Triple

T13893984
Position Surface form Disambiguated ID Type / Status
Subject Hadamard matrix E334040 entity
Predicate hasConstructionMethod P625 FINISHED
Object Goethals–Seidel construction
The Goethals–Seidel construction is a classical combinatorial method for building large Hadamard matrices from smaller ones using structured block and circulant matrix arrangements.
E1067635 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: Goethals–Seidel construction | Statement: [Hadamard matrix, hasConstructionMethod, Goethals–Seidel construction]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Goethals–Seidel construction
Context triple: [Hadamard matrix, hasConstructionMethod, Goethals–Seidel construction]
  • A. Bose construction of Steiner systems
    The Bose construction of Steiner systems is a combinatorial method introduced by mathematician Raj Chandra Bose to systematically build certain highly regular block designs known as Steiner systems.
  • B. Bose–Bush construction of orthogonal arrays
    The Bose–Bush construction of orthogonal arrays is a foundational combinatorial method that systematically builds highly structured experimental designs and error-correcting codes with strong balance and symmetry properties.
  • C. Golay code
    The Golay code is a highly symmetric, perfect error-correcting code in coding theory, notable for its deep connections to sporadic simple groups, sphere packings, and the Leech lattice.
  • D. Golomb
    Golomb is a station on the Carmelit underground funicular system in Haifa, Israel.
  • E. Szekeres configuration
    The Szekeres configuration is a notable geometric arrangement in projective geometry consisting of points and lines with specific incidence properties, studied for its combinatorial and symmetry characteristics.
  • 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: Goethals–Seidel construction
Triple: [Hadamard matrix, hasConstructionMethod, Goethals–Seidel construction]
Generated description
The Goethals–Seidel construction is a classical combinatorial method for building large Hadamard matrices from smaller ones using structured block and circulant matrix arrangements.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Goethals–Seidel construction
Target entity description: The Goethals–Seidel construction is a classical combinatorial method for building large Hadamard matrices from smaller ones using structured block and circulant matrix arrangements.
  • A. Bose construction of Steiner systems
    The Bose construction of Steiner systems is a combinatorial method introduced by mathematician Raj Chandra Bose to systematically build certain highly regular block designs known as Steiner systems.
  • B. Bose–Bush construction of orthogonal arrays
    The Bose–Bush construction of orthogonal arrays is a foundational combinatorial method that systematically builds highly structured experimental designs and error-correcting codes with strong balance and symmetry properties.
  • C. Golay code
    The Golay code is a highly symmetric, perfect error-correcting code in coding theory, notable for its deep connections to sporadic simple groups, sphere packings, and the Leech lattice.
  • D. Golomb
    Golomb is a station on the Carmelit underground funicular system in Haifa, Israel.
  • E. Szekeres configuration
    The Szekeres configuration is a notable geometric arrangement in projective geometry consisting of points and lines with specific incidence properties, studied for its combinatorial and symmetry characteristics.
  • 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_69d81c5dd2d48190b7a5fc1e009de936 completed April 9, 2026, 9:38 p.m.
NER Named-entity recognition batch_69de23a741908190bdf46d76c5f1411a completed April 14, 2026, 11:23 a.m.
NED1 Entity disambiguation (via context triple) batch_69f7c71ca8a881908ac02687fbfe62fb completed May 3, 2026, 10:07 p.m.
NEDg Description generation batch_69f7c7e1247481908073c1e282c3619f completed May 3, 2026, 10:10 p.m.
NED2 Entity disambiguation (via description) batch_69f7c8f2b5588190b6143d676eb648a0 completed May 3, 2026, 10:15 p.m.
Created at: April 9, 2026, 10:15 p.m.