Working glossary
These definitions are local to the corpus unless a standard mathematical meaning is stated. They prevent adjacent ideas from being collapsed by narrative momentum.
| Term | Working meaning | Do not silently replace it with |
|---|---|---|
| Admissibility | The jointly enforced conditions under which states, compositions, transformations, histories and records can coexist in a declared model or experiment. | Truth, existence, probability, morality or empirical realization. |
| Admissibility zone | A mapped region marked as filled, conditional, bounded, excluded, underidentified, inaccessible or uncharted, with evidence and reopening rules. | A single feasible set known to be complete. |
| Carrier | The concrete space or system on which the declared operators act. | A representation label, group name or analogy. |
| Carrier--selector--detector grammar | A carrier supplies the things or degrees of freedom; a dual face selects a relational alternative; a threefold closure produces the first gauge-resistant record. | A claim that every carrier, selector or detector across the corpus is physically identical. |
| Dual-face selector | An intervention or sourced rule choosing between paired relational responses, such as equal versus opposite endpoint motion. | A coordinate relabelling that leaves every response unchanged. |
| Triality detector | A record that exists only after three pairwise relations close, and is invariant under allowed local relabellings; on the weighted resonator triangle it is the loop parity read through the cubic pole product. | Any use of the number three, or three unrelated measurements. |
| Living carrier | The state, response, frame or field space whose elements actually transform under the declared operation. | The invariant form that compares those elements, or physical spacetime without a typed identification. |
| Locally invariant carrier | The comparison structure that is preserved under every admitted local perspective change; in the central symplectic instance, \(M^T\Omega M=\Omega\). The intuitive name emphasizes that a relation can carry identity across changing coordinates. | A claim that \(\Omega\) is globally constant, dynamically selected, unique in nature or itself the full state space. |
| Perspective transformation | An allowed local change \(M\) acting on the living carrier while preserving a declared comparison structure. | A passive coordinate relabelling in every context; it may be an active control or transport only when typed as such. |
| Mirror face | The dual or contragredient action \(M^{-T}\) paired with the direct action \(M\) through the locally invariant carrier. | A second independent system, literal spatial reflection or antimatter without an additional bridge. |
| Typed two-rail carrier | The free pre-quotient relation carrier \(\mathbb R^V\otimes\mathbb R^{\{S,T\}}\otimes\mathbb R^{\mathcal T}\), separating authored source, target and relation-type roles. Its positive Gram kernel reconstructs directed typed adjacency exactly. | A claim that source and target are physical dimensions, that the type channels have derived dynamics, or that the rail swap is already a symplectic quarter-turn. |
| Rail-swap mirror | The involution \(J\) exchanging source and target rails. On the typed two-rail kernel it obeys \(JK(G)J^T=K(G^{\rm rev})\). | The contragredient mirror \(M^{-T}\), a path-algebra dagger or Wick rotation without a typed bridge. |
| Elliptic/hyperbolic/parabolic alphabet | The three normalized real two-dimensional algebras \(\mathbb R[u]/(u^2-\kappa)\) with \(\kappa=-1,+1,0\), giving complex rotations, split-complex boosts and dual-number shears on one local symplectic carrier. | A claim that nature changes number systems, or that the invariant form selects one branch. |
| Split-complex rail | One of the idempotent/null directions \(e_\pm=(1\pm j)/2\) for \(j^2=1\). The discrete rail swap is anti-symplectic, while exponentiating the same matrix as a generator gives a connected symplectic boost. | A physical light cone, source/target dynamics or mass channel without an independently typed lift. |
| Dual-number seam | The square-zero direction in \(\mathbb R[\varepsilon]/(\varepsilon^2)\), retaining tangent and first-order response data through \(f(x+v\varepsilon)=f(x)+vf'(x)\varepsilon\). | A small ordinary real number, a finite trajectory, or the finite-characteristic ramified dual numbers without a base-change map. |
| Nilpotent rung | For anticommuting quarter-turn \(I^2=-1\) and mirror \(J^2=+1\), either directed square-zero map \(N_\pm=(J\pm I)/2\). Together the rungs reconstruct \(I\), \(J\), the grading and the full local \(M_2(\mathbb R)\) algebra. | A physical transition, time step or authored path-algebra arrow until the relevant intertwiner and action are supplied. |
| Source-native Clifford rail cell | On the typed Claimipedia carrier, authored source/target grading \(G=\operatorname{diag}(-1,+1)\) and rail mirror \(J\) anticommute; \(I=GJ\) squares to minus one and derives two nilpotent within-fibre rail transfers. | An invariance of the original incidence kernel: \(I\) exchanges signed incidence with unsigned co-incidence, and it does not descend through rail identification. |
| Co-incidence channel | The positive Gram channel generated by \(c_{u\to v,t}=|v,T,t\rangle+|u,S,t\rangle\), paired with the signed incidence channel by the authored grading and quarter-turn. | A configuration space, physical field or time evolution without a path product, action and detector. |
| Clifford-cell recurrence | The repeated typed grammar \(C^2=-1\), \(R^2=+1\), \(CR=-RC\) on several independently certified corpus carriers. | Evidence that the carriers, operators or physical mechanisms are identical; \(M_2(\mathbb R)\) is a common local algebra. |
| Incidence/co-incidence doublet | The two positive kernels (K-=D-A) and (K+=D+A), exchanged by authored rail grading. Their scalar quotients are the ordinary and signless Laplacians. | Two physical fields or a spacetime/configuration-space split without a source-native action. |
| Semantic adjoint | An authored involution on relation types and paths sending each (u\xrightarrow{t}v) to an existing (v\xrightarrow{t^*}u). | The free rail swap or the formal addition of missing reverse arrows. |
| Relation--face compiler | The typed route from directed relations through a positive kernel and Schur boundary reduction to a Jordan face, cycle holonomy and orientation-sensitive record. | A guarantee that adjacency alone supplies order, dynamics, phase or a physical detector. |
| Support-native order | Positivity derived canonically from finite incidence and counting measure. It orders variation on the relation support but may erase direction and relation type after quotienting. | A semantic order among Supports, Challenges, Qualifies and DependsOn. |
| Carried invariant | A locally invariant structure equipped with compatible transport, normally expressed as \(\nabla\Omega=0\). | Pointwise invariance alone or trivial global return. |
| Higher relation space | A derived carrier of relations among directions of a lower carrier; centrally, \(W=\Lambda^2_0V^*\) is the five-dimensional primitive remainder after the invariant \(\Omega\)-line is separated from \(\Lambda^2V^*\). | Hidden physical dimensions merely because its dimension is larger. |
| Jordan structure | Here, the commutative product/triple structure organizing positive response, composition and elimination on a declared carrier. | All observables in nature or a substitute for dynamics. |
| Lie structure | The infinitesimal transformation algebra generated by typed operators and commutators. | A physical spacetime symmetry merely because the algebra is isomorphic. |
| Typed bridge | A map whose domain, codomain, action, preserved invariant and authority are all declared. | A chain of similar names, dimensions or diagrams. |
| Selector | A physical rule or independently sourced datum that chooses among symmetry-related possibilities. | A coordinate convention, relabelling or projector that neutrally preserves every option. |
| Spontaneous selection | A dynamical or thermodynamic mechanism yielding realized branches from symmetric laws, including its finite-system, environment and record qualifications. | The bare existence of multiple minima. |
| Dynamics | A specified continuous flow, discrete update, open-system channel, measurement-conditioned map or other time/process law. | Any transformation, antiunitary relation or static optimization. |
| Record / memory | A persistent, operationally accessible trace of state preparation or history. | A formal topological label that no detector can read. |
| Detector fold / quotient | The many-to-one map from underlying states and histories through ports, bandwidth, noise and reduction into recorded data. | The full physical state. |
| Detector equivalence | Two mechanisms produce indistinguishable records after declared nuisance projection. | Microscopic identity. |
| Boundary | A mathematical, physical, experimental or authority limit stating where a result stops. | Failure or embarrassment; a sharp boundary is often a result. |
| Reopening datum | The smallest new input that could make a closed or exhausted branch scientifically live again. | A request to repeat the same search with more rhetoric. |
| Internally exhausted | Recombining the present declared inputs no longer addresses the missing datum. | Impossible in every larger theory. |
| Externally open | Progress requires a source, model, calculation, fabrication or observation not currently contained in the corpus. | Unconstrained speculation. |
| Established in model | The result follows exactly or reproducibly from written assumptions on the declared system. | Established in nature. |
| Conditional construction | A mechanism closes after a named input is supplied. | A derivation of that input. |
| Obstruction / no-go | A stated candidate class or identification fails under explicit assumptions. | A universal impossibility theorem unless the scope says so. |
| Ordinary residue | The conventional scientific result that remains useful if the programme-specific interpretation fails. | A consolation prize; it is part of the preregistered scientific value. |
| Kenotic presentation | Giving a claim no more authority than its reasons support while still stating real positive findings clearly. | Sterility, false balance or ritual self-negation. |
| Usewords | Preserving attributed originating language as a search coordinate whose distinctions can be typed and tested. | Treating a phrase as evidence because it was generative. |
| Worldwright bridge | Transfer of mechanism-testing disciplines—counterfactuals, ablations, identity retention and authority boundaries—without turning moral/social quantities into physical fields. | A physical theory imported from narrative or ethics. |
| Frontier target | A maintained physical or mathematical area linked to corpus objects, present evidence, experiments and kill tests. | A claim that the target is explained by the programme. |
| Lightning path | The shortest plausible typed route from a corpus result to a current research frontier, including every missing edge. | A shortcut around those missing edges. |
Core sentence
The corpus's present architecture is:
\[
\text{Jordan admission/composition}
\longrightarrow
\text{living carrier and admissible relations}
\longrightarrow
\text{locally invariant carrier}
\longrightarrow
\text{Lie transport of thing and mirror face},
\]
with compatible connection carrying the invariant, dynamics proposing histories, holonomy retaining global difference, detectors producing records and admissibility tracking which combinations survive all declared gates. The sentence is a research architecture, not a completed ontology of physics.
For authored relation graphs, the canonical pre-quotient refinement is:
\[
\text{directed typed records}
\longrightarrow
\text{typed two-rail positive carrier}
\longrightarrow
\text{declared rail/type quotient}
\longrightarrow
\text{effective Jordan face and record}.
\]
The quotient must name which distinctions it erases. Positivity does not by itself require direction or type to be forgotten.