The release turns a broad compact-phase proposal into a more constrained mathematical-physics program. Its strongest content consists of exact recovery and obstruction results, a common criterion for predictive closure, and one finite compact-holonomy model with a scale-free spectral relation. Conditional sector models and unsuccessful empirical routes remain visible as such.
The paper gives one decision theorem for separating reparameterization, unrestricted functional fitting, finite predictive closure, comparator-specific distinction, and noise-limited measurability. It then applies the criterion to canonical scalars, compact winding sectors, and a symmetric three-mode magnetic graph.
Papers 01, 46, and 47 define the root theory, the closure standard, and one finite realization.
CHC · Covariant core
On every regular connected branch, the constrained action reduces locally to general relativity plus one canonical scalar. The compact branch remains globally distinct through its circumference and winding sectors.
CHC-MCL · Predictive closure
Action integrability, probability completion, passive memory, and positive predictive codimension are stated as common closure conditions. Unrestricted constitutive freedom is proved locally non-predictive when it spans the observable space.
CHC-MHB · Finite holonomy benchmark
A symmetric three-mode loop gives a scale-free spectral invariant. The same finite model fixes phase loading, causal response, loss, and resolved events; an open chain supplies the phase-null control.
Every increase in scope is paired with a stronger proof, closure condition, test, or boundary.
The release states both sides of that distinction.
Claims that do not survive dimensional, rank, identifiability, or held-out tests are narrowed.
The CCL path factor is an inferred parameter rather than an identity fixed to pi.
Planck-unit rescalings leave dimensionless observables unchanged and do not create a prediction.
The PFW calibration family is rank deficient.
Finite compact-mode sums do not constitute ultraviolet completion.
Area or symmetry matching alone does not establish duality or microscopic entropy.
The FRB Catalog 2 held-out result remains negative under the declared comparison.
These checks establish internal consistency and repeatability; they do not substitute for external review.
Each entry states the v2.0 addition and the strongest conclusion supported by the manuscript.
The covariant expansion-phase root and the homogeneous background response used as the public entry point.
Local canonical equivalence is separated from global target topology; circumference, winding conservation, loop-energy bound, phase-only core obstruction, radiative-basis test, and spurion-charge selection are proved.
The regular constrained branch is general relativity plus one locally canonical scalar. Compact winding is globally distinct; a nonzero winding has no regular phase-only disk core. The operator-basis criterion states exactly when a claimed restriction is radiatively closed, and a preserved one-spurion charge fixes the first-order harmonic form.
Phase flatness is restricted to the zero-winding endpoint; joint background probes are placed on a shared compatibility manifold.
A frozen scalar plateau reproduces a cosmological-constant-like homogeneous stress tensor, but the background observables do not identify the microscopic origin or solve radiative stability.
The homogeneous public witness is classified as zero spatial winding; BAO--SN--CMB left-null residuals are required after freezing parameters.
Public BAO, supernova, and CMB background summaries constrain the effective history; they do not distinguish a scalar plateau from an equivalent background component.
Common propagation classes, event statistics, detector-local commit, readout, and shared-fact records.
Local positive-frequency mechanics is preserved within each winding sector, while global spectra and boundary data remain sector dependent.
Positive-frequency reduction and self-adjoint boundary realizations are mathematically controlled; the construction imports its quadratic wave operator and does not derive quantum ontology.
Accessible effects yield event probabilities only through an admitted CPTP instrument; norm loss alone does not derive an outcome space.
Probability representation follows under the admitted effect-space hypotheses. Residual event sharpness and recoverability do not independently derive the physical event space.
Local commit is completed by jump channels whose summed probability equals the no-opening trace loss.
Poisson survival, opening-time, and threshold results are proved from an explicit hazard. Born statistics require the separate rate hypothesis .
Kraus completion of the trigger sink, positive-pole Hankel order, KYP passivity, and minimal passive rational memory order are proved.
The positive sink is completed as a CPTP instrument whose jumps reproduce the trigger current. Positive-pole Hankel rank gives the completely monotone order; the KYP storage inequality and system Hankel rank extend the result to minimal passive rational memory with damped oscillatory poles.
Metastable amplification is required to conserve the incoming resolved jump current without double counting.
Metastable amplification and irreversible readout follow from stated open-system and entropy-production assumptions, not directly from the root scalar action.
Hankel positivity and rank are made prerequisites to interpreting a residual floor with one memory time.
A persistent plateau can reject a zero-floor null under declared controls; it does not uniquely identify CHC or an irreversibility mechanism.
Redundant fragments must descend from resolved instrument outcomes; unlabelled norm depletion cannot seed objectivity.
Redundant records support fragment inference under stated independence and distinguishability hypotheses. Redundancy is not derived from unitary dynamics alone.
Probability completion and memory-order certification are added as the first two conditions of the record hierarchy.
Durable-record and shared-fact criteria are formalized without treating a certificate hierarchy as a microscopic measurement theory.
De Broglie recovery, light-speed distinctions, cosmic time, and phase-decoupling tests.
De Broglie kinematics remains local; compact holonomy and winding distinguish global phase sectors.
The de Broglie relation follows after the standard phase-energy and phase-momentum identifications are assumed; it is not a new dynamical derivation.
Target compactness alone cannot alter a local null cone; one shared probe coupling must satisfy cross-observable restrictions.
Exact homogeneous null speed and travel-delay formulae follow from the common conformal-disformal probe metric. Minimal coupling gives the standard local speed.
Nonzero winding requires a solved inhomogeneous clock background; common clock couplings generate left-null residuals.
Proper-time and chronometer relations use the same probe functions as CR1; clock variation is an additional coupling effect, not a scalar-action prediction.
Nonzero winding obstructs complete smooth relocking and adds an irreducible energy cost.
Every response fraction in the open unit interval can be reproduced by a suitable binding parameter, so the interpolator requires independent calibration.
Analogue boundary memory is assigned a mode count by positive Hankel rank before one-pole calibration.
Boundary-response observables are useful discriminants within a declared laboratory model; analogue agreement is not evidence for cosmological dynamics by itself.
Passivity, complete monotonicity, Hankel positivity, and memory rank become fail-closed noise tests.
Noise and dissipation are included in rejection conditions; a null response constrains the declared coupling window rather than proving universal phase decoupling.
Composite matter, vibrational spectra, tunneling, and boundary-memory prototypes.
Matter loading must pass Helmholtz integrability; compact topology does not derive hadron masses.
For any positive mass catalogue and mass scale, response factors can be chosen to reproduce the catalogue; the relation does not predict hadron masses without new dynamics.
Spectra, global mode sectors, and registered transitions are assigned to action, topology, and instrument layers respectively.
Pure-point spectra yield a countable transition set, not necessarily a locally finite one. Linewidth equivalence requires positive spectral density on the relevant support.
Barrier loading, transient order, event registration, and cross-group prediction receive independent structural tests.
Standard WKB attenuation is retained, while the action and registration factor are proved non-identifiable from a single transmission curve.
Discrete Helmholtz symmetry, Kraus completeness, and sensitivity null spaces are made computational checks.
Public STM images and analytic comparisons verify implementation and support-action arithmetic, not same-instance experimental validity.
Literature support is separated into action, transmission, and instrument evidence.
Digitized STM/STS, MIM, and Fowler–Nordheim curves are compatible with the benchmark form but do not share a calibrated device or fabrication record.
Same-family figure gates require a frozen lower-rank response across barrier and registration observables.
One same-fabrication-family comparison is available; same-surface and same-device cases remain unevaluated because identity-bearing raw data are absent.
The one-state aerodynamic memory receives an exact Hankel determinant and stabilized-rank test.
The retained three-channel source class, memory evolution, and force contribution are derived within the stated quotient and regularity assumptions; no universal turbulence closure is claimed.
Declared calibration ledgers and observational stress windows for cosmology, compact objects, and carrier conversion.
Compact circumference does not determine phase--path calibration; common links must satisfy null residuals.
The path parameter is tied to a declared inverse problem. The special value is hypothesis , not an identity.
Genuine target circumference is separated from unit rescaling and mass-modulus underdetermination.
General mass–length–time rescaling and Planck-triad relations are derived; every dimensionless monomial is invariant and the mass modulus remains free.
Metrology invariance is combined with rank-preserving shared-calibration certificates.
BIPM, NIST/CODATA, and IAU constants verify transcription and dimensional algebra; they provide no evidence for , varying constants, or a quantum-gravity scale.
Counts, selection, exposure, and catalog partitions must descend from one frozen lower-rank map.
The near-Euclidean (F^{-3/2}) law is the controlled anchor. The paper imports the negative Catalog 2 held-out result and makes no propagation detection claim.
Selection-stress residuals are projected onto the left null space after nuisance counting.
Catalog 1 cuts and repeater policies constrain selection sensitivity; the result does not reconstruct the selection function.
Exposure and injection corrections are required to share a map and retain constrained directions.
Public exposure and injection summaries show bounded stability within the selected window, not a luminosity function or population law.
The injection selection surface is audited by its joint sensitivity rank and held-out null residuals.
The public injection response is sufficiently nonuniform to require selection control; it prevents a selection-free population interpretation.
Catalog~2 is explicitly interpreted as a transverse test of the Catalog~1-frozen manifold.
On the non-overlap Catalog 2 holdout, CHC transfer has lower log predictive density than exposure-only and free-power-law comparators by 340.887 and 835.253.
Target topology cannot be inserted as a free delay; shared cross-lens parameters must leave transverse predictions.
Standard thin-lens equations are preserved. A proof shows that propagation and lens/source transformations cannot be separated from the declared observables without external constraints.
Posterior residuals are decomposed into fitted tangent and theory-testing transverse components.
The best fit lies at , while the 95% envelope follows the imposed upper bound; no cutoff-independent upper limit is obtained.
Public-chain stress is required to preserve the model rank and fixed nuisance family.
Public TDCOSMO chains test sensitivity to relaxed profiles but do not constitute a new hierarchical-sampler inference or an measurement.
Scalar winding is separated from horizon topology and microstates; accessibility probabilities require an instrument.
Standard Hawking and accessibility-boundary results are organized consistently; no new information-recovery mechanism or microscopic entropy count is derived.
Return-kernel order is determined by Hankel rank and finite embeddings must remain trace preserving.
JT-bath and Schwarzian kernels support conditional non-Markovian memory statements within the model; they do not establish four-dimensional black-hole microphysics.
Target compactness is separated from material surfaces; morphology, polarization, and wave response share one rank audit.
EHT and GWOSC products establish reproducible target and response summaries, while paper-grade morphology and event-level residual products remain unavailable.
A nonzero winding branch requires a solved strong-field configuration and joint waveform restrictions.
GWTC-3 posterior summaries check compatibility only; they do not reanalyze strain or establish a CHC-specific strong-field correction.
Surface commit, prompt return, delayed return, and unresolved loss are required to form a closed instrument budget.
Public X-ray-binary summaries reproduce standard no-hard-surface diagnostics; the result is not an object-level reanalysis or unique CHC evidence.
The homogeneous branch is zero spatial winding; linked rulers and widths must occupy one compatibility manifold.
The amplitude-width degeneracy is proved. The paper does not supply a Boltzmann likelihood, full recombination, polarization, lensing, or late-transfer calculation.
Primary and linked-ruler summaries are tested through left-null residuals after a frozen calibration.
Width, acoustic-angle, linked-ruler, and later-transfer checks are source-consistent, but they do not validate a full CMB likelihood or select CHC.
A phase-dependent compensation law must be variational and transport across environments with surviving null constraints.
The complete six-reservoir incidence map has rank five and a ten-dimensional cycle kernel; balances do not determine pairwise angular-momentum transfers.
The simulation--observation proxy bridge must retain a nonzero constrained subspace.
Public simulation and observation proxies demonstrate computability, not population-level covariance or causal transfer.
Data expansion is credited only when it adds constrained directions rather than matching nuisance dimensions.
The observational proxy is expanded; the simulation side falls back to the earlier object-level board, so no new group-catalog inference follows.
Environment covariance enters a block response map with cross-environment null contrasts.
Environment and covariance objects are constructed on the simulation side; the observational environment analysis is not completed.
GEMA is treated as a held-out environment relative to a previously fixed manifold.
The effective GEMA-joined sample is five; the result is methodological and cannot support population inference.
Dual-environment harmonization must use one map and report its surviving transverse contrasts.
Dual-environment definitions are made comparable, but harmonization does not identify the transfer field or establish a cosmological law.
Mock-IFU velocity, dispersion, and angular-momentum maps share one rank calculation.
Five simulated and three observed cases verify software and observable construction only.
Mass weighting is fixed as part of the observation map before null-space evaluation.
Five simulated and three observed cases give (z=-0.2045); the result has no evidential power for CHC selection.
Carrier branches close as a CPTP budget, transient order is Hankel-certified, and shared parameters face cross-branch residuals.
Normalized branch-budget identities and estimators hold under a declared calibration and covariance model; branch fractions are not predicted from the root theory.
The pilot requires Kraus closure and a lower-rank common branch map.
Heterogeneous public sources exercise the estimator, while same-instance branch tomography cannot be evaluated.
Same-window optical closure is separated from one-pole memory certification.
With absorption defined by (A=1-R-T), row closure is tautological and supplies no independent physical validation.
Matter-coupled gauge sheets, anomaly ledgers, electroweak structure, confinement grammar, and fit windows.
Scalar target topology is separated from gauge topology; phase-dependent gauge loading and generation-neutral response receive integrability and rank tests.
Charges and currents follow from stipulated representations and field content; the construction does not select those inputs or the generation count.
Anomaly cancellation, variational phase loading, and predictive shared rank are imposed as independent conditions.
The anomaly equations admit an affine two-parameter charge family; normalization, neutral singlets, and field content remain independent assumptions.
Compact scalar topology does not create a doublet or Yukawa spectrum; common mass loading must be variational and overidentified.
Gauge-boson mass splitting and Yukawa flavor data are kept logically distinct; the latter are not determined by the former.
The restricted electroweak completion preserves independent scalar, doublet, and Yukawa data and requires held-out null relations.
The vector mass matrix has rank three with one photon kernel. Arbitrary Yukawa matrices show that fermion masses are not fixed by the gauge sector.
Target compactness is not confinement; a phase-dependent strong sector needs a local action and shared cross-hadron restrictions.
A positive-tension area law implies the stated flux and neutral-exit consequences, but countermodels show that the CHC gauge sheet does not imply the area law.
Rank deficiency is converted into explicit left-null predictions, while full-rank nuisance saturation is excluded.
The observable Jacobian has rank at most eight for fifteen parameters; at least seven local directions remain unidentified, and calibrated targets provide no holdout evidence.
Public covariance and ROOT summaries are evaluated in the transverse, not refittable, subspace.
Public scalar, covariance, contour, and ROOT inputs are reproducible; this does not convert the parent calibration into a global fit.
Vacuum selection, compact fibers, duality benchmarks, large-N comparators, and cross-sector language.
Genuine scalar target topology is separated from internal compactification, finite spectral truncation, and ultraviolet completion.
Conditional compact spectra and vacuum minima are separated from the quadratically divergent ultraviolet sector; finite weights are not a UV completion.
Winding data satisfy none of the necessary duality or microstate conditions; future maps must be overidentified.
Duality, microscopic horizon entropy, and large-(N) correspondence each require additional structures; notation and matching coefficients are insufficient.
Winding labels are not microscopic degeneracies, and shared leading coefficients remain non-identifying without transverse predictions.
Combinatorial area scaling and planar coefficient matching do not determine microstates or a dual description.
Compact-branch data remain distinct from horizon indices and dual maps; observable-wise comparators are ruled non-predictive.
An invertible observable map or equality of generating functionals is required; branch labels and index agreement alone fail.
Function-space saturation, constant-rank compatibility, left-null restrictions, shared-action factorization, and the single-spurion rank bound are proved.
Interface conditions prevent category errors. A split-surjective constitutive map is proved locally non-predictive; a finite one-spurion closure has rank at most two before profiling and can create testable transverse restrictions.
Late-series finite-window identities for phase loading, commit cadence, neutrino response, and charged-lepton loading.
Scalar and joint Helmholtz criteria, homotopy primitive, global Čech gluing criterion, and counterexamples are proved.
Formal self-adjointness is necessary and locally sufficient for a scalar primitive; the full cross-field Helmholtz matrix is required under joint variation, and a Čech coboundary condition determines whether chartwise Lagrangians glue globally.
The DBC--PCD bridge, unitary multi-time completion, influence-functional common primitive, and the Helmholtz obstruction to a PLE lift are proved.
DBC no-event dynamics is embedded in a CPTP instrument. A unitary dilation yields normalized one-time and multi-time reductions, while the influence-functional theorem forces phase loading and response to share one microscopic Hamiltonian derivative.
Worldline loading, commit cadence, and cross-clock response receive separate integrability, instrument, and rank tests.
Phase-load and commit cadence are well-defined after a response law is specified; no universal quantum-transition rate follows from covariance alone.
Compact holonomy is separated from flavor observability; sparse responses must share a lower-rank coupling map.
Global propagation and sparse local response are separated, but mixing parameters, masses, and detector couplings remain empirical inputs.
Global topology and finite response slots do not predict masses; any loading must be variational and overidentified.
The minimal faithful complex dimension of is . The chosen finite response ansatz and numerical mass chain are additional assumptions, not group-theoretic predictions.
The common microscopic-closure criterion and a complete finite loop-holonomy realization with an exact spectral test.
The function-space no-go, finite-spurion normal form, exact loading--response identity, passive realization, enlarged-instrument reduction, and profiled predictive-codimension theorem are assembled into one microscopic-closure chain.
Functional-nuisance saturation, finite-spurion normal form, exact influence-functional loading and response, passive state-space memory, enlarged-instrument reduction, and profiled predictive codimension are proved as one closure chain. The result gives explicit local design and rejection tests; it does not claim that the release has already selected a unique microscopic action.
One controlled compact-phase trimer Hamiltonian yields the tree no-go, cubic spectrum, exact scale-free invariant, codimension-one prediction, common load--response derivative, exact loss instrument, passive response, numerical witness, external figure comparison, and frozen raw-data protocol; an optional autonomous rotor is delimited separately.
An externally controlled compact phase threading a symmetric three-mode loop yields a tree-phase no-go theorem, exact cubic spectrum, scale-free invariant , codimension-one prediction, common loading--response derivative, exact loss instrument, and passive three-port realization. A separately stated autonomous rotor is outside the finite frozen-phase spectral claims. A 1001-phase deterministic witness verifies the identities, invariances, gradient, unitarity, Kraus completeness, and passivity. Thirty-nine digitized points from Roushan et al. (2017) give invariant RMSE 0.02464, but absent raw covariance the comparison is retrospective concordance rather than likelihood confirmation. A twelve-phase raw-data rejection protocol and open-chain null control are frozen.