Triple
T18793012
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hilbert class field |
E459562
|
entity |
| Predicate | unramifiedAt |
P72934
|
FINISHED |
| Object | every nonzero prime ideal of the ring of integers of the base field |
—
|
LITERAL 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: every nonzero prime ideal of the ring of integers of the base field | Statement: [Hilbert class field, unramifiedAt, every nonzero prime ideal of the ring of integers of the base field]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: unramifiedAt Context triple: [Hilbert class field, unramifiedAt, every nonzero prime ideal of the ring of integers of the base field]
-
A.
ramifiedPrime
Indicates that a prime number factors into repeated prime ideals in the ring of integers of a number field, showing that it ramifies in that extension.
-
B.
hasUnramifiedPrimes
chosen
Indicates that, in a given field extension or number-theoretic context, certain prime ideals remain unramified (i.e., do not exhibit ramification) in that extension.
-
C.
primeSplittingProperty
Indicates how a given prime number factors (splits, remains inert, or ramifies) in an extension of number fields or related algebraic structure.
-
D.
rankOverℤ
Indicates that one entity has a higher (or superior) rank than another when ranks are compared as integers over the set of all integers ℤ.
-
E.
isRingOfIntegersOf
Indicates that one mathematical structure is the ring of integers associated with a given number field or algebraic extension.
- F. None of above.
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_69d8d396f54c8190ba49db31e8743842 |
completed | April 10, 2026, 10:40 a.m. |
| NER | Named-entity recognition | batch_69e59787e5988190883ed575ab4b6dec |
completed | April 20, 2026, 3:03 a.m. |
| PD | Predicate disambiguation | batch_69e48d16dd34819096e096d0c0e4c15c |
completed | April 19, 2026, 8:06 a.m. |
Created at: April 10, 2026, 11:53 a.m.