Triple

T787788
Position Surface form Disambiguated ID Type / Status
Subject Mark Kac E16842 entity
Predicate notableWork P4 FINISHED
Object Can one hear the shape of a drum?
"Can one hear the shape of a drum?" is a famous 1966 paper by mathematician Mark Kac that explores whether the geometric shape of a domain can be uniquely determined from the spectrum of its Laplacian, encapsulated in the question of whether one can infer a drum’s shape from the sound it makes.
E92906 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: Can one hear the shape of a drum? | Statement: [Mark Kac, notableWork, Can one hear the shape of a drum?]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Can one hear the shape of a drum?
Context triple: [Mark Kac, notableWork, Can one hear the shape of a drum?]
  • A. Israel–Carter–Robinson uniqueness theorems
    The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
  • B. The Science of Musical Sound
    The Science of Musical Sound is a book by engineer and acoustics researcher John R. Pierce that explains the physical and perceptual principles underlying how music and sound are produced, transmitted, and heard.
  • C. Euler’s polyhedron formula
    Euler’s polyhedron formula is a fundamental result in topology and geometry that relates the numbers of vertices, edges, and faces of a convex polyhedron through the equation V − E + F = 2.
  • D. Theorema Egregium
    Theorema Egregium is Gauss’s celebrated theorem in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
  • E. Hilbert problems
    The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
  • 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: Can one hear the shape of a drum?
Triple: [Mark Kac, notableWork, Can one hear the shape of a drum?]
Generated description
"Can one hear the shape of a drum?" is a famous 1966 paper by mathematician Mark Kac that explores whether the geometric shape of a domain can be uniquely determined from the spectrum of its Laplacian, encapsulated in the question of whether one can infer a drum’s shape from the sound it makes.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Can one hear the shape of a drum?
Target entity description: "Can one hear the shape of a drum?" is a famous 1966 paper by mathematician Mark Kac that explores whether the geometric shape of a domain can be uniquely determined from the spectrum of its Laplacian, encapsulated in the question of whether one can infer a drum’s shape from the sound it makes.
  • A. Israel–Carter–Robinson uniqueness theorems
    The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
  • B. The Science of Musical Sound
    The Science of Musical Sound is a book by engineer and acoustics researcher John R. Pierce that explains the physical and perceptual principles underlying how music and sound are produced, transmitted, and heard.
  • C. Euler’s polyhedron formula
    Euler’s polyhedron formula is a fundamental result in topology and geometry that relates the numbers of vertices, edges, and faces of a convex polyhedron through the equation V − E + F = 2.
  • D. Theorema Egregium
    Theorema Egregium is Gauss’s celebrated theorem in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
  • E. Hilbert problems
    The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
  • 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_69a4936cb7448190914f5fe4b8d81607 completed March 1, 2026, 7:28 p.m.
NER Named-entity recognition batch_69a4a78171908190a38a70274bfbebf9 completed March 1, 2026, 8:54 p.m.
NED1 Entity disambiguation (via context triple) batch_69a6733e47148190bad0ac71cf45dd85 completed March 3, 2026, 5:35 a.m.
NEDg Description generation batch_69a673afbd308190863aea2ff0f650cb completed March 3, 2026, 5:37 a.m.
NED2 Entity disambiguation (via description) batch_69a6743f50d0819089885836b9668466 completed March 3, 2026, 5:40 a.m.
Created at: March 1, 2026, 7:38 p.m.