Triple
T17671651
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Benedict Gross |
E440533
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Gross–Koblitz formula
The Gross–Koblitz formula is a result in number theory that expresses Gauss sums in terms of the p-adic gamma function, linking exponential sums over finite fields with p-adic analysis.
|
E1281173
|
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: Gross–Koblitz formula | Statement: [Benedict Gross, notableWork, Gross–Koblitz formula]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Gross–Koblitz formula Context triple: [Benedict Gross, notableWork, Gross–Koblitz formula]
-
A.
Hasse–Arf theorem
The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
-
B.
Kummer congruences
Kummer congruences are number-theoretic relations describing how special values of Bernoulli numbers and related arithmetic functions behave modulo powers of primes, foundational in the study of p-adic L-functions and cyclotomic fields.
-
C.
Lubin–Tate formal groups
Lubin–Tate formal groups are a class of one-dimensional formal group laws over local fields that play a central role in local class field theory by providing explicit descriptions of abelian extensions.
-
D.
Drinfeld modules
Drinfeld modules are algebraic structures that generalize elliptic curves to the setting of function fields, playing a central role in modern arithmetic geometry and the theory of automorphic forms.
-
E.
Grothendieck–Lefschetz trace formula
The Grothendieck–Lefschetz trace formula is a fundamental result in algebraic geometry that expresses the number of rational points of a variety over a finite field in terms of traces of Frobenius acting on its étale cohomology groups.
- 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: Gross–Koblitz formula Triple: [Benedict Gross, notableWork, Gross–Koblitz formula]
Generated description
The Gross–Koblitz formula is a result in number theory that expresses Gauss sums in terms of the p-adic gamma function, linking exponential sums over finite fields with p-adic analysis.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Gross–Koblitz formula Target entity description: The Gross–Koblitz formula is a result in number theory that expresses Gauss sums in terms of the p-adic gamma function, linking exponential sums over finite fields with p-adic analysis.
-
A.
Hasse–Arf theorem
The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
-
B.
Kummer congruences
Kummer congruences are number-theoretic relations describing how special values of Bernoulli numbers and related arithmetic functions behave modulo powers of primes, foundational in the study of p-adic L-functions and cyclotomic fields.
-
C.
Lubin–Tate formal groups
Lubin–Tate formal groups are a class of one-dimensional formal group laws over local fields that play a central role in local class field theory by providing explicit descriptions of abelian extensions.
-
D.
Drinfeld modules
Drinfeld modules are algebraic structures that generalize elliptic curves to the setting of function fields, playing a central role in modern arithmetic geometry and the theory of automorphic forms.
-
E.
Grothendieck–Lefschetz trace formula
The Grothendieck–Lefschetz trace formula is a fundamental result in algebraic geometry that expresses the number of rational points of a variety over a finite field in terms of traces of Frobenius acting on its étale cohomology groups.
- 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_69d8b9e87e18819087104a44dc4dc5b1 |
completed | April 10, 2026, 8:50 a.m. |
| NER | Named-entity recognition | batch_69e46f69b11c8190b09add33f81776b3 |
completed | April 19, 2026, 6 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a02166234f0819099c452808234e3e4 |
completed | May 11, 2026, 5:48 p.m. |
| NEDg | Description generation | batch_6a0217ca2ec881908573b0423c3610f7 |
completed | May 11, 2026, 5:54 p.m. |
| NED2 | Entity disambiguation (via description) | batch_6a0218636e048190a48bc7f066c7bee1 |
completed | May 11, 2026, 5:56 p.m. |
Created at: April 10, 2026, 9:59 a.m.