of elliptic curves over the rational numbers.
  • E. Artin’s conjecture on L-functions
    Artin’s conjecture on L-functions is a major unproven hypothesis in number theory asserting that nontrivial Artin L-functions associated to Galois representations are entire, with deep implications for the distribution of primes and the structure of number fields.
  • 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: Mauldin’s conjecture
Triple: [Beal conjecture, alsoKnownAs, Mauldin’s conjecture]
Generated description
Mauldin’s conjecture, more commonly known as the Beal conjecture, is an unsolved problem in number theory asserting that any solution in positive integers to A^x + B^y = C^z with exponents greater than 2 must have A, B, and C sharing a common prime factor.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Mauldin’s conjecture
Target entity description: Mauldin’s conjecture, more commonly known as the Beal conjecture, is an unsolved problem in number theory asserting that any solution in positive integers to A^x + B^y = C^z with exponents greater than 2 must have A, B, and C sharing a common prime factor.
  • A. Green’s conjecture
    Green’s conjecture is a central statement in algebraic geometry that predicts a precise relationship between the syzygies of the canonical embedding of a smooth projective curve and its Clifford index.
  • B. Tate Conjecture
    The Tate Conjecture is a major open problem in arithmetic geometry that predicts a deep connection between algebraic cycles on varieties over finite fields and their Galois-invariant étale cohomology classes.
  • C. Fontaine–Mazur conjecture
    The Fontaine–Mazur conjecture is a central open problem in number theory that predicts which p-adic Galois representations of number fields arise from geometry or from automorphic forms.
  • D. Mazur's torsion theorem
    Mazur's torsion theorem is a landmark result in number theory that classifies all possible torsion subgroups of elliptic curves over the rational numbers.
  • E. Artin’s conjecture on L-functions
    Artin’s conjecture on L-functions is a major unproven hypothesis in number theory asserting that nontrivial Artin L-functions associated to Galois representations are entire, with deep implications for the distribution of primes and the structure of number fields.
  • 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.