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[[File:QMM_information_wells_PBH.png|thumb|upright=1.15|Growth of information-well depth leading to PBH collapse.<ref name="PBH" />]]
===Hilbert-space capacity and holographic bound===
* '''Finite cell dimension.''' Each Planck cell carries a Hilbert space of fixed size <math>\dim\mathcal H_x=d_{\max}\simeq\exp\!\bigl[A_{\text{cell}}/(4\ell_P^2)\bigr]\approx5\times10^{121}</math>, which follows from the covariant Bekenstein–Hawking relation and sets the ultimate UV cutoff.
* '''Arrow of time.''' Because the imprint map is CP-T odd, every interaction increases the coarse-grained entropy field <math>S(X)</math>, providing a microscopic origin for the thermodynamic arrow without breaking Lorentz symmetry at long wavelengths.
===Renormalization-group completion===
* '''Informational fixed point.''' Running couplings obey <math>\beta_G=-2G+\mathcal O(G^2)</math> and <math>\beta_\lambda=0</math>, yielding an interacting GIFP at <math>(G_\star,\lambda_\star)</math>; gravity and imprint kinetics therefore share the same asymptotic-safety basin.
* '''Dimensional transmutation.''' Below <math>\Lambda_\star\sim M_P</math> the theory produces effective constants <math>G_{\text{IR}}</math> and <math>\Lambda_{\text{IR}}</math>, while the imprint sector becomes scale-invariant, explaining how lattice QMM reproduces classical GR + SM in the infrared.
===Vacuum-imprint energy and late-time acceleration===
* '''Residual cell energy.''' Fully saturated cells store a uniform zero-point density <math>\rho_{\text{vac}}=d_{\max}^{-1}M_P^4/16\pi^2\approx(2\times10^{-3}\,\text{eV})^4</math>, naturally reproducing the observed cosmological constant.
* '''Slow-roll entropy field.''' If imprint writing remains overdamped (<math>\ddot S\ll H\dot S</math>), the kinetic term <math>\lambda(\partial S)^2</math> gives an equation-of-state <math>w(a)\simeq-1+\lambda\dot S^2/\rho_{\text{vac}}</math>, predicting <math>w(z)+1\propto(1+z)^6</math>.
===Emergent Lorentz symmetry===
* '''Causal microstructure.''' Local commutators vanish outside the discrete light cone; at scales <math>\gg\ell_P</math> the lattice dispersion approaches <math>E^2-p^2\approx m^2</math> up to <math>\mathcal O\!\bigl(p^4\ell_P^2\bigr)</math>.
* '''Boost invariance from RG.''' Coarse-graining drives the dynamical exponent to <math>z\to1</math>; Lorentz symmetry thus emerges as an infrared fixed line rather than a fundamental postulate.
===Baryogenesis by entropy bias===
* '''CP-weighted imprints.''' During the electroweak crossover an initial entropy skew <math>\Delta S/S\sim10^{-9}</math> biases sphaleron transitions, producing the observed baryon-to-photon ratio <math>\eta_B\approx6\times10^{-10}</math>.
* '''No BSM fields required.''' The mechanism uses only Standard-Model CP violation and finite-Hilbert-space bookkeeping; it disappears in the continuum limit <math>d_{\max}\to\infty</math>, directly linking matter genesis to QMM discreteness.
===Cyclic bounce cosmology and primordial black holes===
* '''Bounce condition.''' A cosmological cycle ends when total imprint entropy approaches <math>S_{\max}=A_H/4\ell_P^2</math>; unitary shuffling then resets curvature while preserving quantum coherence.
* '''Information-well collapse.''' Blue-tilted imprint fluctuations (<math>P_S\!\propto k^{n_S-1}</math> with <math>n_S>1</math>) re-enter the horizon during radiation domination; regions with <math>\delta S/S\gtrsim0.3</math> form PBHs of mass <math>M_{\mathrm{PBH}}\simeq\gamma M_H(k/aH)^{-2}</math>, spanning <math>10^{-16}\!-\!10^{3}\,M_\odot</math> and seeding dark-matter and PTA signals across cycles.
==Experimental verification==
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