Triple
T9297006
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Diophantine geometry |
E223662
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Siegel's theorem on integral points
Siegel's theorem on integral points is a fundamental result in number theory and Diophantine geometry stating that certain algebraic curves, notably those of genus at least one, have only finitely many integral points.
|
E790515
|
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: Siegel's theorem on integral points | Statement: [Diophantine geometry, relatedTo, Siegel's theorem on integral points]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Siegel's theorem on integral points Context triple: [Diophantine geometry, relatedTo, Siegel's theorem on integral points]
-
A.
Faltings' theorem
Faltings' theorem is a landmark result in arithmetic geometry that proves every algebraic curve of genus greater than one over a number field has only finitely many rational points.
-
B.
Siegel’s theorem on zeros of L-functions
Siegel’s theorem on zeros of L-functions is a result in analytic number theory that gives strong bounds on how close nontrivial zeros of Dirichlet L-functions can approach 1, with deep implications for the distribution of primes in arithmetic progressions.
-
C.
Baker theorem on linear forms in logarithms
The Baker theorem on linear forms in logarithms is a fundamental result in transcendental number theory that provides explicit lower bounds for nonzero linear combinations of logarithms of algebraic numbers, with powerful applications to Diophantine equations and Diophantine approximation.
-
D.
Hilbert’s irreducibility theorem
Hilbert’s irreducibility theorem is a fundamental result in number theory and algebraic geometry that ensures many polynomial equations with parameterized coefficients retain irreducibility for infinitely many specializations of those parameters.
-
E.
Mordell–Weil theorem
The Mordell–Weil theorem is a fundamental result in number theory stating that the group of rational points on an abelian variety (in particular, an elliptic curve) over a number field is finitely generated.
- 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: Siegel's theorem on integral points Triple: [Diophantine geometry, relatedTo, Siegel's theorem on integral points]
Generated description
Siegel's theorem on integral points is a fundamental result in number theory and Diophantine geometry stating that certain algebraic curves, notably those of genus at least one, have only finitely many integral points.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Siegel's theorem on integral points Target entity description: Siegel's theorem on integral points is a fundamental result in number theory and Diophantine geometry stating that certain algebraic curves, notably those of genus at least one, have only finitely many integral points.
-
A.
Faltings' theorem
Faltings' theorem is a landmark result in arithmetic geometry that proves every algebraic curve of genus greater than one over a number field has only finitely many rational points.
-
B.
Siegel’s theorem on zeros of L-functions
Siegel’s theorem on zeros of L-functions is a result in analytic number theory that gives strong bounds on how close nontrivial zeros of Dirichlet L-functions can approach 1, with deep implications for the distribution of primes in arithmetic progressions.
-
C.
Baker theorem on linear forms in logarithms
The Baker theorem on linear forms in logarithms is a fundamental result in transcendental number theory that provides explicit lower bounds for nonzero linear combinations of logarithms of algebraic numbers, with powerful applications to Diophantine equations and Diophantine approximation.
-
D.
Hilbert’s irreducibility theorem
Hilbert’s irreducibility theorem is a fundamental result in number theory and algebraic geometry that ensures many polynomial equations with parameterized coefficients retain irreducibility for infinitely many specializations of those parameters.
-
E.
Mordell–Weil theorem
The Mordell–Weil theorem is a fundamental result in number theory stating that the group of rational points on an abelian variety (in particular, an elliptic curve) over a number field is finitely generated.
- 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_69ca8423edb08190bc0c91287a484768 |
completed | March 30, 2026, 2:09 p.m. |
| NER | Named-entity recognition | batch_69cd089c9c588190967404c9eb938dfb |
completed | April 1, 2026, 11:59 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d0b251c4148190a94fafdc23a601d6 |
completed | April 4, 2026, 6:40 a.m. |
| NEDg | Description generation | batch_69d0b65ea4548190b445563ac695b008 |
completed | April 4, 2026, 6:57 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69d0b6f504a48190878db828312e8a97 |
completed | April 4, 2026, 7 a.m. |
Created at: March 30, 2026, 7:36 p.m.