Triple
T5570613
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Fermat's theorem on sums of two squares |
E146190
|
entity |
| Predicate | hasIntegerCaseStatement |
P64863
|
FINISHED |
| Object | A positive integer n is a sum of two squares if and only if every prime factor q ≡ 3 (mod 4) occurs with even exponent in the prime factorization of n |
—
|
LITERAL 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: A positive integer n is a sum of two squares if and only if every prime factor q ≡ 3 (mod 4) occurs with even exponent in the prime factorization of n | Statement: [Fermat's theorem on sums of two squares, hasIntegerCaseStatement, A positive integer n is a sum of two squares if and only if every prime factor q ≡ 3 (mod 4) occurs with even exponent in the prime factorization of n]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: hasIntegerCaseStatement Context triple: [Fermat's theorem on sums of two squares, hasIntegerCaseStatement, A positive integer n is a sum of two squares if and only if every prime factor q ≡ 3 (mod 4) occurs with even exponent in the prime factorization of n]
-
A.
hasCase
Indicates that one entity is involved in, associated with, or characterized by a particular case, instance, or occurrence represented by another entity.
-
B.
hasTypeOfCase
Indicates that an entity is associated with or classified under a particular type or category of case.
-
C.
hasNumberOfCasesApprox
Indicates that an entity is associated with an approximate (not exact) count of cases.
-
D.
hasCanonicalNumber
Indicates that an entity is associated with its officially recognized or standard reference number.
-
E.
isIntegerUnitIn
Indicates that one integer-valued unit is contained within, or belongs to, a specified larger unit or unit set.
- F. None of above. chosen
Provenance (4 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_69c008ffed108190a084602227af6157 |
completed | March 22, 2026, 3:21 p.m. |
| NER | Named-entity recognition | batch_69c020502a288190af37f9ebb88fccae |
completed | March 22, 2026, 5:01 p.m. |
| PD | Predicate disambiguation | batch_69c01b12826c8190969a584d0f53aa44 |
completed | March 22, 2026, 4:38 p.m. |
| PDg | Predicate description generation | batch_69c01f4032408190a4f0d2eb21ebd870 |
completed | March 22, 2026, 4:56 p.m. |
Created at: March 22, 2026, 3:37 p.m.