Triple
T718423
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Stanislaw Ulam |
E14360
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Ulam sequence
The Ulam sequence is an integer sequence starting with 1 and 2 in which each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms.
|
E85412
|
NE FINISHED |
How this triple was built (4 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: Ulam sequence | Statement: [Stanislaw Ulam, notableWork, Ulam sequence]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Ulam sequence Context triple: [Stanislaw Ulam, notableWork, Ulam sequence]
-
A.
Look-and-say sequence
The look-and-say sequence is a famous integer sequence where each term is generated by verbally describing the digits of the previous term, studied for its surprising combinatorial and growth properties.
-
B.
Fibonacci sequence
The Fibonacci sequence is an infinite series of numbers where each term is the sum of the two preceding ones, widely used in mathematics, art, and design due to its connection with the golden ratio and natural growth patterns.
-
C.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
-
D.
Surreal numbers
Surreal numbers are a class of numbers introduced by John H. Conway that form an extensive ordered field encompassing the real numbers, infinite quantities, and infinitesimals within a unified framework.
-
E.
Gauss’s constant
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Ulam sequence Triple: [Stanislaw Ulam, notableWork, Ulam sequence]
Generated description
The Ulam sequence is an integer sequence starting with 1 and 2 in which each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Ulam sequence Target entity description: The Ulam sequence is an integer sequence starting with 1 and 2 in which each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms.
-
A.
Look-and-say sequence
The look-and-say sequence is a famous integer sequence where each term is generated by verbally describing the digits of the previous term, studied for its surprising combinatorial and growth properties.
-
B.
Fibonacci sequence
The Fibonacci sequence is an infinite series of numbers where each term is the sum of the two preceding ones, widely used in mathematics, art, and design due to its connection with the golden ratio and natural growth patterns.
-
C.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
-
D.
Surreal numbers
Surreal numbers are a class of numbers introduced by John H. Conway that form an extensive ordered field encompassing the real numbers, infinite quantities, and infinitesimals within a unified framework.
-
E.
Gauss’s constant
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
- F. None of above. chosen
Provenance (5 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_69a4934a36e081909e7abef98b898a4e |
completed | March 1, 2026, 7:28 p.m. |
| NER | Named-entity recognition | batch_69a4a577658881909c12951d63d96377 |
completed | March 1, 2026, 8:45 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69a5dcb77bc481909d79542001fafbd2 |
completed | March 2, 2026, 6:53 p.m. |
| NEDg | Description generation | batch_69a5de57bbec81908a5d1202299194f4 |
completed | March 2, 2026, 7 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69a60952c6388190a23a178d695eec6e |
completed | March 2, 2026, 10:04 p.m. |
Created at: March 1, 2026, 7:37 p.m.