Triple
T21494632
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Fermat surface |
E530319
|
entity |
| Predicate | hasKodairaDimension |
P144611
|
FINISHED |
| Object | 2 for n ≥ 5 |
—
|
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: 2 for n ≥ 5 | Statement: [Fermat surface, hasKodairaDimension, 2 for n ≥ 5]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: hasKodairaDimension Context triple: [Fermat surface, hasKodairaDimension, 2 for n ≥ 5]
-
A.
hasKrullDimension
Indicates that a mathematical structure (typically a ring or scheme) is associated with a specific Krull dimension, measuring the maximal length of chains of its prime ideals.
-
B.
hasAnticanonicalEmbedding
Indicates that a variety or geometric object is embedded into projective space via its anticanonical line bundle (i.e., by the complete linear system of the anticanonical divisor).
-
C.
hasHodgeNumbers
Indicates that an entity (typically a geometric or algebraic object) is associated with specific Hodge numbers describing its Hodge decomposition or Hodge structure.
-
D.
isHolomorphicallyContractible
Indicates that a space can be continuously shrunk to a point through holomorphic maps, preserving complex-analytic structure throughout the contraction.
-
E.
isRationalSurface
Indicates that a given algebraic surface is birationally equivalent to the projective plane, i.e., it has the rationality property.
- F. None of above. chosen
Provenance (4 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_69e0c45bd15481909fba5910765cdda2 |
completed | April 16, 2026, 11:13 a.m. |
| NER | Named-entity recognition | batch_69e9ea567244819091863350fedae3ae |
completed | April 23, 2026, 9:45 a.m. |
| PD | Predicate disambiguation | batch_69e631f6e68081908f5ee4ce7413803e |
completed | April 20, 2026, 2:02 p.m. |
| PDg | Predicate description generation | batch_69e6386c5a4481909c37f7de7e9fc025 |
completed | April 20, 2026, 2:30 p.m. |
Created at: April 16, 2026, 6:23 p.m.