Triple
T11098650
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | (2,3,7) triangle group |
E262443
|
entity |
| Predicate | hasAreaOfFundamentalTriangle |
P39260
|
FINISHED |
| Object | π(1 - 1/2 - 1/3 - 1/7) |
—
|
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: π(1 - 1/2 - 1/3 - 1/7) | Statement: [(2,3,7) triangle group, hasAreaOfFundamentalTriangle, π(1 - 1/2 - 1/3 - 1/7)]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: hasAreaOfFundamentalTriangle Context triple: [(2,3,7) triangle group, hasAreaOfFundamentalTriangle, π(1 - 1/2 - 1/3 - 1/7)]
-
A.
hasHyperbolicArea
chosen
Indicates that one entity possesses or is associated with a specific area measured in hyperbolic geometry.
-
B.
hasFundamentalDomain
Indicates that a mathematical object (such as a group action or tiling) is associated with a fundamental domain that represents a minimal region whose copies under the given symmetries cover the entire space without overlaps.
-
C.
hasTriangle
Indicates that an entity possesses, contains, or is associated with a triangle.
-
D.
fundamentalDomain
Indicates that one entity is a fundamental domain for the action of another (such as a group or transformation), meaning it is a minimal region whose images under that action cover the entire space without overlapping interiors.
-
E.
hasFiniteAreaQuotient
Indicates that the quotient space formed by the given object under a specified group action has finite total area with respect to the relevant geometric or measure-theoretic structure.
- 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_69d6aa9a40d88190a373e2c7e48285db |
completed | April 8, 2026, 7:20 p.m. |
| NER | Named-entity recognition | batch_69d79a0c46308190889b94c23ebaca62 |
completed | April 9, 2026, 12:22 p.m. |
| PD | Predicate disambiguation | batch_69d7441aa3548190b92dbde57841c135 |
completed | April 9, 2026, 6:15 a.m. |
Created at: April 8, 2026, 9:27 p.m.