Triple

T21494131
Position Surface form Disambiguated ID Type / Status
Subject abc conjecture E530309 entity
Predicate relatedTo P37 FINISHED
Object Szpiro conjecture
The Szpiro conjecture is a deep unproven statement in arithmetic geometry about the relationship between the discriminant and conductor of elliptic curves over the rationals, and is known to be essentially equivalent to the abc conjecture.
E1487645 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: Szpiro conjecture | Statement: [abc conjecture, relatedTo, Szpiro conjecture]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Szpiro conjecture
Context triple: [abc conjecture, relatedTo, Szpiro conjecture]
  • A. 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.
  • B. Birch and Swinnerton-Dyer Conjecture
    The Birch and Swinnerton-Dyer Conjecture is a central unsolved problem in number theory that predicts a deep connection between the arithmetic of rational points on an elliptic curve and the behavior of its associated L-function at a specific value.
  • C. 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.
  • D. 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.
  • E. Bloch–Kato conjecture
    The Bloch–Kato conjecture is a deep statement in arithmetic geometry and K-theory that predicts an exact correspondence between Galois cohomology and Milnor K-theory, linking algebraic K-groups to field arithmetic.
  • 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: Szpiro conjecture
Triple: [abc conjecture, relatedTo, Szpiro conjecture]
Generated description
The Szpiro conjecture is a deep unproven statement in arithmetic geometry about the relationship between the discriminant and conductor of elliptic curves over the rationals, and is known to be essentially equivalent to the abc conjecture.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Szpiro conjecture
Target entity description: The Szpiro conjecture is a deep unproven statement in arithmetic geometry about the relationship between the discriminant and conductor of elliptic curves over the rationals, and is known to be essentially equivalent to the abc conjecture.
  • A. 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.
  • B. Birch and Swinnerton-Dyer Conjecture
    The Birch and Swinnerton-Dyer Conjecture is a central unsolved problem in number theory that predicts a deep connection between the arithmetic of rational points on an elliptic curve and the behavior of its associated L-function at a specific value.
  • C. 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.
  • D. 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.
  • E. Bloch–Kato conjecture
    The Bloch–Kato conjecture is a deep statement in arithmetic geometry and K-theory that predicts an exact correspondence between Galois cohomology and Milnor K-theory, linking algebraic K-groups to field arithmetic.
  • 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.