Triple

T1043667
Position Surface form Disambiguated ID Type / Status
Subject Johan Håstad E22525 entity
Predicate notableWork P4 FINISHED
Object “Inapproximability results for SAT and other problems”
“Inapproximability results for SAT and other problems” is a seminal theoretical computer science paper by Johan Håstad that establishes tight hardness-of-approximation bounds for satisfiability and related optimization problems using probabilistically checkable proofs.
E124291 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: “Inapproximability results for SAT and other problems” | Statement: [Johan Håstad, notableWork, “Inapproximability results for SAT and other problems”]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: “Inapproximability results for SAT and other problems”
Context triple: [Johan Håstad, notableWork, “Inapproximability results for SAT and other problems”]
  • A. Interactive Proofs and the Hardness of Approximating Cliques
    "Interactive Proofs and the Hardness of Approximating Cliques" is a seminal theoretical computer science paper that introduced powerful interactive proof techniques to show that finding near-maximum cliques in graphs is computationally intractable to approximate within strong bounds.
  • B. Håstad’s switching lemma
    Håstad’s switching lemma is a fundamental result in computational complexity theory that provides powerful bounds on the simplification of Boolean formulas under random restrictions, with major applications in circuit lower bounds.
  • C. PCP theorem
    The PCP theorem is a fundamental result in computational complexity theory stating that every problem in NP has probabilistically checkable proofs that can be verified by examining only a constant number of bits, with major implications for the hardness of approximation.
  • D. “Almost optimal lower bounds for small depth circuits”
    “Almost optimal lower bounds for small depth circuits” is a seminal theoretical computer science paper by Johan Håstad that establishes near-tight lower bounds on the size of constant-depth Boolean circuits, profoundly influencing circuit complexity theory.
  • E. Blum complexity measures
    Blum complexity measures are a formal framework in computational complexity theory that rigorously define and compare the resource usage (such as time or space) of algorithms via axiomatic conditions.
  • 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: “Inapproximability results for SAT and other problems”
Triple: [Johan Håstad, notableWork, “Inapproximability results for SAT and other problems”]
Generated description
“Inapproximability results for SAT and other problems” is a seminal theoretical computer science paper by Johan Håstad that establishes tight hardness-of-approximation bounds for satisfiability and related optimization problems using probabilistically checkable proofs.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: “Inapproximability results for SAT and other problems”
Target entity description: “Inapproximability results for SAT and other problems” is a seminal theoretical computer science paper by Johan Håstad that establishes tight hardness-of-approximation bounds for satisfiability and related optimization problems using probabilistically checkable proofs.
  • A. Interactive Proofs and the Hardness of Approximating Cliques
    "Interactive Proofs and the Hardness of Approximating Cliques" is a seminal theoretical computer science paper that introduced powerful interactive proof techniques to show that finding near-maximum cliques in graphs is computationally intractable to approximate within strong bounds.
  • B. Håstad’s switching lemma
    Håstad’s switching lemma is a fundamental result in computational complexity theory that provides powerful bounds on the simplification of Boolean formulas under random restrictions, with major applications in circuit lower bounds.
  • C. PCP theorem
    The PCP theorem is a fundamental result in computational complexity theory stating that every problem in NP has probabilistically checkable proofs that can be verified by examining only a constant number of bits, with major implications for the hardness of approximation.
  • D. “Almost optimal lower bounds for small depth circuits”
    “Almost optimal lower bounds for small depth circuits” is a seminal theoretical computer science paper by Johan Håstad that establishes near-tight lower bounds on the size of constant-depth Boolean circuits, profoundly influencing circuit complexity theory.
  • E. Blum complexity measures
    Blum complexity measures are a formal framework in computational complexity theory that rigorously define and compare the resource usage (such as time or space) of algorithms via axiomatic conditions.
  • 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_69a493d91478819094cc01fb65564bc1 completed March 1, 2026, 7:30 p.m.
NER Named-entity recognition batch_69a4b8475ab48190848388eea6448cb6 completed March 1, 2026, 10:05 p.m.
NED1 Entity disambiguation (via context triple) batch_69ac429ad45481908641fcaf72f7d1b9 completed March 7, 2026, 3:22 p.m.
NEDg Description generation batch_69ac4365965881909ff2cdf8eda07f91 completed March 7, 2026, 3:25 p.m.
NED2 Entity disambiguation (via description) batch_69ac43d1cd1c8190852f8811703ebd5f completed March 7, 2026, 3:27 p.m.
Created at: March 1, 2026, 7:42 p.m.