## The Cinematic Leaf I–II — Unified Abstract This two-note collection develops an exact mathematical framework for three distinct questions: when a restricted readout of a discrete system supports autonomous dynamics, which hidden distinctions must be retained for complete prediction, and when the resulting discrete history can be realized by a continuous flow. The framework keeps the internal carrier, observable readout, sampling grain, and physical interpretation separate; the integers 24 and 48 remain fixed rather than serving as parameters in a continuum limit. **Part I — Factor Closure, Minimal Predictors, and Flow Embeddability in Exact 24/48 Dynamics** establishes the factor-closure criterion for compact Hausdorff systems and constructs the canonical predictor as the quotient by equality of complete observable futures. In a cyclic torus skew-translation laboratory, it derives exact block-closure conditions, minimal future-relevant register size, torus-versus-lift recurrence laws, and 24/48 Fourier and correlation-revival identities. Every closed torus block is an exact sample of a translation flow, although its continuous generator is not uniquely determined. A parabolic counterexample proves that an autonomous canonical predictor need not embed in a continuous flow on the same state space, even when a larger unrolled cover supports one. **Part II — Minimal Amplitude Predictors, Fine-Compatible Flows, and 24/48 Half-Step Lifts** applies these gates to a frozen unitary weighted cycle $T=DX_{24}$ with a phase-sensitive rank-eight primitive readout. It obtains an exact accumulated-word criterion for block closure and computes canonical amplitude predictors by positive observability Gramians. The simple spectrum of the weighted cycle ensures that every Hermitian logarithm of the fine transaction preserves the one-click predictor's invisible subspace. A coarsely sampled predictor admits a flow of that same fine transaction precisely when it retains the full one-click predictive subspace. An exact example yields complex predictor dimensions 20, 16, and 8 at sampling intervals of 1, 12, and 24 clicks. A separate population-record analysis proves an obstruction to continuous all-state population autonomy along unitary paths ending in a nontrivial permutation. The 48-register analysis distinguishes central-cover memory, adjacent-pair fine-step parity, and square-root spectral branches. Opposite square roots at fixed squared eigenvalue have the same central deck parity, while a prescribed half-step fixes only the parity of each integer logarithm branch. A positive sharp-record-preserving encoder cannot reproduce a coherence-sensitive half-step through monomial fine evolution for all inputs. An explicit coherent doubled realization exists, but changes the ordinary paired population camera. Together, the notes distinguish predictive closure, continuous interpolation, and fidelity to the same underlying transaction. Proofs are accompanied by reproducible exact certificates and numerical flow checks. The native Bank dynamics, physical preparation and readout, generator selection, click duration, locality, Lorentzian structure, and spacetime attribution remain open; no emergence of physical spacetime or experimental confirmation is claimed. **Keywords:** factor closure; canonical predictor; observable-future equivalence; observability; unitary dynamics; flow embeddability; stroboscopic sampling; logarithm branches; quantum records; 24/48 clock; Bank–Leaf framework.
The Cinematic Leaf I–II — Unified Abstract This two-note collection develops an exact mathematical framework for three distinct questions: when a restricted readout of a discrete system supports autonomous dynamics, which hidden distinctions must be retained for complete prediction, and when the resulting discrete history can be realized by a continuous flow. The framework keeps the internal carrier, observable readout, sampling grain, and physical interpretation separate; the integers 24 and 48 remain fixed rather than serving as parameters in a continuum limit. Part I — Factor Closure, Minimal Predictors, and Flow Embeddability in Exact 24/48 Dynamics establishes the factor-closure criterion for compact Hausdorff systems and constructs the canonical predictor as the quotient by equality of complete observable futures. In a cyclic torus skew-translation laboratory, it derives exact block-closure conditions, minimal future-relevant register size, torus-versus-lift recurrence laws, and 24/48 Fourier and correlation-revival identities. Every closed torus block is an exact sample of a translation flow, although its continuous generator is not uniquely determined. A parabolic counterexample proves that an autonomous canonical predictor need not embed in a continuous flow on the same state space, even when a larger unrolled cover supports one. Part II — Minimal Amplitude Predictors, Fine-Compatible Flows, and 24/48 Half-Step Lifts applies these gates to a frozen unitary weighted cycle T=DX24 with a phase-sensitive rank-eight primitive readout. It obtains an exact accumulated-word criterion for block closure and computes canonical amplitude predictors by positive observability Gramians. The simple spectrum of the weighted cycle ensures that every Hermitian logarithm of the fine transaction preserves the one-click predictor's invisible subspace. A coarsely sampled predictor admits a flow of that same fine transaction precisely when it retains the full one-click predictive subspace. An exact example yields complex predictor dimensions 20, 16, and 8 at sampling intervals of 1, 12, and 24 clicks. A separate population-record analysis proves an obstruction to continuous all-state population autonomy along unitary paths ending in a nontrivial permutation. The 48-register analysis distinguishes central-cover memory, adjacent-pair fine-step parity, and square-root spectral branches. Opposite square roots at fixed squared eigenvalue have the same central deck parity, while a prescribed half-step fixes only the parity of each integer logarithm branch. A positive sharp-record-preserving encoder cannot reproduce a coherence-sensitive half-step through monomial fine evolution for all inputs. An explicit coherent doubled realization exists, but changes the ordinary paired population camera. Together, the notes distinguish predictive closure, continuous interpolation, and fidelity to the same underlying transaction. Proofs are accompanied by reproducible exact certificates and numerical flow checks. The native Bank dynamics, physical preparation and readout, generator selection, click duration, locality, Lorentzian structure, and spacetime attribution remain open; no emergence of physical spacetime or experimental confirmation is claimed. Keywords: factor closure; canonical predictor; observable-future equivalence; observability; unitary dynamics; flow embeddability; stroboscopic sampling; logarithm branches; quantum records; 24/48 clock; Bank–Leaf framework.
A tensor factorization specifies a mathematical subsystem, but it does not by itself establish that its reduced state is a complete description of the physical bearer it claims to represent. This paper supplies an exact selection criterion and a quantitative certificate without altering the global physics. It retains the observable-induced algebraic formulation, the quotient-dynamics theorem, the strict two-qubit counterexample, the autonomy defect, additive error accumulation, nested persistence margins, the coupling–time estimate and the non-circular selection argument. The physical-cut theorem now distinguishes three independent descent requirements: complete constitution, retained existence and identity verdicts, and autonomous dynamics. A realization x=(c,ρ,η) separates the physical profile, quantum state and preparation/history/continuation data. This prevents a historical identity verdict from being silently treated as a function of a momentary density matrix. The CNOT-conjugated cut has identical reduced inputs and orthogonal reduced outputs at t=π/4. A second witness has perfectly closed baseline dynamics while a partial trace erases two physically distinguishable coupling profiles. Dynamic closure alone therefore does not establish physical completeness. The quantitative results bound unavoidable prediction error from below by half the fibre defect and, with an admissible lift in the chosen model class, from above by that defect. Reachable-state error bounds accumulate under CPTP comparison. A bound below an independently grounded Q1, Q2a or Q2b margin is a sufficient persistence certificate; loss of that inequality is not an identity-loss verdict. For a bounded interaction the specified decoupled predictor has the sharper error bound |λ|(t−s)‖V‖/ℏ, while the fibre defect has twice that bound. The resulting criterion links the physical cut to emergence, thermodynamic process closure and record memory without identifying those questions. All exact theorems below are finite-dimensional and relative to explicitly named preparation and continuation domains.
The Dirac Time programme begins from memory rather than from a metric, a clock or an assumed time coordinate. Its question is operational: what distinction must survive a change of description for a system to stay predictively distinguishable from what it has been? For a finite linear system with continuation map L and declared observation R, the state directions invisible to every future observation form a subspace N∞, and the quotient V/N∞ is the minimal autonomous predictive state. Dirac families then serve as controlled tests of what scalar spectra forget and spectral subspaces retain. Under a chiral symmetry every odd scalar-spectral record, including signed spectral flow and the eta invariant, vanishes, while the spectral projector keeps an orientation and carries holonomy. The intrinsic Grassmannian tensor Q(A,B) = Tr(Π A†B) supplies the geometry. Main results:- Spectral flow is an endpoint label exactly when every admitted loop carries zero flow. A covariant criterion decides when many internal clocks form one common time, and projector geometry alone cannot fix an absolute rate.- An exact equal-endpoint model in which a Wilson-loop phase absent from every present marginal returns in a later observable, with the history equivalence depending on the probe.- A finite memory engine in which retained state changes later work while the energy ledger closes. Under a declared slow-driving relaxation model, the friction on projector rotations is the intrinsic metric reweighted level pair by level pair, to first order in the driving rate.- For every torus knot T(p,q): on each irreducible SU(2) arc the peripheral law is L = (−1)^a M^(−pq), the arc ends are unit-circle roots of the Alexander polynomial, and the number of arcs over a meridian phase is half the Levine–Tristram signature, which is minus the Atiyah–Patodi–Singer ρ-invariant of the twisted odd signature operator of the zero-surgery. The Dirac-time arcs are the window on which this bulk eta ledger is nonzero, and chirality fixes its sign. A 13-crossing pair that agrees on the HOMFLY, Jones and Alexander polynomials and on Khovanov and knot Floer homology is separated on one such window.- The magnetic zero-mode electron seed has field B = 12 j_W and zero Pauli current, and no static magnetic zero mode is self-consistent. A candidate must carry a non-constant electric potential. The electron and Gigantefermion hypotheses stay outside the theorem layer. Time is proposed as a structure of typed pieces (orientation, local distinguishability, multi-time structure, predictive memory and synchronization), with duration a calibration and the arrow an additional dynamical cost. Files: the manuscript (PDF, 101 pages, and HTML) and the full research package, with every script and output needed to reproduce each computation, including the 13-crossing census.
A finitist, relational axiomatization of physics: quantum theory and a relativity sector derived from four axioms about group-valued relations and closure. Contributions to the foundations of quantum mechanics (Born rule derivation, quantum reconstruction, local tomography, complex field selection), the emergence of time and causal structure in discrete networks, discrete Noether theorems, lattice gauge structure, and the Schrödinger equation derived by two independent routes. Every claim is graded in a Claim Ledger; every numerical claim is machine-verified with archived scripts; negative results are reported at full strength. What this paper does The universe is taken to be constituted by relations rather than objects. Stable relations form closures (self-consistent cycles) whose holonomies carry the physical content. Four axioms — primacy of relations (group-valued, edge-borne), closure stability, chirality from order, and observation as bidirectional group exchange — yield, at explicitly graded and conditional levels: Quantum sector Exchange-completeness theorems for finite label groups: abelian at all cycle ranks; non-abelian on the single cycle (Wilson readouts plus class-sum convolutions generate the full matrix algebra); the multi-cycle non-abelian case on the operational-equivalence quotient, with the obstruction completely characterized via class-preserving outer automorphisms — and the quotient's necessity now stratified by the source of word blindness (see New in Version 24.0). The Born rule, proved for finite abelian networks from a strictly weaker relational readout premise (statistics of realizable effects depend only on relational content); non-contextuality has this single source; additivity is basis-relative and declared as such. The Schrödinger equation by two routes of unequal premise grade, maintained side by side: a spectral route — the action operator is a weighted Cayley-graph Laplacian in the Pontryagin dual basis, the derived Gibbs state's unique canonical (modular) flow yields the Schrödinger equation with Hamiltonian equal to the action operator, no continuum limit, zero conjectures consumed, the single non-theorem step one flagged identification; and a Madelung route — physical and mechanism-rich (probability density derived from constraint gaps), valid exactly on the domain of the pseudo-continuity conjecture, with its full premise bill stated (continuity equation, Wallstrom circulation condition, m, V). A dedicated comparison subsection gives the line-by-line premise accounting and the machine-measured agreement region. Complex field selection: ℂ selected over ℝ and ℍ within the GPT comparison class in the covered sectors, with a second independent route from chirality (Frobenius–Schur dichotomy, quaternionic double exclusion); "uniquely selected" expressly not claimed. Positivity as pairing: all five in-text positive-semidefiniteness theorems traced to one mechanism (M = B†B with native factor); the Kraus form and complete positivity derived rather than assumed. The Noether sector on Noether's two theorems exactly: Noether I recovered on the holonomy action (compact Lie realization); Noether II identified as present (Bianchi as horn-filling, Schläfli as its Regge form); selection rules recovered for finite groups; the GNS bridge proved non-vacuously on the full exchange algebra; the sole potential extension — conservation as the kernel of exchange — isolated as a registered conjecture, consumed nowhere. A local–global representation theorem: six generative quantities (closure invariant, flux quantization, Weyl phase, non-abelian Stokes, orientation visibility, terminal normalization) are evaluations of cohomology classes against closed chains — one syntax, six exact machine probes. The gatekeeper no-go theorems registered and discharged: Kochen–Specker (the framework posits no global valuation — outcomes are resolutions of constraint gaps, and basis-relative additivity blocks state-independent variants), Pusey–Barrett–Rudolph (the statistical envelope is over resolutions yet to happen, not values already held; machine witness: identical configuration ensembles with opposite relative phase have opposite statistics), Wallstrom (registered as an explicit input, structurally discharged in the finite-abelian sector), Hegerfeldt (the Lieb–Robinson exponential tail identified as the only claimable front form for the continuum limit), Frauchiger–Renner (cross-agent certainty transfer presupposes kernel-free record transport, exactly what exchange-incompleteness excludes), and no-cloning (inherited in the covered sectors); Conway–Kochen and Colbeck–Renner noted as concordant. Relativity sector Time from finite capacity plus genuine randomness: the staging theorem (Θ(d) dependency depth, unbounded chains via the Moore bound; the quantitative failure law conditionalized on measure-level independence with exact minimal witnesses); the temporal quantum defined combinatorially, no Hamiltonian input. The speed of light grounded in an exact discrete dependency cone (combinatorial, no quantum input), the Lieb–Robinson bound consumed at cross-check grade only; a boost no-go theorem reducing Lorentz invariance to named statistical conditions, with the Collins fine-tuning objection recorded as a gate. The trace-descent theorem group: the growth-history measure forced onto the Mazurkiewicz trace quotient; chain reflection positivity at every depth with completely explicit spectrum. An equation sector of nine verification families (Schrödinger, Dirac, Maxwell/U(1), canonical commutator, Yang–Mills SU(2), Regge calculus, Klein–Gordon, Noether loop, Cartan curvature), where every machine-precision claim is the shadow of a proved backbone lemma — including the factor ½ of H = ½L + V, identified as the Wilson Fourier coefficient fixed by the action theorem. Four experimentally testable predictions, including a discriminating flat-versus-sigmoid visibility protocol. The Standard Model gauge group, ħ, and G remain open, with attack routes registered. How to read Three entry paths are marked in the document. Path A (derivational core): axioms → group structure → Noether sector → least action → Born rule → positivity. Path B (physical mechanisms): constraint propagation → time as determination → wave function as gap envelope → fields. Path C (scope and limits): the Claim Ledger, then Discussion and Open Problems — for the reader who wants to know what is claimed and what is not before reading anything else. The Claim Ledger is the single authoritative register of claim status; wherever body text sounds stronger, the Ledger governs. New in Version 24.0 (Version 23.0 is the immediately preceding public release; this version supersedes the internal V12–V15 and V17–V19 series, whose numbers are not used externally.) Version 24.0 resolves the structure of the multi-cycle non-abelian obstruction — the sector's longest-standing open front — following an external research exchange with three rounds of independent re-verification (fourteen core figures, three commutant instruments implemented independently, exact integer arithmetic on the obstruction side) and two rounds of counter-review that corrected one quantifier on each side: A dichotomy of the multi-cycle obstruction (new remark). Word blindness on multi-cycle networks has two identified sources, jointly covering every tested case, with opposite behaviour as cycle rank grows. Type I (global; graded): a class-preserving outer automorphism yields a commutant element by an argument free of cycle-rank reference; its non-triviality holds at theorem grade for b₁ ≥ d(G) via generating tuples, is monotone in b₁, and the threshold is measured at b_σ = 2 on the tested Wall group (at b₁ = 1 the permutation is the identity — no universal claim is made, and the existence of groups with threshold above 2 is registered open). Type II (local; measured): Out_c trivial but fusion fails on a proper subgroup, the blind pairs sitting in non-generating sectors — the same mechanism that defeats Wilson generation; this blindness heals: on every verified group (A₄, SL(2,3), A₄×ℤ₂) the full commutant collapses to trivial at b₁ = 3 by exact computation on two independently implemented instruments, although word readouts remain blind — the shift primitives separate, above a threshold, and the natural explanation (tuples becoming generating) is refuted by the persistence of blind blocks. Three boundaries at full strength: no exhaustiveness proof (a third source is not excluded); no general healing theorem (the verified groups all heal at 3, cause unidentified); the verified Type II sample is narrow. The quotient proposition restated in stratified form. The operational-equivalence quotient's necessity is now part of the proposition's own statement, in three strata: necessary where Out_c ≠ 1 at every b₁ ≥ b_σ(G), with b_σ ≤ d(G) at theorem grade; one-dimensional at b₁ = 2 on the fusion-type groups (verified cases); trivial at b₁ ≥ 3 on every verified fusion-type group and at every tested b₁ for word-separation-complete groups (a fourteen-group scan of orders ≤ 31 found no third source). Pre-registered validation preceded the restatement: a stratification-exhaustiveness scan (pass), a new-witness search (no new witness in range, downgrade clause applied as pre-registered), and a zero-conflict audit of the three strata against all archived data. The residual open problem is now precisely located. What remains of multi-cycle completeness: the rare Out_c ≠ 1 groups (54 in the exhaustive range through order 96) above their measured thresholds, the low-b₁ fusion stratum, a general healing theorem, and whether a threshold above 2 occurs. The multiplicity-freeness conjecture's mechanism sentence is corrected with the two regimes stated separately (at b₁ = 2 the shifts do not separate — the blind-pair transposition commutes with every primitive, integer-exact — and reduce the commutant to
1. This note records a claim-bounded theorem-target route from the R^8 non-split Z48/Z24 Bank/Leaf scaffold toward quantum kinematics and record stability. It does not claim that R^8 derives quantum mechanics from finite arithmetic alone, solves the measurement problem, derives hbar, predicts a numerical collapse threshold, or supplies a complete stochastic record dynamics. The narrower claim is that an interleaved 48/24 fine-step coordinate exposes projective phase in its complexified character decomposition; a faithful real local calculus for generic projective phase naturally uses a two-dimensional phase plane, equivalently a complex structure J^2 = -I, once an effective real Hilbert carrier is admitted. Given such a complex Hilbert carrier and standard operational projector/POVM additivity, Born weights follow by standard representation theorems. The record problem is then reformulated as a stability and settlement problem: a stable Leaf record is a branch sector whose phase debt has become unrecoverable at the Leaf level through leakage, decoherence, and coarse-graining stability. The resulting pointer-basis and single-outcome mechanisms are theorem targets, not completed physical derivations. 2. This note records a claim-bounded theorem-target response to the phase-per-information conversion problem in the R^8 Bank/Leaf scaffold. The coefficient χ_{φI}, if it exists as an effective scalar, should not be introduced as a primitive naked constant. Nor should it be identified with a direct contraction such as Tr(F h^{-1}) or Tr(FG). When F is a curvature two-form and h is a symmetric information metric, such a direct contraction is naturally trace-trivial, skew, or convention-dependent rather than positive. The safer theorem target is a positive phase-information stress tensor K_{μν} = <F_{μα}, h^{αβ} F_{νβ}>_g, where F is Bank phase curvature, h_{μν} is a positive Leaf information metric on the record or connector base, h^{μν} = (h^{-1})^{μν}, and <·,·>_g is an invariant positive inner product on the compact physical phase sector. Effective scalar quantities such as χ_{φI}^{eff} are to be read from generalized eigenvalues or other invariants of the pair (K,h), with the readout map left open. Integer carry is a separate topological object, defined by phase winding, normalized flux, Chern/Hopf number, or spectral-flow integrality under appropriate geometric conditions; it is not stress magnitude. This note does not derive collapse, a CP record-selection instrument, a numerical threshold, or a universal phase-per-nat constant. 3. This note records a claim-bounded theorem-target route for selecting the Leaf information metric h_{μν} in the R^8 phase-information response architecture. It does not claim that the correct metric h*, the phase-per-information coefficient χ_{φI}, the record threshold ε_rec, a Bank throttle law, or a CP record-settlement instrument has been derived. The narrower proposal is that h* should not be chosen by taste or by fitting a desired threshold. It should be selected, if at all, by compatibility with exact governance, normalized monotone quantum-information geometry, phase-information stress viability, and bounded throttle clearability. The previous Phase-Information Response Court replaced the rejected primitive scalar Tr(F h^{-1}) with the positive theorem-target stress tensor K^{(h)}_{μν} = <F_{μα}, h^{αβ}F_{νβ}>_g. The present note asks which metric field h_ρ can make the generalized spectrum of the pair (K_h, h) both alive and non-runaway while keeping the information debt clearable by a bounded Bank response. The result is a concrete metric-sensitivity protocol comparing normalized monotone candidates such as SLD/Bures, Wigner-Yanase, and Kubo-Mori. The key methodological patches are built in: h is treated as a metric field evaluated at a record state, spectra are computed through the generalized pair (K_h, h), monotonicity is required for unconditional CPTP coarse-graining rather than arbitrary postselected CP maps, curvature ensembles must be normalized independently of the tested metric, and metric selection is Pareto-first rather than a hidden weighted scalar fit. The note remains a PASS/YELLOW theorem-target architecture: it defines a disciplined court for h* without pretending that h*, χ_{φI}, ε_rec, or record dynamics have already been solved.
This revised note consolidates a falsifier-first route developed around the heuristic word “nostalgia”: the possibility that a visible Leaf record pays a cost because it must realize a hidden Bank structure that does not descend globally into the Leaf geometry. The metaphor is retained only as a mnemonic. The mathematical content is a constrained Bank descent, a faithful affine clock with an internal order-two kernel fibre, a selected-cell doorway, and a projected room-response problem. The principal affine correction is exact. A faithful affine generator g of order 48, with linear part Λ of order 24, contains a bottom C2 holonomy kernel. For the lifted hidden generator h=g2, one has1⟶⟨h12⟩≃C2⟶⟨h⟩≃C24,aff⟶⟨Λ2⟩≃C12,lin⟶1,with h12=g24=te1/2 on the torus in both certified Bank-locked branches. Thus the two affine-kernel states are internal states of one lifted affine orbit, not external replicas. This internal fibre supplies a natural kinematic home for a rank-two same-kernel-character pair sector. Tensoring it with the exact rank-three cyclic-neutral pair sector yields a six-dimensional candidate room. The minimum operator court therefore consists of one string operator and six combined room operators, forming a 7×7 correlation court. The selected-cell residue remains an exact mode-specific doorway coefficient, and conjugate legs cancel its complex phase under a stated factorization hypothesis. The remaining central boundary concerns spectral attribution. A projected pole or positive projected density establishes room-seeded spectral response, but does not by itself prove an independent asymptotic open room. Such a claim requires a reducing-subspace, wave-operator, or asymptotic-flux certificate. Moreover, a vanishing direct doorway does not exclude corridor-mediated access; the relevant source is the energy-dependent Feshbach effective source. The finite/affine architecture therefore receives a strong conditional pass, while the physical room-channel attribution remains focused major work. No derivation of QCD, physical quark-pair creation, confinement, a string-breaking distance, or the Standard Model is claimed.
We develop a finite operational response theory for controlled quantum systems in which observer closure, hidden microscopic structure, and higher-order response are treated within a single algebraic framework. The central distinction is between generic higher-order observability and Closure–Residue (CR)-constrained generative response. Standard finite-dimensional quantum theory does not, by itself, impose the specific CR accessibility condition introduced here; physically realizable controls are ordinarily determined by the microscopic Hamiltonian, hardware connectivity, conservation laws, and environmental couplings of the system under study. We therefore formulate First-Residue Accessibility as an additional finite selection principle for the coherent-control sector studied here: the infinitesimal deformation of the observer closure algebra generated by any admissible tangent in the declared target control manifold must lie in the first-residue derivation space inherited from an underlying microscopic CR sector. The algebraic consequences are rigid. Within this coherent-control sector, the maximal abelianness of the population algebra implies that the infinitesimal action of a control on the closure algebra determines its anti-Hermitian generator uniquely modulo a diagonal population gauge. First-Residue Accessibility therefore forces the declared coherent control class, up to this gauge, to lie in a canonical graph-internal subtype extracted from the microscopic CR sector. For diagonal prepared states, the visible first-order population response is silent, while the second variation factorizes through a graph-divergence map of a microscopic bilinear edge flow. A three-site single-excitation benchmark realizes the factorization exactly and yields an even response law of the form Sigma(epsilon X) = epsilon^2 Q_CR(X,X) + O(epsilon^4). We also separate exact discrete support transport from continuous-time quasilocality. A hard one-step support cone has a singular continuous-time limit whenever the limiting generator genuinely spreads local observables; finite propagation in the continuous limit must therefore be formulated by soft tails rather than exact support. We introduce a normalized-trace visible-leakage profile and derive a soft causal readout bound. In the coherent single-excitation sector this profile is uniformly equivalent, up to fixed observer-volume constants, to intrinsic operator-norm quasilocality. For finite-range exchange with simultaneous site dephasing we prove an N-uniform normalized-trace quasilocality estimate without using rank preservation. This genuinely nonunitary extension establishes a common finite-time exponential locality class with standard open-system quasilocality, while the stronger two-sided intrinsic equivalence is claimed only for the coherent unitary subclass. We further show that divergence-image membership is non-discriminating for connected full-population readout, construct an explicit standard CPTP control family that is first-order silent but violates the CR component constraint on a disconnected graph, and isolate experimentally measurable null tests. We distinguish a declared target-control manifold from the larger independently calibrated manifold of physically available coherent controls, thereby separating a conditional declared-manifold accessibility hypothesis from the stronger Physical First-Residue Accessibility statement. Under star-compatible oriented provenance we also derive an observable cross-prediction bound that links independently fixed static CR data to a measurable quadratic response coefficient. A framework-discriminating test requires both that the CR structure be fixed without using the target Hessian data and that the resulting constraint be stronger than what follows from the same calibrated microscopic information in a standard quantum model. We further exhibit a connected three-site collective-mode candidate in which CR Accessibility predicts an exact left–right quadratic null, while a same-support standard comparator constrained only by independently fixed aggregate tangent norms permits a nonzero response envelope. This yields a strict prediction-set separation under an explicit Dataset-A information condition, while also making clear that the separation disappears if standard microscopic calibration independently fixes the same collective tangent relation. We map this strict comparator onto a single-electron linear triple quantum dot, construct a four-point mixed-Hessian estimator, and propagate swap-odd instrumental asymmetry, finite-difference bias, and shot noise into a preregistered experimental envelope. The deeper derivation of the accessibility principle from the full Generative Map is left to the subsequent axiomatic stage of the program.