Triple
T19327811
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Kurt Hensel |
E483404
|
entity |
| Predicate | nameGivenTo |
P63
|
FINISHED |
| Object | Hensel lemma |
—
|
NE NERFINISHED |
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: Hensel lemma | Statement: [Kurt Hensel, nameGivenTo, Hensel lemma]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hensel lemma Context triple: [Kurt Hensel, nameGivenTo, Hensel lemma]
-
A.
Hensel’s lemma
chosen
Hensel’s lemma is a fundamental result in number theory and p-adic analysis that allows one to lift solutions of polynomial congruences modulo a prime power to higher powers, analogous to Newton’s method in the p-adic setting.
-
B.
Henselization
Henselization is a construction in commutative algebra that minimally modifies a local ring to satisfy Hensel’s lemma, making it “Henselian” while preserving much of its original structure.
-
C.
Kummer's lemma
Kummer's lemma is a result in algebraic number theory that provides conditions on ideal factorization in cyclotomic fields, particularly relating to divisibility properties of class numbers and units.
-
D.
Hensel
Hensel is a German surname most notably associated with mathematician Kurt Hensel, known for introducing p-adic numbers.
-
E.
Henselian ring
A Henselian ring is a local ring in which Hensel’s lemma holds, allowing certain types of polynomial factorizations and root liftings from the residue field to the ring itself.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (2 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_69d8e8d13e3c81909d91d1d5ec37c095 |
completed | April 10, 2026, 12:10 p.m. |
| NER | Named-entity recognition | batch_69e6163f32f48190be17cccf4e537372 |
completed | April 20, 2026, 12:04 p.m. |
Created at: April 10, 2026, 1:33 p.m.