Topics — What a work is about. Nucleation holds whatever reading the owner files here, whether or not an Anthology of the SOTA topic could also hold it; instruction for ML practice belongs to the anthology (ADR-048). The words are seeded from the clusters the reading-time triage of 2026-09-25 found, and grow by decision.
Mathematics — mathematics read for itself — category theory, topoi and sheaves, spectral geometry, set and measure theory — including mathematical frameworks applied to other fields.
14 of 100 TERM documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| TERM-004 | equivariance | A105: a representation F is equivariant when F(g·s) = ρ_g F(s), with invariance the case ρ_g = identity. “equivariance may be the more general principle for translation”, as when irony in a text becomes posture in an image. The manuscript §4. | Active |
| TERM-007 | fidelity, as preserving the dynamics of interpretation | A30: a faithful rendering makes interpreting-then-mapping agree with mapping-then-interpreting, T_τ(f) Φ ≈ Φ T_f. Adds to distribution matching rather than replacing it. The origin of the manuscript’s intertwining defects (§9). | Active |
| TERM-008 v3 | transport | The owner’s word at U20 for the map Φ from source to target communicative states: directed, possibly stochastic and non- invertible, required only to get within ε. Renames A48’s “state correspondence” and A49’s “admissible correspondence”. The manuscript’s central term (§6). | Active |
| TERM-015 | fidelity, as graded, directed transport distortion | U20 and A50: fidelity is how little a transport distorts selected structure, within ε, and need not be symmetric or transitive; equivalence is its zero-distortion limit. The manuscript’s graded fidelity (§6, §12). | Active |
| TERM-036 | fidelity, as preservation of selected observables and structural symmetries | A105, after the owner’s U37 objection: “Fidelity ≈ preservation of selected observables and structural symmetries”, “a proposed operational criterion, relative to a selected class of observables, not a universal identity”. The manuscript states it in §4, beside the §6 functional rather than in it. | Active |
| TERM-041 | character-like structural signature, as a realization-independent invariant of a communicative kind, called a character only when it is the trace of a specified representation | A proposed invariant χ_A of a communicative kind, the same across the kind’s realizations and required to keep independently specified pragmatic and decision-relevant distinctions. A203 §36 fixed the usage: “character” literally only for the trace character of a specified representation, otherwise “character-like structural signature”. None has yet been constructed for any communicative case. | Active |
| TERM-046 | notation for the threshold, drive and unity criteria | One place for the symbols used across the threshold criterion, the drive profile and the unity and persistence claims of 2026-10-11: δ, ε, τ, d′, Occam, D, G, Φ and γ. It records that δ/ε is used in two senses, a spectral gap against off-block coupling and a posterior effect against its uncertainty, and that treating them as one is an assumption carried over from MOM-CLM-160. | Active |
| TERM-069 v2 | observational equivalence, under a probe family: two models, states or distributions agreeing on the outcome law of every probe in a declared admissible family; coarser than identity unless the family is rich enough, and, when probes are run one at a time, weaker on their marginals than on the joint law across them | ”Probe family” is in some two dozen argument entries (CLAIM-139, 142, 149, 190, 193, 206, 209, 215, 217, 223, 241, 264, 266, 269, 302 and 322; QUESTION-005, 031, 055, 067 and 135; CASE-041, 070 and 071) with no TERM. CLAIM-264 (Active, demonstrated) holds the mathematics. Asked for at A13 and A14 of the exchange of 2026-10-20. TERM-033, fidelity as observational equivalence over response trajectories, is its case with response trajectories as the probes, and TERM-014’s communicative object is a class of it. Adopted by the owner on 2026-10-21. | Active |
| TERM-077 v2 | ordinal potential: of a negotiation over a finite set of options in a window of time, an ordering of the options that every move winning one of its conflicts climbs; it exists exactly when the wins never cycle, which is ordinal extendibility, that some complete ordering agrees with every win, and not observed comparability, since pairs never contested are not compared; and it is fixed only up to a class: every strictly increasing transform of one is one, and on a sparse record several orderings can be | The first level of the hierarchy the review of PR #327 proposed: ordinal coherence. Separated from the Hodge decomposition, which measures cardinal inconsistency and can reverse an ordinal comparison (CLAIM-434, part 4), and from a real-valued currency (CLAIM-436). | Active |
| TERM-078 v3 | persistent potential: an ordinal potential of a negotiation that is the same, up to its class, across successive windows of time, that decides the conflicts it bears on (priority), and towards which the dynamics climb again after a perturbation (resumption); exact when no move outside a perturbation descends it, and then a Lyapunov function of the one-move-at-a-time dynamics, and approximate when some do, and then no Lyapunov function, short of a drift condition that needs a cardinal potential and further assumptions | The second level of the hierarchy the review of PR #327 proposed, which the review called “dynamical ascendancy”. Named for the potential rather than reviving “ascendancy”, which the record retired the same day (TERM-076). It reads Frijda’s three marks of control precedence (THEORY-055) as properties of an ordinal potential over time. | Active |
| TERM-090 v2 | effective boundary constraint, of a composite: the relation its interconnected parts impose on the variables an outside system can reach, once the interior is eliminated; approximately instantaneous or history-dependent, and, independently, possibly of a kind the parts’ relations could not state | What CLAIM-480 demonstrates and CLAIM-474, QUESTION-283 and CASE-179 use. A composite presents the systems that interact with its boundary with a relation among its accessible variables. Its examples are the series spring’s k₁k₂/(k₁ + k₂), Baez and Fong’s black box, a memory kernel, and Hansen and Ghrist’s three-way v₁ = v₂ + v₃. The term fixes three points: the relation is a constraint whether instantaneous or history-dependent; it is effective, not a new fundamental law; and it can exceed the parts’ relational vocabulary. Adopted 2026-10-29. | Active |
| TERM-091 v2 | relational vocabulary, of a class of descriptions: the arities and kinds of relation it can state (pairwise or higher-order, among states or among histories, of which declared types), and so which constraints are expressible in it at all | What QUESTION-283 asks about: whether composition can force a description to adopt relations its parts never needed. A sheaf on a graph has a pairwise vocabulary. Eliminating an interior can leave a constraint outside it (THEORY-1090). A luria record’s relational vocabulary is its declared relation types and fields, and amendments that add one (ADR-043, ADR-044) enlarge it. The term lets the record say that a constraint is inexpressible in a vocabulary, which is different from saying that it is false or unknown. Adopted 2026-10-29. | Active |
| TERM-093 v3 | correspondence structure, and how it is held: the maps that say which local states or descriptions of interacting systems count as agreeing, distinct from the physical coupling between them, and held as formed, discovered or adapted | The object CLAIM-471, QUESTION-282, CLAIM-474 and CASE-179 all turn on. It is a family of comparison maps from local descriptions into shared spaces, whose joint kernel (the global sections) is what “compatible” and “glued” mean. It is not the coupling that moves the states. How a correspondence structure is held is one of three ways: formed by physical interconnection, discovered by measurement, or adapted by an apparatus. A claim using “gluing” should say which. Adopted at the thirteenth status review, once the formed sense was stated as the maps that wiring sets and not the joint behaviour they admit. | Active |
| TERM-097 v2 | coherence, of a family of descriptions, transports or judgements: their agreement with one another under a stated correspondence structure (on overlaps, around cycles, between routes), distinct from fidelity to a source, from integration by dynamics, and from knowledge of the world | The sense in which the record keeps saying coherence is not something else: “coherence without integration” and “without knowledge” (CASE-179), a coherent record as the product of a legibility regime (CLAIM-448), and agreement between translation routes as coherence, not fidelity (CLAIM-496). It is a relation among the members of a family, read through the maps that say what counts as agreeing (TERM-093). Filed on the owner’s question of 2026-10-29 whether the record had TERMs for fidelity and coherence: fidelity has several, coherence none, though the word is in some 145 entries. Adopted the same day. | Active |