Triple

T14334391
Position Surface form Disambiguated ID Type / Status
Subject Ramanujan tau function E355432 entity
Predicate recurrencePrimePowers P43787 FINISHED
Object τ(p^{k+1}) = τ(p)τ(p^k) - p^{11}τ(p^{k-1}) for prime p and k ≥ 1 LITERAL 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: τ(p^{k+1}) = τ(p)τ(p^k) - p^{11}τ(p^{k-1}) for prime p and k ≥ 1 | Statement: [Ramanujan tau function, recurrencePrimePowers, τ(p^{k+1}) = τ(p)τ(p^k) - p^{11}τ(p^{k-1}) for prime p and k ≥ 1]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: recurrencePrimePowers
Context triple: [Ramanujan tau function, recurrencePrimePowers, τ(p^{k+1}) = τ(p)τ(p^k) - p^{11}τ(p^{k-1}) for prime p and k ≥ 1]
  • A. primePowerFormula chosen
    Indicates that a value is computed using a formula specifically involving powers of prime numbers.
  • B. primeFactorization
    Indicates that one entity is the decomposition of another entity into a multiset or sequence of prime factors whose product equals the original.
  • C. numberOfPrimeMovers
    Indicates the quantity of entities that serve as primary initiators or driving forces in a given context.
  • D. hasPrimeDecomposition
    Indicates that an entity is associated with the factorization of a number into its constituent prime factors.
  • E. hasPrimeDivisorsOfOrder
    Indicates that one entity possesses prime divisors whose multiplicities (orders in its factorization) satisfy a specified relational condition with respect to another entity.
  • F. None of above.

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.
PD Predicate disambiguation batch_69de2a9515f4819081aabf251bca5878 completed April 14, 2026, 11:52 a.m.
Created at: April 10, 2026, 1:13 a.m.