Cophonicity¶
A vibrational-overlap metric measuring how strongly two atomic species contribute together within a selected frequency range.
Core Idea¶
The score is derived from species-resolved phonon participation or density-of-states information and depends on frequency window, mode normalization and structural model. Mode eigenvectors are projected onto the two atomic species, their spectral contributions are compared across the target band and normalized overlap quantifies whether the pair moves in the same vibrational region. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
Scope of Application¶
Cophonicity belongs to condensed matter physics and is useful where the analyst can specify the typed condensed matter physics carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, then evaluate the material and structure, atomic species pair, phonon calculation or measurement, frequency window, eigenvector or projected-density convention, normalization, overlap formula, sign or range, computational uncertainty and interpretation alongside bonding descriptors are explicit. The scope is broad within that domain but bounded by the need for the material and structure, atomic species pair, phonon calculation or measurement, frequency window, eigenvector or projected-density convention, normalization, overlap formula, sign or range, computational uncertainty and interpretation alongside bonding descriptors are explicit. Descriptive computational-materials metric only; no synthesis or laboratory procedure is provided.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the material and structure, atomic species pair, phonon calculation or measurement, frequency window, eigenvector or projected-density convention, normalization, overlap formula, sign or range, computational uncertainty and interpretation alongside bonding descriptors are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Cophonicity. Cophonicity compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed condensed matter physics carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the material and structure, atomic species pair, phonon calculation or measurement, frequency window, eigenvector or projected-density convention, normalization, overlap formula, sign or range, computational uncertainty and interpretation alongside bonding descriptors are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of condensed matter physics because they reuse the typed condensed matter physics carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, Mode eigenvectors are projected onto the two atomic species, their spectral contributions are compared across the target band and normalized overlap quantifies whether the pair moves in the same vibrational region., and type the carrier, state every parameter and convention in the definition, test that the material and structure, atomic species pair, phonon calculation or measurement, frequency window, eigenvector or projected-density convention, normalization, overlap formula, sign or range, computational uncertainty and interpretation alongside bonding descriptors are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Cophonicity Domain-specific
Parents (1) — more general patterns this builds on
-
Cophonicity is a kind of Correlation Prime
The proposed strict upward parent is
prime:correlation.
Hierarchy path (1) — routes to 1 parentless root
- Cophonicity → Correlation
Neighborhood in Abstraction Space¶
Cophonicity sits in a crowded region of the domain-specific corpus (29th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Superconductivity & Quantum Circuits (10 abstractions)
Nearest neighbors
- Phase space crystal — 0.93
- Frenkel–Kontorova model — 0.91
- Glass formation — 0.91
- Particle in a one-dimensional lattice — 0.91
- Second sound — 0.90
Computed from structural-signature embeddings · 2026-09-08