Triple

T21783559
Position Surface form Disambiguated ID Type / Status
Subject Higher composition laws I–IV E537777 entity
Predicate relatesTo P37 FINISHED
Object higher degree composition laws — 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: higher degree composition laws | Statement: [Higher composition laws I–IV, relatesTo, higher degree composition laws]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: higher degree composition laws
Context triple: [Higher composition laws I–IV, relatesTo, higher degree composition laws]
  • A. Higher composition laws I–IV chosen
    Higher composition laws I–IV is a landmark four-part series of papers by Manjul Bhargava that generalizes Gauss’s composition of binary quadratic forms and develops new structures and methods in algebraic number theory.
  • B. cubic reciprocity law
    The cubic reciprocity law is a number-theoretic result that extends the quadratic reciprocity law to describe how prime numbers behave with respect to cubic residues in certain algebraic number fields.
  • C. Artin reciprocity law
    The Artin reciprocity law is a fundamental theorem in class field theory that generalizes quadratic reciprocity by describing abelian extensions of number fields in terms of characters of their idele class groups.
  • D. Hilbert’s twelfth problem
    Hilbert’s twelfth problem is one of David Hilbert’s famous list of 23 problems, asking for a general explicit class field theory that would generate all abelian extensions of a given number field using special values of analytic functions.
  • E. quartic reciprocity law
    The quartic reciprocity law is a number-theoretic result that extends quadratic reciprocity by characterizing when an integer is a fourth power residue modulo an odd prime, using properties of Gaussian integers and higher power residue symbols.
  • 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_69e0c47198f881908cb0d237266c10e9 completed April 16, 2026, 11:13 a.m.
NER Named-entity recognition batch_69f046303d54819096b3fab4ab5678e6 completed April 28, 2026, 5:31 a.m.
Created at: April 16, 2026, 6:52 p.m.