Triple

T10991843
Position Surface form Disambiguated ID Type / Status
Subject Schwarz lemma E259769 entity
Predicate relatedResult P96512 FINISHED
Object Bloch theorem
Bloch theorem is a fundamental result in complex analysis stating that any holomorphic function on the unit disk with bounded derivative maps some subdisk onto a disk of a universal minimum radius, known as Bloch's constant.
E898493 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: Bloch theorem | Statement: [Schwarz lemma, relatedResult, Bloch theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Bloch theorem
Context triple: [Schwarz lemma, relatedResult, Bloch theorem]
  • A. Bloch waves
    Bloch waves are quantum-mechanical wavefunctions that describe particles, such as electrons, propagating through a periodic crystal lattice and form the basis for understanding electronic band structure in solids.
  • B. Brillouin theorem
    Brillouin theorem is a fundamental result in quantum chemistry and Hartree–Fock theory stating that single excitations from a Hartree–Fock ground state do not mix with the ground state and therefore do not lower its energy to first order.
  • C. Brillouin zone
    The Brillouin zone is the fundamental region of reciprocal space in a crystal lattice, defining the allowed wavevectors for electrons and underpinning the structure of electronic band diagrams.
  • D. Bloch
    Bloch is a surname most notably associated with Felix Bloch, the Swiss-American physicist and Nobel laureate known for his pioneering work in nuclear magnetic resonance.
  • E. Bloch oscillations
    Bloch oscillations are periodic oscillations of electrons in a crystal lattice subjected to a constant electric field, arising from the band structure and leading to oscillatory motion in momentum space.
  • 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: Bloch theorem
Triple: [Schwarz lemma, relatedResult, Bloch theorem]
Generated description
Bloch theorem is a fundamental result in complex analysis stating that any holomorphic function on the unit disk with bounded derivative maps some subdisk onto a disk of a universal minimum radius, known as Bloch's constant.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Bloch theorem
Target entity description: Bloch theorem is a fundamental result in complex analysis stating that any holomorphic function on the unit disk with bounded derivative maps some subdisk onto a disk of a universal minimum radius, known as Bloch's constant.
  • A. Bloch waves
    Bloch waves are quantum-mechanical wavefunctions that describe particles, such as electrons, propagating through a periodic crystal lattice and form the basis for understanding electronic band structure in solids.
  • B. Brillouin theorem
    Brillouin theorem is a fundamental result in quantum chemistry and Hartree–Fock theory stating that single excitations from a Hartree–Fock ground state do not mix with the ground state and therefore do not lower its energy to first order.
  • C. Brillouin zone
    The Brillouin zone is the fundamental region of reciprocal space in a crystal lattice, defining the allowed wavevectors for electrons and underpinning the structure of electronic band diagrams.
  • D. Bloch
    Bloch is a surname most notably associated with Felix Bloch, the Swiss-American physicist and Nobel laureate known for his pioneering work in nuclear magnetic resonance.
  • E. Bloch oscillations
    Bloch oscillations are periodic oscillations of electrons in a crystal lattice subjected to a constant electric field, arising from the band structure and leading to oscillatory motion in momentum space.
  • 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_69d6aa8a6a548190a750f944ccdc8064 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d795d1e918819090c71f5a077fa15a completed April 9, 2026, 12:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69e34504ebec8190a78e4795765b0c24 completed April 18, 2026, 8:47 a.m.
NEDg Description generation batch_69e3556fd3548190a33f04604be947cf completed April 18, 2026, 9:57 a.m.
NED2 Entity disambiguation (via description) batch_69e3593b0f8481909ed7a90f8bb9839d completed April 18, 2026, 10:13 a.m.
Created at: April 8, 2026, 9:24 p.m.