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.