The Stream and the Algebra - A mathematics and physics paper series

The book series ‘The Stream and the Algebra’ presents a speculative research programme — a thought-experiment in the mathematics of relation, offered for scrutiny, not yet peer-reviewed or tested. Its wager: nothing physical is an absolute number (a mass means nothing until a unit is chosen), only how one quantity stands to another. It fixes the dimensionless relations the world determines and concedes one scale, the anchor; a firewall shares a structure's form across domains, never a bare number. Its sharpest stakes: an axion-free zero of strong CP, few-GeV asymmetric dark matter, and the tau mass from Koide read forward. From the fundamental particles it carries this idea to the vacuum, the classical world, and physics' open problems.

The second volume of the series ‘The Vacuum, the Dark, the Crystallisation of Matter, and the Law’ widens the geometry from the visible sector to the vacuum, the dark sector, and the constituents of matter.

— Dark matter: the E₆ singlet riding in every generation — a few-GeV asymmetric relic from a cogenesis shared with the baryons, so the coincidence Ω_dm ≈ 5 Ω_b is explained, not tuned; its “exotic” face (a vector-like quark, an extra Higgs pair, a Z′) ties collider and direct-detection signatures into one falsifiable correlation.

— The foundations: the axion-free zero of strong CP; a structural reduction of the cosmological-constant problem; and the exceptional-topology floor — an E₈ index giving three generation slots (their chiral count carried by the discrete Δ(54) dynamics), with the exceptional-Jordan “Koide object” completed by the modular dynamics.

— Matter downward — quarks into nucleons and the “stream mass” of visible matter, the atom read relationally — gathering into the Law of Crystallisation: as energy falls, symmetry falls, each fall depositing a dimensionless relation (kept) or a dimensionful anchor (conceded). It is an organising descent–threshold–deposit grammar shared across Landau theory, RG fixed points, and topological order — not a new force, with the firewall holding at the Law's own level.