Triple

T14334404
Position Surface form Disambiguated ID Type / Status
Subject Ramanujan tau function E355432 entity
Predicate satisfies P4233 FINISHED
Object Ramanujan–Petersson conjecture (proved by Deligne) E355436 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: Ramanujan–Petersson conjecture (proved by Deligne) | Statement: [Ramanujan tau function, satisfies, Ramanujan–Petersson conjecture (proved by Deligne)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Ramanujan–Petersson conjecture (proved by Deligne)
Context triple: [Ramanujan tau function, satisfies, Ramanujan–Petersson conjecture (proved by Deligne)]
  • A. Ramanujan–Petersson conjecture chosen
    The Ramanujan–Petersson conjecture is a fundamental statement in number theory and the theory of modular forms that predicts strong bounds on the Fourier coefficients of modular cusp forms, with deep connections to automorphic forms and the Langlands program.
  • B. Ribet's theorem
    Ribet's theorem is a result in number theory that linked certain modular forms to Galois representations and played a crucial role in the proof of Fermat's Last Theorem.
  • C. Taniyama–Shimura–Weil conjecture
    The Taniyama–Shimura–Weil conjecture, now the modularity theorem, asserts that every elliptic curve over the rational numbers is modular and played a central role in the proof of Fermat’s Last Theorem.
  • 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. Weil conjectures
    The Weil conjectures are a set of deep statements about the zeta functions of algebraic varieties over finite fields that guided the development of modern algebraic geometry and were ultimately proved using étale cohomology.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69d8278fa2108190bc0d0e7939c1eb03 completed April 9, 2026, 10:26 p.m.
NER Named-entity recognition batch_69de8c20d2148190bb534bef338e871d completed April 14, 2026, 6:49 p.m.
NED1 Entity disambiguation (via context triple) batch_69fd469634688190980df59ee482b792 completed May 8, 2026, 2:12 a.m.
Created at: April 10, 2026, 1:13 a.m.