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.