Triple

T17671669
Position Surface form Disambiguated ID Type / Status
Subject Benedict Gross E440533 entity
Predicate knownFor P22 FINISHED
Object Gross–Zagier formula on heights of Heegner points NE NERFINISHED

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: Gross–Zagier formula on heights of Heegner points | Statement: [Benedict Gross, knownFor, Gross–Zagier formula on heights of Heegner points]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gross–Zagier formula on heights of Heegner points
Context triple: [Benedict Gross, knownFor, Gross–Zagier formula on heights of Heegner points]
  • A. Gross–Zagier formula chosen
    The Gross–Zagier formula is a fundamental result in number theory that relates the heights of Heegner points on elliptic curves to the derivatives of associated L-functions, with deep implications for the Birch and Swinnerton-Dyer conjecture.
  • B. Siegel’s theorem on zeros of L-functions
    Siegel’s theorem on zeros of L-functions is a result in analytic number theory that gives strong bounds on how close nontrivial zeros of Dirichlet L-functions can approach 1, with deep implications for the distribution of primes in arithmetic progressions.
  • C. Bloch–Kato conjecture
    The Bloch–Kato conjecture is a deep statement in arithmetic geometry and K-theory that predicts an exact correspondence between Galois cohomology and Milnor K-theory, linking algebraic K-groups to field arithmetic.
  • D. Shimura reciprocity law
    The Shimura reciprocity law is a fundamental result in number theory that generalizes classical reciprocity laws by describing how values of modular functions at complex multiplication (CM) points transform under the action of Galois groups.
  • E. Birch and Swinnerton-Dyer Conjecture
    The Birch and Swinnerton-Dyer Conjecture is a central unsolved problem in number theory that predicts a deep connection between the arithmetic of rational points on an elliptic curve and the behavior of its associated L-function at a specific value.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69d8b9e87e18819087104a44dc4dc5b1 completed April 10, 2026, 8:50 a.m.
NER Named-entity recognition batch_69e46f69b11c8190b09add33f81776b3 completed April 19, 2026, 6 a.m.
Created at: April 10, 2026, 9:59 a.m.