--- { "path": "/en/research/glossary", "title": "ASD Terminology Database", "category": "Research", "summary": "Find definitions in context, distinguish reused symbols, and follow the current source and equation records.", "related": [ "/en/theory/lve", "/en/theory/space-dynamics", "/ai/knowledge-base" ], "id": "ASD-DOC-EN-RESEARCH-GLOSSARY", "template": "document", "version": "1.1", "updated": "2026-10-24", "canonical": false, "source_tier": "website-guide", "depends_on": [], "open_problems": [], "equations": [], "sources": [ { "label": "Current canonical module MDX and equation registry; term source sections are linked below.", "kind": "website-content-registry" } ], "theory_status": "FOUNDATION", "evidence_status": "DOCUMENT", "title_en": "ASD Terminology Database", "locale": "en", "section_anchors": [ "using-terminology", "length-realization", "reference-process", "lve", "gamma", "mechanical-momentum", "true-distance", "area-radius", "gravity-omega", "gravity-phi", "gravity-state-potential", "true-line-element", "optical-path", "continuum-state", "longitudinal-compression", "transverse-rotation", "helmholtz", "fcc", "particle-candidate", "stability", "accompanying-field", "phase-momentum", "modal-action", "quantum-phi", "quantum-envelope", "quantum-omega", "fourier-width", "conditional-detection", "envelope-tunneling", "semantic-symbols" ], "legacy_anchors": { "s0": "lve", "s1": "true-distance", "s2": "longitudinal-compression", "s3": "accompanying-field", "s4": "particle-candidate", "s5": "gamma" }, "translation_path": "/research/glossary", "translation_of": "/research/glossary", "translation_version": "1.1", "section_final_sources": { "semantic-symbols": { "source_id": "ASD-BOOK-ddbade997b45", "chapter": "Chapters 1–5", "reference": "Semantic-symbol section: chapter, equation and paragraph contexts are recorded per entry; existing terminology entries retain their module sources.", "locators": [ "p0961", "p0962", "p1780", "p1740", "p2254", "p2256", "p0573", "p0575", "p0588", "p1351", "p1939", "p2298", "p2299", "p1600", "p1880", "p1993", "p1995", "p2281", "p0580", "p0582", "p1321", "p1343", "p2028", "p2029", "p2018", "p2037", "p2040", "p2224", "p0981", "p0983", "p0985", "p0987", "p0999", "p1983", "p2023", "p1000", "p1907", "p2044" ], "adopted_scope": "Only the added semantic-symbols section: definitions, units and explicit editorial mappings. This does not declare every existing glossary entry migrated.", "conditions": [ "Identical glyphs do not automatically denote the same physical quantity", "Cross-model mappings retain variable, reference and normalization conditions" ], "unresolved": [], "migration_status": "reviewed" } } } --- ## Using this database Definitions here are reading aids derived from the current module text. A term link opens the relevant physical assumptions and derivation; it does not replace them. Search either language, a symbol or an equation ID. The module filter separates symbols such as Ω, Φ and Ψ whose meanings change across modules. ## Length realization An operational relation between a specified propagation path and its elapsed time. One-way and return geometries, synchronization and endpoint conditions must be specified; a unit definition does not determine moving-space or gravitational response. Source context: [Metrological Foundations · What r = ct specifies · Operational Meaning](/en/theory/metrology#s2)。 Related registered equations: [ASD-WEB-MET-001](/equations/ASD-WEB-MET-001)。 ## Reference process and cycle counting A reference process supplies a shared counting standard; the measured process supplies the path, rate or period under comparison. A readout converted with a reference frequency must be distinguished from physical changes in the measured process. Counting identities do not replace response dynamics. Source context: [Time · Measurement and Process · Reference and measured processes · Starting Definitions](/en/theory/time/measurement-and-process#s0)。 Related registered equations: [ASD-WEB-TIME-002](/equations/ASD-WEB-TIME-002) · [ASD-WEB-TIME-003](/equations/ASD-WEB-TIME-003)。 ## Length Vector Effect The directional response of ASD true spatial lengths to motion. The reference transverse length and motion-associated true length play different roles. The result retains Chapter 1’s forward/reverse construction and path-pairing conditions. Source context: [Length Vector Effect · Core Statement](/en/theory/lve#s0)。 Related registered equations: [ASD-WEB-LVE-001](/equations/ASD-WEB-LVE-001) · [ASD-WEB-LVE-008](/equations/ASD-WEB-LVE-008)。 ## Motion factor γ In LVE, γ is defined using the relative speed divided by c and enters directional length relations. Its ASD spatial-response interpretation and derivation conditions are retained; a shared symbol does not import another theory’s derivation. Source context: [Length Vector Effect · Derivation at a Glance](/en/theory/lve#s2)。 Related registered equations: [ASD-WEB-LVE-001](/equations/ASD-WEB-LVE-001) · [ASD-WEB-LVE-008](/equations/ASD-WEB-LVE-008)。 ## Total mechanical momentum Momentum obtained by integrating the inertial response of the core and accompanying field. Chapter 2 uses LVE geometry together with mass normalization and a constitutive angular inertial distribution; geometry alone does not determine it. Source context: [Dynamics · Inertia and Momentum · Total momentum and intermediate steps · Momentum Integration](/en/theory/dynamics/momentum#s4)。 Related registered equations: [ASD-WEB-DYN-007](/equations/ASD-WEB-DYN-007) · [ASD-WEB-DYN-008](/equations/ASD-WEB-DYN-008)。 ## True interaction distance The electromagnetic construction adopts the LVE true length as the interaction distance and applies an inverse-square law there. This is a constitutive choice. Forces obtained by differentiating with respect to true separation and reference coordinates require a virtual-work mapping before comparison. Source context: [Coulomb Interaction: Distances and Physical Quantities · Constitutive Choice in True Distance](/en/theory/electromagnetism/coulomb-interaction#s2)。 Related registered equations: [ASD-WEB-EM-005](/equations/ASD-WEB-EM-005) · [ASD-WEB-EM-008](/equations/ASD-WEB-EM-008)。 ## Area radius The radial coordinate defined by spherical surface area in the spherical model. It differs from accumulated true radial distance. Tangential arc length already contains the area-radius information and does not acquire a second radial stretch factor. Source context: [Gravity · Spatial Structure and Observables · From scale variation to the gravitational field](/en/theory/gravity#gravity-scale-field)。 Related registered equations: [ASD-WEB-GRV-002](/equations/ASD-WEB-GRV-002)。 ## Linear expansion coefficient Ω The dimensionless linear-scale coefficient of the static exterior gravity model, normalized to one far away. Coupling standard-process lengths and frequencies to it is an explicit input. It is not the slow angular frequency of a quantum envelope. Source context: [Gravity · Spatial Structure and Observables · From scale variation to the gravitational field](/en/theory/gravity#gravity-scale-field)。 Related registered equations: [ASD-WEB-GRV-002](/equations/ASD-WEB-GRV-002)。 ## Linear-density coefficient Φ The inverse of the linear expansion coefficient in gravity. It is dimensionless, not a three-dimensional material density or the quantum effective field. Converting line scales to volume density requires the actual deformation’s volume ratio. Source context: [Gravity · Spatial Structure and Observables · From scale variation to the gravitational field](/en/theory/gravity#gravity-scale-field)。 Related registered equations: [ASD-WEB-GRV-002](/equations/ASD-WEB-GRV-002) · [ASD-WEB-GRV-003](/equations/ASD-WEB-GRV-003)。 ## Spatial state X and gravitational potential Ψ X is a dimensionless state variable defined as the squared linear-density coefficient. Ψ is a gravitational potential with units of speed squared, set to zero far away. The weak-field force on a slow test body also uses an external-energy coupling. This Ψ is not a complex envelope. Source context: [Gravity · Spatial Structure and Observables · From scale variation to the gravitational field](/en/theory/gravity#gravity-scale-field)。 Related registered equations: [ASD-WEB-GRV-003](/equations/ASD-WEB-GRV-003) · [ASD-WEB-GRV-004](/equations/ASD-WEB-GRV-004)。 ## True spatial line element The increment of true spatial path length, combining radial and tangential contributions in the spherical exterior background. It measures spatial length before conversion to a shared reference counting standard. Source context: [Gravity · Spatial Structure and Observables · Propagation and motion in the same spatial background](/en/theory/gravity#gravity-paths-motion)。 Related registered equations: [ASD-WEB-GRV-006](/equations/ASD-WEB-GRV-006)。 ## Reference optical path A propagation quantity combining true path length with standard-process counting conversion. Its integral divided by c enters reference propagation counts. Its weighting is not merely a Euclidean detour, and coordinate representation must not be counted as an additional effect. Source context: [Gravity · Spatial Structure and Observables · Propagation and motion in the same spatial background](/en/theory/gravity#gravity-paths-motion)。 Related registered equations: [ASD-WEB-GRV-008](/equations/ASD-WEB-GRV-008)。 ## Continuum state field An effective field with dimensions of length represents small displacement or normalized spatial-state variation; its meaning is fixed by the model. Continuum variables and their dimensions do not require a particular microscopic lattice. Source context: [Continuum Degrees of Freedom · Continuum variables and dimensions](/en/theory/space-dynamics/degrees-of-freedom#s0)。 ## Longitudinal compression degree of freedom Divergence describes volume change at small deformation: positive divergence means expansion, while positive σ denotes compression in this module. These definitions do not identify a static gravitational background, a free longitudinal wave and a matter-associated structure as the same solution. Source context: [Continuum Degrees of Freedom · Divergence and curl have different roles](/en/theory/space-dynamics/degrees-of-freedom#s2)。 Related registered equations: [ASD-WEB-SD-003](/equations/ASD-WEB-SD-003)。 ## Transverse sector and local rotation The divergence-free transverse projection is related to local rotation, but full shear also includes symmetric traceless strain. Curl is twice local rotation; the entire transverse deformation cannot be reduced to curl alone. Source context: [Continuum Degrees of Freedom · Divergence and curl have different roles](/en/theory/space-dynamics/degrees-of-freedom#s2)。 Related registered equations: [ASD-WEB-SD-004](/equations/ASD-WEB-SD-004) · [ASD-WEB-SD-001](/equations/ASD-WEB-SD-001)。 ## Helmholtz longitudinal–transverse decomposition Under decay or compatible boundary conditions, a field splits into curl-free longitudinal and divergence-free transverse parts. Zero-wave-number and harmonic components need global conditions. Geometric projection need not commute with propagation in an inhomogeneous constitutive model, so it does not guarantee dynamical decoupling. Source context: [Continuum Degrees of Freedom · Decomposition and boundaries](/en/theory/space-dynamics/degrees-of-freedom#s1)。 Related registered equations: [ASD-WEB-SD-001](/equations/ASD-WEB-SD-001) · [ASD-WEB-SD-002](/equations/ASD-WEB-SD-002)。 ## FCC-like microscopic candidate A candidate microscopic implementation using face-centred cubic adjacency. Symmetry and neighbor geometry alone do not supply the complete dynamical matrix, stable particles or experimental response. The continuum core does not assume FCC is unique. Source context: [FCC-like Microscopic Model · What geometry supplies](/en/theory/space-dynamics/fcc-model#s1)。 Related registered equations: [ASD-WEB-SD-020](/equations/ASD-WEB-SD-020)。 ## Particle-topology candidate A candidate physical picture for localized electron or proton structures, distinct from a solved field configuration. Finite energy, boundary conditions, topology, stability, moving families and external-field response each require demonstration. Source context: [How Can Spatial Dynamics Become Matter? · Three distinct levels](/en/theory/matter#s1)。 ## Stability test A test of response to allowed perturbations for a specified action and constraints. Static stationarity, second variation, symmetry zero modes and negative modes are distinct. A minimum along one scaling family is not proof of stability against all perturbations. Source context: [What Could Stabilize a Localized Structure? · Define admissible perturbations first](/en/theory/matter/stability#s0)。 Related registered equations: [ASD-WEB-MAT-007](/equations/ASD-WEB-MAT-007)。 ## Accompanying field A spatial response associated with a localized core and its preparation history, potentially including co-moving near fields, deformation and phase. It is distinct from the core and is not automatically free radiation carrying energy away; sources, boundaries and energy flow determine the solution. Source context: [Why Would Moving Matter Generate an Accompanying Field? · The localized core moves with its surrounding field](/en/theory/quantum/accompanying-field#accompanying-objects)。 Related registered equations: [ASD-WEB-QM-003](/equations/ASD-WEB-QM-003) · [ASD-WEB-QM-006](/equations/ASD-WEB-QM-006)。 ## Phase–momentum matching The physical matching of total mechanical momentum to the field’s phase gradient. Relations involving modal energy, momentum and action additionally require single-excitation action and mass matching. Writing the de Broglie form does not independently close those inputs. Source context: [From Mechanical Momentum to Matter-Wave Phase · How mode action connects energy, momentum and phase](/en/theory/quantum/matter-wave#matter-phase-matching)。 Related registered equations: [ASD-WEB-QM-009](/equations/ASD-WEB-QM-009)。 ## Modal action An action quantity relating mode energy, frequency and momentum for a specified mode and normalization. Matching a single excitation to the reduced Planck constant is an explicit condition, not a consequence of complex notation or normalization. Source context: [From Mechanical Momentum to Matter-Wave Phase · How mode action connects energy, momentum and phase](/en/theory/quantum/matter-wave#matter-phase-matching)。 Related registered equations: [ASD-WEB-QM-009](/equations/ASD-WEB-QM-009)。 ## Positive-frequency channel field Φ⁽⁺⁾ The positive-frequency effective field on a selected extended gapped propagation branch. Its channel, source and constitutive inputs precede the envelope approximation. It is not gravity’s dimensionless linear-density coefficient Φ. Source context: [How Does a Spatial Field Yield an Effective Wave Equation? · Why a propagation channel must be selected first](/en/theory/quantum/effective-wave-equation#envelope-channel)。 Related registered equations: [ASD-WEB-QM-005](/equations/ASD-WEB-QM-005) · [ASD-WEB-QM-011](/equations/ASD-WEB-QM-011)。 ## Complex envelope Ψ A complex quantity extracted from a fast carrier to describe slow amplitude and phase variation. Its real and imaginary parts can encode two real quadrature components; complex notation itself does not define detection probability. It is distinct from gravitational potential Ψ. Source context: [How Does a Spatial Field Yield an Effective Wave Equation? · Separating the fast carrier from the slow envelope](/en/theory/quantum/effective-wave-equation#envelope-carrier)。 Related registered equations: [ASD-WEB-QM-012](/equations/ASD-WEB-QM-012) · [ASD-WEB-QM-013](/equations/ASD-WEB-QM-013)。 ## Slow envelope angular frequency Ω A slow frequency relative to the carrier, not the total field frequency. Scale separation from the carrier controls omission of the second slow-time derivative. It has frequency units and differs from gravity’s dimensionless expansion coefficient Ω. Source context: [How Does a Spatial Field Yield an Effective Wave Equation? · How slow variation and mass matching enter](/en/theory/quantum/effective-wave-equation#envelope-matching)。 Related registered equations: [ASD-WEB-QM-014](/equations/ASD-WEB-QM-014) · [ASD-WEB-QM-016](/equations/ASD-WEB-QM-016)。 ## Fourier standard-deviation widths Position and wave-number standard deviations of a normalized envelope and its Fourier spectrum. The mathematical bound requires finite second moments and suitable boundaries. Momentum widths additionally require phase–momentum matching and do not automatically specify measured core-event statistics. Source context: [Uncertainty: Fourier Width Bounds for Wave Packets · What width does a localized wave packet have?](/en/theory/quantum/uncertainty-probability#uncertainty-widths)。 Related registered equations: [ASD-WEB-QM-022](/equations/ASD-WEB-QM-022) · [ASD-WEB-QM-023](/equations/ASD-WEB-QM-023)。 ## Conditional detection-position distribution A position distribution obtained by normalizing event rates over a specified time window, thickness and active screen, conditional on detection. A squared-amplitude form depends on linear material response, energy conversion and efficiency. This normalization alone proves neither universal Born statistics nor exactly one record per excitation. Source context: [How Can Continuous Fields Yield Discrete Detection Statistics? · From event rate to a conditional screen distribution](/en/theory/quantum/detection-statistics#detection-distribution)。 Related registered equations: [ASD-WEB-QM-026](/equations/ASD-WEB-QM-026) · [ASD-WEB-QM-027](/equations/ASD-WEB-QM-027)。 ## Effective-envelope tunneling A barrier boundary-value problem in a matched effective channel, with transmission defined by transmitted-to-incident flux. A decaying envelope in the barrier does not prove that the nonlinear matter core crosses it; core–field–barrier dynamics require separate closure. Source context: [Tunneling: Effective Transmission and Core Transport · What must be compared on the two sides of a barrier](/en/theory/quantum/tunneling#tunneling-problem)。 Related registered equations: [ASD-WEB-QM-030](/equations/ASD-WEB-QM-030) · [ASD-WEB-QM-031](/equations/ASD-WEB-QM-031)。 ## Symbols across model layers {/* BEGIN GENERATED SEMANTIC SYMBOLS */} The same symbol can have different meanings in different models. This table records definitions and explicit editorial aliases; it does not globally replace manuscript characters. Source paragraph locators refer to the final combined manuscript. | Symbol | Meaning / units | Mapping and conditions | Source context | | --- | --- | --- | --- | | $\phi$ | Angle between motion and the directed measurement direction.
$\mathrm{rad}\ (1)$ | The website uses φ for this meaning, specifying velocity, measurement direction and paired events. Orbital azimuth and field phase are not replaced with it. | [lve](/en/theory/lve) · [moving charge field](/en/theory/electromagnetism/moving-charge-field)
p0961, p0962, p1780 | | $\varphi,\ \Phi_N$ | Dimensionless long-range linear stretch and dimensional weak static gravitational potential.
$1;\ \mathrm{m^2\,s^{-2}}$ | Chapter 5 uses $\Phi_N=-c^2\varphi$ and $\mathbf g=-\nabla\Phi_N=c^2\nabla\varphi$. It is neither a motion angle nor automatically the local compression variable. | [longitudinal field](/en/theory/space-dynamics/longitudinal-field)
p1740, p2254, p2256 | | $\Phi,\ \Omega,\ X,\ \Psi$ | Linear-density coefficient, linear expansion, state function and gravitational potential.
$1,1,1;\ \mathrm{m^2\,s^{-2}}$ | $\Phi=\Omega^{-1}$, $X=\Phi^2$, $\Psi=c^2(X-1)/2$ in the static spherical exterior with common references. Mapping to Chapter 5 requires weak-field and reference normalization; capital Φ and Ψ are not globally renamed. | [gravity](/en/theory/gravity)
p0573, p0575, p0588 | | $\vartheta,\ S/\hbar,\ \Xi$ | Wave phase, action phase and exterior phase of a dressed state; orientation variables are defined separately.
$\mathrm{rad}\ (1)$ | ϑ is only an explicitly marked editorial notation for wave phase. It does not replace orientation Θ, topological matrices Q/U or orbital azimuth. Specify whether the phase belongs to the full carrier or a slow envelope. | [matter wave](/en/theory/quantum/matter-wave) · [topological matter](/en/theory/matter/topological-matter)
p1351, p1939, p2298, p2299 | | $h,\ \hbar;\ f,\ \nu,\ \omega$ | Cycle action and reduced action; ordinary and angular frequency.
$\mathrm{J\,s};\ \mathrm{s^{-1}}$ | $\hbar=h/(2\pi)$ and $\omega=2\pi f$. Matching $E=\hbar\omega$ and $E=hf$ requires the same state and reference. Chapter 4 model parameter $h_{\mathrm{eff}}$ retains its distinct meaning alongside the fixed SI numerical h. | [matter wave](/en/theory/quantum/matter-wave) · [creation](/en/theory/matter/creation)
p1600, p1880, p2299 | | $R,\ R_*;\ R_{\mathrm{refl}}$ | Core scale and stationary radius; reflected-flux ratio.
$\mathrm{m};\ 1$ | $R_{\mathrm{refl}}$ distinguishes the reflected-flux ratio, corresponding to manuscript R in (5.3.33)–(5.3.34); $R_*$ is the scale stationary point in (5.6.25). The label changes neither equation numbers nor flux normalization. | [stability](/en/theory/matter/stability) · [tunneling](/en/theory/quantum/tunneling)
p1993, p1995, p2281 | | $\rho_s;\ n_s;\ \eta,\sigma$ | Medium volume density or field-inertia normalization; element number density; relative compression.
$\mathrm{kg\,m^{-3}};\ \mathrm{m^{-3}};\ 1$ | In the small-deformation convention, η or σ is positive for compression. Volume density uses the actual Jacobian; Φ is not volume density. The core perturbation also named η elsewhere in Chapter 5 has its own definition. | [degrees of freedom](/en/theory/space-dynamics/degrees-of-freedom) · [longitudinal field](/en/theory/space-dynamics/longitudinal-field)
p0580, p0582, p1321, p1343, p2028, p2029 | | $Z_A,\ Z_u,\ Z_\varphi$ | Positive normalization coefficients of time-derivative terms for specified fields.
$\mathrm{kg\,m^{-3}}\ (u);\ \mathrm{J\,s^2m^{-3}}\ (\varphi)$ | Displacement and dimensionless stretch have different dimensions. $Z_A=\rho_s$, $Z_Ac_A^2=K_A$ require shared fields, compatible boundaries and constant coefficients; they do not turn a density action into an arbitrary scalar action. | [continuum dynamics](/en/theory/space-dynamics/continuum-dynamics)
p2018, p2037, p2040, p2224, p2254 | | $F_T,\ F_r,\ F_0,\ \Delta F_m$ | True physical force, reference-coordinate generalized force, static Coulomb baseline and signed magnetic correction.
$\mathrm N$ | At fixed common velocity in the transverse configuration, $dr_T=\gamma dr$ and $F_r=\gamma F_T$ follow from $F_Tdr_T=F_rdr$. Neither is an interchangeable instrument readout; distinguish a signed component from a positive decrease. | [magnetic force](/en/theory/electromagnetism/magnetic-force)
p0981, p0983, p0985, p0987 | | $E,\ \mathcal E;\ \mathbf E$ | Total energy, effective-envelope energy or energy density; electric-field vector.
$\mathrm J,\ \mathrm{J\,m^{-3}};\ \mathrm{V\,m^{-1}}$ | Bold electric-field E and scalar energy E are distinguished by meaning. Barrier E excludes the rest carrier and is not the full dressed-state energy. Energy density requires its integration volume. | [electromagnetic waves](/en/theory/electromagnetism/electromagnetic-waves) · [tunneling](/en/theory/quantum/tunneling)
p0999, p1983, p2023, p2299 | | $\Phi_\tau,V_{em};\ \Phi^{(+)},\Psi$ | Electromagnetic scalar potential; selected channel field and slow complex envelope.
$\mathrm V;\ \text{model-dependent}$ | Electromagnetic potential is not Chapter 2 linear-density Φ, and envelope Ψ is not Chapter 2 gravitational Ψ. Units of $\Phi^{(+)}$ and envelope normalization follow the selected action, channel and source coupling. | [vector potential](/en/theory/electromagnetism/vector-potential) · [effective wave equation](/en/theory/quantum/effective-wave-equation)
p0999, p1000, p1907, p2044 | {/* END GENERATED SEMANTIC SYMBOLS */}