Triple

T6800988
Position Surface form Disambiguated ID Type / Status
Subject Lagrange's four-square theorem E156185 entity
Predicate specialCaseOf P7025 FINISHED
Object Waring's problem E451523 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: Waring's problem | Statement: [Lagrange's four-square theorem, specialCaseOf, Waring's problem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Waring's problem
Context triple: [Lagrange's four-square theorem, specialCaseOf, Waring's problem]
  • A. Waring's problem chosen
    Waring's problem is a famous conjecture in number theory that concerns representing natural numbers as sums of fixed powers of integers and determining how many such powers are needed.
  • B. Erdős–Turán conjecture
    The Erdős–Turán conjecture is an unsolved problem in additive number theory asserting that any subset of the positive integers with divergent sum of reciprocals must contain arbitrarily long arithmetic progressions.
  • C. Lagrange's four-square theorem
    Lagrange's four-square theorem is a fundamental result in number theory stating that every natural number can be expressed as the sum of four integer squares.
  • D. Fermat polygonal number theorem
    The Fermat polygonal number theorem is a result in number theory stating that every positive integer can be expressed as a sum of a fixed number of polygonal numbers of a given order.
  • E. Vinogradov's three-primes theorem
    Vinogradov's three-primes theorem is a landmark result in analytic number theory proving that every sufficiently large odd integer can be expressed as the sum of three prime numbers.
  • 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_69c68826e6a48190a3d220b541e639de completed March 27, 2026, 1:37 p.m.
NER Named-entity recognition batch_69c6d2e595188190a0bb4b595df3adb2 completed March 27, 2026, 6:56 p.m.
NED1 Entity disambiguation (via context triple) batch_69c71a9b0cc48190819380aeaf0228e7 completed March 28, 2026, 12:02 a.m.
Created at: March 27, 2026, 2:16 p.m.