Triple

T11098587
Position Surface form Disambiguated ID Type / Status
Subject PSL(2,7) E262442 entity
Predicate isomorphicTo P29599 FINISHED
Object projective linear group of 2×2 matrices over F_7 with determinant 1 modulo scalars E262442 NE 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: projective linear group of 2×2 matrices over F_7 with determinant 1 modulo scalars | Statement: [PSL(2,7), isomorphicTo, projective linear group of 2×2 matrices over F_7 with determinant 1 modulo scalars]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: projective linear group of 2×2 matrices over F_7 with determinant 1 modulo scalars
Context triple: [PSL(2,7), isomorphicTo, projective linear group of 2×2 matrices over F_7 with determinant 1 modulo scalars]
  • A. PSL(2,7) chosen
    PSL(2,7) is a finite simple group of order 168, notable as the full automorphism group of the Klein quartic and as a key example in the theory of projective linear groups over finite fields.
  • B. special linear group SL(n,R)
    The special linear group SL(n,ℝ) is the Lie group of all n×n real matrices with determinant 1, fundamental in linear algebra and differential geometry as the group of volume-preserving linear transformations.
  • C. PSL(2,ℤ/Nℤ)
    PSL(2,ℤ/Nℤ) is the projective special linear group of 2×2 matrices with entries in the ring of integers modulo N, modulo scalar matrices, forming a fundamental example of a finite (or, for composite N, generally non-simple) group in algebra and number theory.
  • D. special linear group SL(n,C)
    The special linear group SL(n,ℂ) is the Lie group of n×n complex matrices with determinant 1, fundamental in representation theory, geometry, and many areas of modern mathematics and physics.
  • E. SL(2,ℤ)
    SL(2,ℤ) is the group of 2×2 integer matrices with determinant 1, fundamental in number theory, geometry, and the theory of modular forms.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

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_69d79a0b2890819081c4efc50e995cdd completed April 9, 2026, 12:22 p.m.
NED1 Entity disambiguation (via context triple) batch_69e3e7eca9bc8190b43bae081d97d804 completed April 18, 2026, 8:22 p.m.
Created at: April 8, 2026, 9:27 p.m.