Triple

T10991716
Position Surface form Disambiguated ID Type / Status
Subject Riemann sphere E259767 entity
Predicate alsoKnownAs P39 FINISHED
Object complex projective line E259767 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: complex projective line | Statement: [Riemann sphere, alsoKnownAs, complex projective line]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: complex projective line
Context triple: [Riemann sphere, alsoKnownAs, complex projective line]
  • A. Riemann sphere chosen
    The Riemann sphere is the complex plane plus a point at infinity, forming a one-dimensional complex manifold topologically equivalent to a sphere and used to study meromorphic functions and complex analysis.
  • B. Fano plane
    The Fano plane is the smallest finite projective plane, consisting of seven points and seven lines with rich symmetrical and combinatorial properties.
  • C. Lefschetz pencil
    A Lefschetz pencil is a geometric structure on an algebraic variety given by a one-parameter family of hyperplane sections with only isolated, well-controlled singularities, fundamental in the study of its topology and geometry.
  • D. The Real Projective Plane
    The Real Projective Plane is a classic mathematical monograph by H. S. M. Coxeter that systematically develops the geometry and topology of the real projective plane, emphasizing its axiomatic foundations and non-Euclidean properties.
  • E. Plücker coordinates
    Plücker coordinates are a system of homogeneous coordinates used in projective geometry to represent lines (and other subspaces) in higher-dimensional spaces.
  • 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_69d6aa8a6a548190a750f944ccdc8064 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d795d1e918819090c71f5a077fa15a completed April 9, 2026, 12:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69e34504ebec8190a78e4795765b0c24 completed April 18, 2026, 8:47 a.m.
Created at: April 8, 2026, 9:24 p.m.