Raoul Bianchetti

Cold-atom experiments now control the exchange phase of strongly interacting one-dimensional gases and resolve the asymmetric momentum distribution of a driven impurity together with its relaxation after trap release. We introduce a finite-memory closure from Viscous Time Theory (VTT) for the preparation-history dependence of this observable. The prepared exchange phase remains the experimental control variable; a causal reduced coordinate follows it with a finite response time, and the mismatch between the two is the VTT state variable. Under an odd-response condition on the impurity momentum distribution, the momentum skewness acquires a linear, history-resolved correction. We test the closure in a microscopic reference model, a spinful Bose–Hubbard ring with exact time evolution, using protocols that end at the same exchange phase and differ only in their history. Interacting systems develop a history-dependent skewness that is small and oscillatory for slow preparation and of order one for fast preparation. An oscillatory generalization of the closure, calibrated on monotonic ramps alone and then frozen, predicts the held-out reversal protocols and reduces the mean-square error of the memoryless adiabatic baseline in the slow regime by 30 to 45% at fixed interaction strength and by 12% after averaging over a 20% spread of interaction strength. The response persists at a larger system size, where its frequency follows the lower level spacing of the system. The results define a quantitative experimental programme: calibrate on monotonic pulses, predict reversal pulses, and compare with a full microscopic baseline supplied with the same pulse history.

Nuclear fission is a topology-changing collective process: a connected density distribution evolves through a necked configuration into separated fragments. This paper formulates a Viscous Time Theory (VTT) closure for that transition without modifying mass-energy equivalence, nuclear conservation laws, or the microscopic energy density functional. The proposed closure introduces an operational topological scission coordinate extracted from nuclear density isosurfaces and a finite-memory coherence variable that relaxes toward that coordinate on a viscous time scale. A positive free-energy functional and a dissipative energy identity follow directly. The result is a bounded, history-sensitive correction to the partition of a fixed fission Q value among collective motion and intrinsic excitation, rather than a new source of energy or an informational reinterpretation of c squared. A dimensionless M1 calculation shows that two scission histories with the same initial and final topology acquire different transient memory burdens and irreversible partitions. The framework therefore makes a sharp falsifiable proposal: after standard collective coordinates are controlled, held-out scission trajectories with different history must exhibit a residual correlated with the finite-memory state. Failure of that residual to improve over a Markovian EDF or TDDFT baseline would rule out the closure in its proposed form.

Consciousness is often discussed through integration, recurrence, global availability, or predictive organization. This paper isolates a more elementary structural question: what must a physical system retain and causally re-use if it is to remain dynamically self-conditioned through time? We formulate a Viscous Time Theory (VTT) hypothesis in which a candidate conscious organization requires-not is exhausted by-a Φα-persistent causal loop: a finite-memory, history-sensitive, causally closed process that remains within a measurable corridor of coherence and recoverability under bounded perturbation. The formulation separates an observable state x from an internal causal-memory state h, treats informational viscosity as a positive intrinsic-time density η, and introduces Φα only as an operational alignment/recoverability score. From these definitions we derive a matched-state prediction: two systems matched in present observable state but differing in reconstructed causal memory can diverge under an identical future perturbation; the effect should collapse when the memory-to-state channel is neutralized. This is a discriminating experimental signature, not a phenomenological proof. The paper positions the proposal relative to recurrent processing, global neuronal workspace, integrated information theory, and predictive-processing approaches; identifies explicit failure conditions; and outlines biological and artificial test beds. VTT therefore enters the consciousness debate as a constrained research programme: ambitious in its target, but accountable to causal intervention, held-out prediction, and claim boundaries.

The supermassive-black-hole-host-galaxy mass relation at high redshift is potentially informative but observationally selection-sensitive. We formulate a bounded Viscous Time Theory (VTT) mechanism for central gas capture on a fixed physical galactic background. A dimensionless, past-only memory state modulates a nonnegative, bounded physical sink; it is not identified with mass density, stress-energy, or a modification of general relativity. The model carries an explicit gas-to-central-mass ledger. We then provide a nondimensional endpointmatched mechanism test: two smooth assembly histories with the same terminal driver value yield distinct integrated central masses, while a memory-neutral control eliminates the difference. The result is an existence demonstration of history dependence, not a fit to JWST data or a prediction of a universal offset. Its observational signature is a preregistered, causal history proxy that must improve held-out black-hole-host residual prediction after host covariates, measurement error, and survey selection have been modelled. Failure of that comparison rejects the M1 increment for the stated realization.

We formulate a minimal criterion under which an imaginary solution can be assigned physical status without treating the symbol i, by itself, as an ontological object. The construction recasts the Viscous Time Theory expression Ψ = ΔC + iΦα as a real rank two phase bundle equipped with a positive metric G and a compatible complex structure J_G. The phase sector is therefore a geometry with an explicit transport law, not a decorative complex notation. A candidate branch is physically admissible only when it possesses a non arbitrary real phase geometry, an invariant or causal transport quantity, a declared map to observables, a controlled null or real limit, and a discriminable prediction relative to a baseline model. We distinguish three notions that are often conflated: the symmetric pre informational tensor T0, a present but non projected M3 phase branch, and the Anatholy tensor as a boundary of excluded admissibility. An exact dissipative minimal model verifies G compatibility, phase orthogonality, the energy identity, frame invariance, and the null phase limit. The result is a mathematical and operational foundation for a future empirical programme, one that stops short of a modified gravity theory or any claim that dark components have been identified or removed.

The Euclidean perimeter of an ellipse is a geometric length fixed by a reference metric. This article introduces a different, explicitly scoped object: a coherence-weighted boundary functional that assigns a state-dependent cost to a closed curve while retaining the classical perimeter as its null limit. The construction is motivated by the differentiable M3 regime of Viscous Time Theory, in which a positive intrinsic-time rate, a declared admissibility indicator, an operational coherence field, and a bounded regime weight must be specified before use. For a regular curve Γ, the proposed functional adds a dimensionally consistent directional-coherence term to the reference length. We prove reparameterization invariance, classical reduction, total-variation bounds, and a separate signed balance identity. For an ellipse, the correction reduces exactly to a weighted total variation of the pullback coherence field; this shows that the ellipse enters through the sampled ambient field and regime weight rather than through an unexplained change of Euclidean geometry. Synthetic tests recover the exact elliptic-integral reference, satisfy the derived bounds, and remain invariant under smooth changes of parameterization. The result is a falsifiable mathematical model family that cleanly separates the geometric and VTT-motivated contributions to the boundary cost.

The Laplace resonance of Io, Europa, and Ganymede is a benchmark of celestial mechanics within the Jupiter-Galilean-satellite system. This article does not alter Newtonian gravity, replace established tidal theory, or claim a new explanation of the observed resonance. Instead, it formulates a structure-preserving auxiliary Viscous Time Theory (VTT) layer that can be evaluated alongside a conventional averaged resonant Hamiltonian. The orbital variables remain in a classical reduced phase space. A separate state combines an octonionic coherence coordinate, an internal memory coordinate, and a positive-definite response geometry. From these declared objects we construct a regularized informational potential, its covariant Hessian, a symmetric response tensor, and the Anatholy exclusion dyad. Three elementary propositions establish the exact classical no-feedback limit, a local M3 stability and susceptibility bound, and the negative-semidefinite rank-one character of the boundary tensor. A pendulum-type resonant normal form and cyclic synthetic protocol illustrate how libration, softening, memory, and boundary clearance can be reported without being mistaken for astrometric evidence. The resulting paper is a falsifiable modelling architecture: any later claim of predictive value must survive pre-registered ablations, conserved-quantity checks, identifiability tests, and comparison with a purely classical baseline. This narrow scope preserves the original VTT idea while making its mathematical and empirical obligations explicit.

This article gives a narrow, testable meaning to zero-latency coherence transport in Viscous Time Theory (VTT). The label does not assert zero experimental duration, a superluminal process, an instantaneous collapse law, or a modification of standard quantum mechanics. It denotes a formal noncontinuability statement: a continuously recoverable regime (M3) reaches a boundary at which no further continuous M3 interpolation is available, so a separately declared post-boundary regime (M4) must supply an explicit selection relation. The construction begins with the standard quantuminstrument baseline: a density operator evolves on M3 through a completely-positive-compatible normal form in a positive intrinsic coordinate, while a multimargin combines recoverability, the spectrum of a declared diagnostic Hessian, and clock regularity. At first exit, the M4 relation must agree with a valid quantum instrument whenever it represents a measurement outcome. Three results delimit the proposal. Positive intrinsic-clock density reparametrizes a continuous M3 path rather than establishing an absolute physical time. A nonselective trace-preserving local instrument leaves the remote marginal invariant, so the proposed selection relation cannot be used for signaling. Preboundary M3 information alone does not identify a unique M4 image. Synthetic normal forms distinguish a resolved finite record from an ideal endpoint relation and illustrate margin loss, without presenting empirical evidence. The framework preserves VTT's original ambition at the precise point where its quantum specialization must become operational: any added predictive content must be benchmarked against standard quantum filtering, constrained by complete positivity and nosignaling, and tested prospectively.

The invariance of the vacuum speed of light is ordinarily expressed through the Lorentzian causal cone. This article develops a complementary, explicitly limited interpretation within Viscous Time Theory (VTT): the observed null cone is treated as the maximal cone of coherence-preserving transport. The formal core is a hyperbolic coherence field with independent temporal and spatial principal coefficients. Its characteristic speed is the ratio of those coefficients, rather than a constant inserted into the Lagrangian. A massless comoving sector then yields an exact Hessian criterion: the M3 admissibility margin-VTT's label for a continuously recoverable, differentiable regime-is positive for subcharacteristic transport, vanishes at the characteristic speed, and becomes indefinite beyond it. In vacuum, matching this cone to the electromagnetic null cone identifies the characteristic speed with c; this is a compatibility condition rather than a numerical derivation of c. In a nondispersive dielectric, the same construction reproduces the Cherenkov phase-matching condition and reinterprets the onset of radiation as a transition from a bound source response to propagating channels. The article keeps the standard empirical content of relativity and electrodynamics intact, states the assumptions needed for the VTT interpretation, and provides a falsifiable constitutive test for any future medium-dependent extension.