Four statements about time and energy, traditionally treated as separate postulates or empirical facts, are shown to be theorems of the Fano spacetime lattice and the Huniverse = Hlattice identity (Paper XCVII). (1) Conservation of energy = shape memory. Noether's theorem applied to the Fano lattice gives dHlattice/dt = 0 ⇔ ∂L/∂t = 0 ⇔the Fano lattice topology (G2 symmetry, 7 nodes, Poisson ratio ν = −1) is time-invariant. This time-invariance is the shape memory: the Weissenberg number Wi →∞ensures the lattice never relaxes, so G2 symmetry is permanent, so Hlattice is conserved. Energy conservation and shape memory are the same statement in dierent languages. (2) Time is a phenomenon of brane expansion. The arrow of time is the direction of increasing H+ real-unit advance, which is identical to the direction of increasing Hubble parameter H(t) > 0 (brane expansion). The rate of time at any point equals the local lattice propagation speed divided by c: dτ/dt = clocal(r)/c = p gtt(r). (3) Time reversal is topologically prohibited. T-reversal requires H(t) →−H(t), i.e., a0 →ia0 (imaginary sump tilt). This crosses from the H+ sector to the H−sector of O = H+ ⊕H− a topological sector change, not a statistical uctuation. The H−sector is the CPT-conjugate universe (Boyle & Turok 2018), permanently separated from H+ after the nucleation event. T is violated by topology, not by any asymmetric microphysics. (4) Lattice dimension change = local time dilation. A change in the local Fano lattice metric by factor f(r) = p 1 −rs/r (Schwarzschild) produces an identical change in local clock rate for external observers. Spatial lattice compression ⇒temporal lattice stretching ⇒slower clocks: gravitational time dilation is a lattice metric identity. Four new predictions are made (P56P59). Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.
Bharathi Jagadeesan (Fri,) studied this question.