Triple

T21047206
Position Surface form Disambiguated ID Type / Status
Subject Lindelöf hypothesis E518478 entity
Predicate hasGeneralization P2372 FINISHED
Object Lindelöf hypothesis for automorphic L-functions NE NERFINISHED

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: Lindelöf hypothesis for automorphic L-functions | Statement: [Lindelöf hypothesis, hasGeneralization, Lindelöf hypothesis for automorphic L-functions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lindelöf hypothesis for automorphic L-functions
Context triple: [Lindelöf hypothesis, hasGeneralization, Lindelöf hypothesis for automorphic L-functions]
  • A. Euler products for automorphic L-functions
    Euler products for automorphic L-functions are infinite product expansions attached to automorphic representations that encode deep arithmetic information and generalize the classical Euler product of the Riemann zeta function to a broad class of L-functions in the Langlands program.
  • B. Siegel’s theorem on zeros of L-functions
    Siegel’s theorem on zeros of L-functions is a result in analytic number theory that gives strong bounds on how close nontrivial zeros of Dirichlet L-functions can approach 1, with deep implications for the distribution of primes in arithmetic progressions.
  • C. 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.
  • D. Lindelöf hypothesis chosen
    The Lindelöf hypothesis is an unproven conjecture in analytic number theory about the growth rate of the Riemann zeta function along the critical line, with deep implications for the distribution of prime numbers.
  • E. Automorphic Forms and the Reciprocity Law
    "Automorphic Forms and the Reciprocity Law" is a seminal mathematical work by Goro Shimura that develops deep connections between automorphic forms, number theory, and reciprocity laws in arithmetic geometry.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69e0b50438e08190917e2538bb8bc034 completed April 16, 2026, 10:08 a.m.
NER Named-entity recognition batch_69e6fcf4d26481908b639996500a8319 completed April 21, 2026, 4:28 a.m.
Created at: April 16, 2026, 2:34 p.m.