Topology of Totality (TOT): Emergent Spacetime, Mass, and Quantum Mechanics from Informational Topology

We present the Topology of Totality (TOT), a unified theoretical framework in which spacetime, mass, gravity, and quantum mechanics emerge from a single informationaltopological substrate termed the Light Canvas. The central quantity is the Sheaf Compressibility Index (SCI), measuring the compressibility of descriptive sheaves on a causal graph. Time is not a fundamental coordinate but an emergent functional driven by informational Ricci flow; its arrow follows from the monotonic increase of SCI. We construct an SCI-deformed Heisenberg algebra [ Ĥ, τ ] = iℏ(1-Ŝ) that interpolates between full quantum uncertainty (SCI → 0) and classical determinism (SCI → 1), resolving the Pauli objection to a self-adjoint time operator. In the Standard Model of Topology (SM-TOT), particle masses arise parameterfree from the spectral complexity of graph Laplacians via the Kirchhoff-TOT mass formula m(G)/m e = det ′ (L G)/ det ′ (L C 8), reproducing the proton mass to 0.115% accuracy. Matter crystallises as topological motifs-the proton is the complete graph K 7 (the collinearity graph of the Fano plane encoding octonions), while leptons are cycles C n. Cosmological applications yield an emergent Hubble tension of ∆H 0 ≈ 3.4 km/s/Mpc from the SCI difference between epochs, a topological seesaw mechanism for neutrino Topology of Totality masses converging to the Planck bound Σm ν < 0.12 eV, and a decoherence ratio Γ late /Γ early ≈ 2.7× between cosmological epochs-all without free parameters. The framework extends the Landauer bound with a topological correction and addresses the Yang-Mills mass gap via the Cheeger inequality on torsion-bearing graphs.