Triple

T10807750
Position Surface form Disambiguated ID Type / Status
Subject Richard S. Hamilton E255012 entity
Predicate knownFor P22 FINISHED
Object Hamilton’s maximum principle for tensors E255014 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: Hamilton’s maximum principle for tensors | Statement: [Richard S. Hamilton, knownFor, Hamilton’s maximum principle for tensors]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hamilton’s maximum principle for tensors
Context triple: [Richard S. Hamilton, knownFor, Hamilton’s maximum principle for tensors]
  • A. Hamilton’s maximum principle chosen
    Hamilton’s maximum principle is a fundamental analytical tool in geometric analysis that extends the classical maximum principle to tensor-valued quantities, playing a key role in studying the behavior of solutions to the Ricci flow and related geometric evolution equations.
  • B. Pontryagin maximum principle
    The Pontryagin maximum principle is a fundamental result in optimal control theory that provides necessary conditions for an optimal control process by characterizing optimal trajectories via a Hamiltonian maximization condition.
  • C. Mathematical Theory of Optimal Processes
    Mathematical Theory of Optimal Processes is a foundational work in control theory that systematically develops the mathematical principles of optimal control, including what is now known as Pontryagin’s maximum principle.
  • D. Vessiot theory of differential equations
    The Vessiot theory of differential equations is a geometric framework that studies differential equations via their symmetry and structure using concepts from Lie groups and differential geometry.
  • E. Hamilton–Jacobi equation
    The Hamilton–Jacobi equation is a fundamental partial differential equation in classical mechanics that reformulates dynamics in terms of a generating function, providing a powerful bridge to quantum mechanics and modern analytical methods.
  • 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_69d6aa61c15c8190a1839550c56e75e1 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d733b506488190921e6a1f4168dd9e completed April 9, 2026, 5:05 a.m.
NED1 Entity disambiguation (via context triple) batch_69de8513fe0881909d6833c85aac03a8 completed April 14, 2026, 6:19 p.m.
Created at: April 8, 2026, 9:18 p.m.