Triple

T6834499
Position Surface form Disambiguated ID Type / Status
Subject Noga Alon E157415 entity
Predicate notableWork P4 FINISHED
Object Alon–Boppana bound
The Alon–Boppana bound is a fundamental result in spectral graph theory that gives an asymptotic lower bound on the second-largest eigenvalue of large regular graphs, showing inherent limitations on how well such graphs can approximate expanders.
E621145 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: Alon–Boppana bound | Statement: [Noga Alon, notableWork, Alon–Boppana bound]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Alon–Boppana bound
Context triple: [Noga Alon, notableWork, Alon–Boppana bound]
  • A. Erdős–Stone theorem
    The Erdős–Stone theorem is a fundamental result in extremal graph theory that asymptotically determines the maximum number of edges in an n-vertex graph that avoids containing a given subgraph.
  • B. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • C. Erdős–Ko–Rado theorem
    The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
  • D. Furst–Saxe–Sipser lower bounds
    Furst–Saxe–Sipser lower bounds are foundational results in circuit complexity theory that established superpolynomial lower bounds for constant-depth Boolean circuits (AC⁰), demonstrating inherent limitations of such circuits for computing certain functions.
  • E. May–Wigner stability theorem
    The May–Wigner stability theorem is a result in theoretical ecology and random matrix theory showing that large, complex systems with many random interactions are generically unstable beyond a critical level of complexity.
  • 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: Alon–Boppana bound
Triple: [Noga Alon, notableWork, Alon–Boppana bound]
Generated description
The Alon–Boppana bound is a fundamental result in spectral graph theory that gives an asymptotic lower bound on the second-largest eigenvalue of large regular graphs, showing inherent limitations on how well such graphs can approximate expanders.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Alon–Boppana bound
Target entity description: The Alon–Boppana bound is a fundamental result in spectral graph theory that gives an asymptotic lower bound on the second-largest eigenvalue of large regular graphs, showing inherent limitations on how well such graphs can approximate expanders.
  • A. Erdős–Stone theorem
    The Erdős–Stone theorem is a fundamental result in extremal graph theory that asymptotically determines the maximum number of edges in an n-vertex graph that avoids containing a given subgraph.
  • B. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • C. Erdős–Ko–Rado theorem
    The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
  • D. Furst–Saxe–Sipser lower bounds
    Furst–Saxe–Sipser lower bounds are foundational results in circuit complexity theory that established superpolynomial lower bounds for constant-depth Boolean circuits (AC⁰), demonstrating inherent limitations of such circuits for computing certain functions.
  • E. May–Wigner stability theorem
    The May–Wigner stability theorem is a result in theoretical ecology and random matrix theory showing that large, complex systems with many random interactions are generically unstable beyond a critical level of complexity.
  • 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_69c6882c53608190b99aebef079b23bd completed March 27, 2026, 1:37 p.m.
NER Named-entity recognition batch_69c6d67936288190829fedc3729aadd8 completed March 27, 2026, 7:11 p.m.
NED1 Entity disambiguation (via context triple) batch_69c723fd50c88190af005fd58ca0aee6 completed March 28, 2026, 12:42 a.m.
NEDg Description generation batch_69c7247806808190ac60c134cec612c8 completed March 28, 2026, 12:44 a.m.
NED2 Entity disambiguation (via description) batch_69c7253b94f081909e7cee870a12af6b completed March 28, 2026, 12:47 a.m.
Created at: March 27, 2026, 2:18 p.m.