Triple

T7705271
Position Surface form Disambiguated ID Type / Status
Subject SO(3) E174596 entity
Predicate fundamentalGroup P78388 FINISHED
Object ℤ₂ 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: ℤ₂ | Statement: [SO(3), fundamentalGroup, ℤ₂]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: fundamentalGroup
Context triple: [SO(3), fundamentalGroup, ℤ₂]
  • A. 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.
  • B. homeomorphicTo
    Indicates that two topological spaces can be continuously deformed into each other via a bijective, continuous map with a continuous inverse, preserving their topological structure.
  • C. EulerCharacteristic
    Indicates the topological invariant of a space that equals, in a suitable decomposition, the alternating sum of the counts of its cells (e.g., vertices − edges + faces).
  • D. 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.
  • E. isSimplyConnected
    Indicates that a topological space has no "holes," meaning every loop within it can be continuously contracted to a single point.
  • 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_69c6995b3e8c8190833108f883d5f53c completed March 27, 2026, 2:51 p.m.
NER Named-entity recognition batch_69c70402169481909b219dc5f4a64b9b completed March 27, 2026, 10:26 p.m.
PD Predicate disambiguation batch_69c70165e78c8190bf6b3c34e243cb81 completed March 27, 2026, 10:15 p.m.
PDg Predicate description generation batch_69c7040091608190a9e46ecfb2ff0bca completed March 27, 2026, 10:26 p.m.
Created at: March 27, 2026, 4:03 p.m.