Triple

T1645085
Position Surface form Disambiguated ID Type / Status
Subject Max Noether E35562 entity
Predicate notableWork P4 FINISHED
Object Noether’s theorem on rationality of surfaces E186169 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: Noether’s theorem on rationality of surfaces | Statement: [Max Noether, notableWork, Noether’s theorem on rationality of surfaces]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Noether’s theorem on rationality of surfaces
Context triple: [Max Noether, notableWork, Noether’s theorem on rationality of surfaces]
  • A. Noether’s theorem in algebraic geometry (Noether’s AF+BG theorem) chosen
    Noether’s AF+BG theorem is a foundational result in algebraic geometry that provides conditions under which a polynomial vanishing on the intersection of two plane curves can be expressed as a linear combination of their defining equations.
  • B. Hilbert’s irreducibility theorem
    Hilbert’s irreducibility theorem is a fundamental result in number theory and algebraic geometry that ensures many polynomial equations with parameterized coefficients retain irreducibility for infinitely many specializations of those parameters.
  • C. Riemann–Roch theorem
    The Riemann–Roch theorem is a fundamental result in algebraic geometry and complex analysis that relates the dimension of spaces of meromorphic sections of a line bundle on a curve to topological data such as genus and degree.
  • D. Hilbert’s Nullstellensatz
    Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
  • E. Hilbert’s syzygy theorem
    Hilbert’s syzygy theorem is a fundamental result in commutative algebra that describes the finite length and structure of free resolutions of modules over polynomial rings.
  • 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_69a88604618c81908b41f6429c431eb6 completed March 4, 2026, 7:20 p.m.
NER Named-entity recognition batch_69a90a41e5a08190b97dd1c0b12c662a completed March 5, 2026, 4:44 a.m.
NED1 Entity disambiguation (via context triple) batch_69ad71a61de8819095005c222ec50810 completed March 8, 2026, 12:55 p.m.
Created at: March 4, 2026, 7:28 p.m.