Triple
T16150925
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Todd class |
E391905
|
entity |
| Predicate | appearsAsFactorIn |
P90033
|
FINISHED |
| Object | Grothendieck–Riemann–Roch integrand |
E254119
|
NE FINISHED |
How this triple was built (3 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: Grothendieck–Riemann–Roch integrand | Statement: [Todd class, appearsAsFactorIn, Grothendieck–Riemann–Roch integrand]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Grothendieck–Riemann–Roch integrand Context triple: [Todd class, appearsAsFactorIn, Grothendieck–Riemann–Roch integrand]
-
A.
Grothendieck–Riemann–Roch theorem
chosen
The Grothendieck–Riemann–Roch theorem is a fundamental result in algebraic geometry that generalizes the classical Riemann–Roch theorem by relating pushforwards in K-theory to pushforwards in cohomology via characteristic classes.
-
B.
Grothendieck–Ogg–Shafarevich formula
The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
-
C.
Hirzebruch–Riemann–Roch theorem
The Hirzebruch–Riemann–Roch theorem is a fundamental result in algebraic geometry and topology that expresses the holomorphic Euler characteristic of a complex manifold in terms of characteristic classes, unifying and extending classical Riemann–Roch type formulas.
-
D.
Grothendieck–Lefschetz trace formula
The Grothendieck–Lefschetz trace formula is a fundamental result in algebraic geometry that expresses the number of rational points of a variety over a finite field in terms of traces of Frobenius acting on its étale cohomology groups.
-
E.
Bott residue formula
The Bott residue formula is a fundamental result in differential and algebraic geometry that expresses global invariants, such as characteristic numbers, as sums of local contributions at the fixed points of a holomorphic vector field or group action.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: appearsAsFactorIn Context triple: [Todd class, appearsAsFactorIn, Grothendieck–Riemann–Roch integrand]
-
A.
factor
chosen
Indicates that one entity is a contributing cause, influence, or component affecting the state, outcome, or existence of another entity.
-
B.
arisesIn
Indicates that something originates, emerges, or comes into existence within a specified context, source, or location.
-
C.
considersFactor
Indicates that one entity takes another entity into account as a factor when forming a judgment, decision, or evaluation.
-
D.
areUsedIn
Indicates that certain entities serve as components, tools, or resources within a particular process, context, or application.
-
E.
isUsedAs
Indicates that one entity serves a particular function, role, or purpose as another entity.
- F. None of above.
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_69d87f1c65e48190aa2b4c472e9bafc4 |
completed | April 10, 2026, 4:39 a.m. |
| NER | Named-entity recognition | batch_69e21d9724808190a8332987583a345a |
completed | April 17, 2026, 11:46 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69fff7a9ebf08190aa21cdff051f4ba2 |
completed | May 10, 2026, 3:12 a.m. |
| PD | Predicate disambiguation | batch_69e1828abb608190a99d86bce1d77de2 |
completed | April 17, 2026, 12:44 a.m. |
Created at: April 10, 2026, 5:01 a.m.