Triple
T9843393
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hardy Z-function |
E239280
|
entity |
| Predicate | constructedFrom |
P909
|
FINISHED |
| Object | Riemann–Siegel theta function θ(t) |
E239279
|
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: Riemann–Siegel theta function θ(t) | Statement: [Hardy Z-function, constructedFrom, Riemann–Siegel theta function θ(t)]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Riemann–Siegel theta function θ(t) Context triple: [Hardy Z-function, constructedFrom, Riemann–Siegel theta function θ(t)]
-
A.
Riemann–Siegel theta function
chosen
The Riemann–Siegel theta function is a special function that appears in the study of the Riemann zeta function, used to express its values on the critical line in a form suitable for high-precision numerical computation.
-
B.
Riemann–Siegel formula
The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
-
C.
Riemann zeta function
The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
-
D.
Riemann xi function
The Riemann xi function is an entire, symmetrized version of the Riemann zeta function that encodes its nontrivial zeros and plays a central role in the study of the Riemann Hypothesis and related analytic number theory.
-
E.
Ramanujan tau function
The Ramanujan tau function is a multiplicative arithmetic function arising from the Fourier coefficients of a modular discriminant form, central to the study of modular forms and number theory.
- 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_69ca84e3f0c48190ada72a65ebd50efd |
completed | March 30, 2026, 2:12 p.m. |
| NER | Named-entity recognition | batch_69cdb35c8e348190aa090c71bf6f30eb |
completed | April 2, 2026, 12:07 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d1ead49b14819086a9bbd256f298a9 |
completed | April 5, 2026, 4:53 a.m. |
Created at: March 30, 2026, 8:33 p.m.