Spatial Displacement Theory · Section Paper II · Prepared for Submission

The Six Laws: Formal Statements, Theorem Inventory, and Certification

J. C. Harvey

Melbourne, Australia · July 2026 · Atlas Chapter Two — The Six Laws

Keywords: six laws · theorem inventory · occlusion force · movement budget · winding quantisation · certification

Law I — Cosmological Relay Throughput (Axioms R1–R6; T1–T2)

Shell cancellation (T1) renders each of the N = 5.894 × 10⁶¹ shells' contribution distance-independent; T2 fixes the burden. The boundary count S = 4πN² = 4.366 × 10¹²⁴ dissolves the vacuum-energy discrepancy as shell counting. Class B; magnitudes conditioned on the observed R_CMB (class X, disclosed).

Law II — The Release Cascade (Corollaries of Law I)

The CMB is the present operating pressure of the lattice, not a cooling relic; the pressure tensor is topologically stiff (four W ± 1 degrees of freedom per cell) and drops by the exact integer factor 4 at recombination when independent winding defects bind into neutral hydrogen. Stars are convergence-processing nodes (Paper 09). Pressure-domain radius: r = √(L/4πF_CMB), F_CMB = c·u_CMB/4.

Law III — Convergent Boundary Pressure: the Occlusion Force (T3–T4)

One law carries Coulomb, gravitational, and nuclear couplings; the hierarchy is cross-section geometry, not species. Certification is split and stated: the 1/r² occlusion structure and R₁²R₂² product are DERIVED (class C, pass the delete-test); the coefficient P_eff = 4k_ee²/(πR_p²r_e²) = 5.225 × 10³¹ Pa is anchored at the hydrogen Coulomb datum — the calibration point, class E, fails the delete-test. The electropause closed form P_eff = m_p²m_e²c⁵/(4παℏ³) is the recorded companion derivation (Papers 03, 16); the coexistence of the two provenances is an open item, stated, not silently resolved.

Law IV — Inertial Mass as Reorganisation Cost (T5–T7)

Mass is the throughput-reorganisation cost of translating an exclusion volume; the factor 3 is the angular-averaging quadrature share. Inertial and gravitational response read the same V_disp — the equivalence principle holds as an identity, not a postulate. V_disp(e⁻) = 9.988 × 10⁻⁶² m³; V_disp(p) = 1.834 × 10⁻⁵⁸ m³; each particle carries three radii (exclusion, wake, quantum), and conflating them is the classical source of paradox.

Law V — The Movement Budget (Axioms M1–M3; T10–T17)

T10–T17 recover dilation dτ/dt = √(1−v²/c²), contraction, E₀ = m₀c², E² = (pc)² + (m₀c²)², and the photon limit (v_circ = 0 ⟹ v = c, m = 0, E = pc) — the complete Lorentz sector as allocation of one fixed budget, with no transformation postulate. The closure z·k² = 1 (z = (v/c)², k = c/v) is true by construction and is carried in the benchmark ledger as IDENTITY, never as evidence; the k-ladder it anchors runs k(H) = 1/α = 137.036 through k(☉) = 686.4, one hierarchy from the atom to the star (Papers 04, 06).

Law VI — Vortex Topology Quantisation (T18)

The winding spectrum is analytic (PPT09, class A): the (1,1) unknot is the electron, confined by its own displacement; the (2,3) trefoil is the proton, protected by Δ(t) ≠ 1 — which is why the proton does not decay; W = 2 is unknotted and merely metastable, never observed. The W+1 radius rule agrees with the muonic-hydrogen boundary radius to 0.02% with nothing adjustable and remains a labelled conjecture pending derivation from trefoil geometry; its falsification gate (W_eff departing from the integer 3 beyond 3σ) is pre-registered. The zero-parameter mass-ratio hook 6π⁵ = 1836.118 (19 ppm) stays OPEN — the identity is exact, the mapping to V_disp is asserted, not derived.

Certification summary

References