Triple
T34585661
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | S^2 × R geometry |
E888036
|
entity |
| Predicate | fundamentalGroupOfCompactQuotient |
P78388
|
FINISHED |
| Object | extension of Z by finite group |
—
|
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: extension of Z by finite group | Statement: [S^2 × R geometry, fundamentalGroupOfCompactQuotient, extension of Z by finite group]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: fundamentalGroupOfCompactQuotient Context triple: [S^2 × R geometry, fundamentalGroupOfCompactQuotient, extension of Z by finite group]
-
A.
fundamentalGroup
chosen
Indicates the relationship that assigns to a topological space its fundamental group, capturing how loops in the space can be continuously deformed into one another.
-
B.
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.
-
C.
congruenceSubgroups
Indicates that there is a relationship between groups where one is a congruence subgroup of the other, typically defined by congruence conditions modulo some integer or ideal.
-
D.
torsionSubgroup
Indicates that one group is the torsion subgroup of another, consisting of all elements that have finite order under the group operation.
-
E.
isFuchsianGroupContainer
Indicates that one entity serves as a container or holder for a Fuchsian group associated with the other entity.
- 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_69f349d25cbc8190869998de5915886b |
completed | April 30, 2026, 12:23 p.m. |
| NER | Named-entity recognition | batch_69f720c7ea608190bd92d69643330823 |
completed | May 3, 2026, 10:17 a.m. |
| PD | Predicate disambiguation | batch_69f71cc8074c81909ae09bea2acf1a09 |
completed | May 3, 2026, 10 a.m. |
Created at: May 1, 2026, 2:03 a.m.