Triple
T21783540
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Higher composition laws I–IV |
E537777
|
entity |
| Predicate | part |
P3120
|
FINISHED |
| Object | Higher composition laws IV |
—
|
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 composition laws IV | Statement: [Higher composition laws I–IV, part, Higher composition laws IV]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Higher composition laws IV Context triple: [Higher composition laws I–IV, part, Higher composition laws IV]
-
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.
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.
-
C.
Automorphic Forms and the Reciprocity Law
"Automorphic Forms and the Reciprocity Law" is a seminal mathematical work by Goro Shimura that develops deep connections between automorphic forms, number theory, and reciprocity laws in arithmetic geometry.
-
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.
Siegel mass formula
The Siegel mass formula is a fundamental result in number theory that relates the weighted count (mass) of quadratic forms in a given genus to special values of zeta and L-functions, providing deep connections between arithmetic and geometry.
- 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.