Triple

T12138863
Position Surface form Disambiguated ID Type / Status
Subject Pafnuty Chebyshev E289130 entity
Predicate notableWork P4 FINISHED
Object Chebyshev bias
Chebyshev bias is a phenomenon in number theory describing the tendency for primes to favor certain residue classes modulo a given integer, particularly the apparent predominance of primes congruent to 3 rather than 1 modulo 4.
E968216 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: Chebyshev bias | Statement: [Pafnuty Chebyshev, notableWork, Chebyshev bias]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Chebyshev bias
Context triple: [Pafnuty Chebyshev, notableWork, Chebyshev bias]
  • A. Chebyshev’s estimates for π(x)
    Chebyshev’s estimates for π(x) are 19th-century bounds on the prime-counting function that showed it grows on the order of x/log x and provided a crucial precursor to the prime number theorem.
  • B. Montgomery's pair correlation conjecture
    Montgomery's pair correlation conjecture is a deep number-theoretic prediction about the statistical spacing of the nontrivial zeros of the Riemann zeta function, linking them to eigenvalues of random matrices and suggesting profound connections between number theory and quantum physics.
  • C. Turán–Kubilius inequality
    The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
  • D. Siegel–Walfisz theorem
    The Siegel–Walfisz theorem is a result in analytic number theory that gives strong uniform estimates for the distribution of prime numbers in arithmetic progressions with relatively small moduli.
  • E. Linnik’s theorem on the least prime in an arithmetic progression
    Linnik’s theorem on the least prime in an arithmetic progression is a result in analytic number theory that gives an explicit upper bound, depending only on the modulus, for the size of the smallest prime in any given coprime residue class.
  • 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: Chebyshev bias
Triple: [Pafnuty Chebyshev, notableWork, Chebyshev bias]
Generated description
Chebyshev bias is a phenomenon in number theory describing the tendency for primes to favor certain residue classes modulo a given integer, particularly the apparent predominance of primes congruent to 3 rather than 1 modulo 4.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Chebyshev bias
Target entity description: Chebyshev bias is a phenomenon in number theory describing the tendency for primes to favor certain residue classes modulo a given integer, particularly the apparent predominance of primes congruent to 3 rather than 1 modulo 4.
  • A. Chebyshev’s estimates for π(x)
    Chebyshev’s estimates for π(x) are 19th-century bounds on the prime-counting function that showed it grows on the order of x/log x and provided a crucial precursor to the prime number theorem.
  • B. Montgomery's pair correlation conjecture
    Montgomery's pair correlation conjecture is a deep number-theoretic prediction about the statistical spacing of the nontrivial zeros of the Riemann zeta function, linking them to eigenvalues of random matrices and suggesting profound connections between number theory and quantum physics.
  • C. Turán–Kubilius inequality
    The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
  • D. Siegel–Walfisz theorem
    The Siegel–Walfisz theorem is a result in analytic number theory that gives strong uniform estimates for the distribution of prime numbers in arithmetic progressions with relatively small moduli.
  • E. Linnik’s theorem on the least prime in an arithmetic progression
    Linnik’s theorem on the least prime in an arithmetic progression is a result in analytic number theory that gives an explicit upper bound, depending only on the modulus, for the size of the smallest prime in any given coprime residue class.
  • 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_69d6ab4b5e4c81909950b17151eb0951 completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d9158eef48819083bdce283a363414 completed April 10, 2026, 3:21 p.m.
NED1 Entity disambiguation (via context triple) batch_69f5f690ae408190966bb4fe8feaa7d2 completed May 2, 2026, 1:05 p.m.
NEDg Description generation batch_69f6022ecf38819080f0eb6a3a815c5b completed May 2, 2026, 1:54 p.m.
NED2 Entity disambiguation (via description) batch_69f606560934819092ba4d4fa162b799 completed May 2, 2026, 2:12 p.m.
Created at: April 8, 2026, 9:49 p.m.