Triple

T6117018
Position Surface form Disambiguated ID Type / Status
Subject G. H. Hardy E136383 entity
Predicate notableFor P22 FINISHED
Object Hardy–Ramanujan asymptotic formula E123877 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: Hardy–Ramanujan asymptotic formula | Statement: [G. H. Hardy, notableFor, Hardy–Ramanujan asymptotic formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hardy–Ramanujan asymptotic formula
Context triple: [G. H. Hardy, notableFor, Hardy–Ramanujan asymptotic formula]
  • A. Hardy–Ramanujan asymptotic formula chosen
    The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
  • B. Ramanujan partition congruences
    Ramanujan partition congruences are remarkable number-theoretic results discovered by Srinivasa Ramanujan that describe surprising modular patterns in the partition function, such as specific arithmetic progressions where the number of integer partitions of an integer is divisible by a given prime.
  • C. Ramanujan’s sum
    Ramanujan’s sum is a number-theoretic function introduced by Srinivasa Ramanujan, expressing certain periodic arithmetic functions as finite trigonometric sums over primitive roots of unity.
  • D. Hardy–Littlewood circle method
    The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
  • E. Ramanujan’s lost notebook
    Ramanujan’s lost notebook is a posthumously discovered collection of Srinivasa Ramanujan’s final mathematical formulas and insights, many of which were decades ahead of their time in number theory and q-series.
  • 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_69c0089f851c81909e5e189a617dcff6 completed March 22, 2026, 3:19 p.m.
NER Named-entity recognition batch_69c05beb4cfc8190ab67a5338ec59cea completed March 22, 2026, 9:15 p.m.
NED1 Entity disambiguation (via context triple) batch_69c1256ddb38819095f582b6468db407 completed March 23, 2026, 11:35 a.m.
Created at: March 22, 2026, 4:14 p.m.