Wave-Nature Unification Theory: Foundational Document and Derivation Notes (English Edition)

Abstract

[v6] The Foundational Overview is updated to v2.2. (1) Refinements from the literature check of Chapter 4 — the lineage note is sharpened (Kelvin (1867) identified vortices with atoms, not charge; the closest precedent for "a conserved quantum number as soliton winding" is Skyrme, baryon number as topological winding), and Sec. 4.5(1) now records that particle-vortex duality is a theorem of 2+1 dimensions, the 3+1-dimensional dual of a vortex string being a string coupled to a two-form gauge field. (2) Resolution of ledger item (21) — the charging problem of the dark vortex strings is resolved by the two kinds of winding (wavefront phase = charge; arrest-field phase = dark strings), restricting the scope of identification A to the wavefront phase, with the falsifiable corollary (dark strings interact through tension alone) agreeing with Chapter 7. See Appendix C inside the document. [v5] The Foundational Overview is updated to v2.1. Main changes: (1) a new Chapter 4, "The Electromagnetic Force — Where Does Sign Come From?" — the two-sector structure (gravity = the scalar sector of arrest density; electromagnetism = the signed sector of winding number); from the identification charge = winding there follow charge quantization, charge conservation (= a rediscovery of the existing pair-creation prohibition), the identification of the annihilation channel, and the emergence of sign structure; subsequent chapters are renumbered and ledger items (18)-(21) added. (2) The zero-extinction refinement in Chapter 3, Sec. 3.4 — the transparency requirement is extended from zero absorption to zero extinction (absorption plus scattering); by the optical theorem, drag and heating are resolved simultaneously by one condition; the observational bound from the persistence of stellar peculiar velocities is registered as ledger item (22). See Appendix C (Change History) inside the document. [v4] The Foundational Overview is fully revised (document v2). Main changes: separation of the two roles of the arrest parameter (a: degree of arrest / χ: time velocity / Φ: pressure-deficit potential); Chapter 3 restated at the level of a field equation, with a new section answering the classical objections to Le Sage-type gravity (drag, heating, aberration); retraction of the overtone law m_n = n²·m_e and its replacement by the equipartition constraint of the charged-lepton triplet (Koide\u2019s formula, known); consolidation of the MOND attribution onto the coherence-time mechanism; claim labels [A/B/C/Open] applied throughout, with a new Chapter 0 and a change-history Appendix C. See Appendix C inside the document for details. [v3.1 Corrigendum] A corrigendum (corrigendum_v3_1_EN.pdf) concerning the lattice numerical claims of Derivation Note v3, Sec. 7, has been added. The Sec. 7(i) values depend solely on matrix-valued couplings not derivable from the medium model, and Sec. 7(ii) could not be reproduced under pre-registered protocols; the network-level claims of Sec. 7 are therefore withdrawn. The single-link results (plasticity equation, retention law, non-destructive readout) are unaffected. The independent reimplementation code (lattice_reimplementation_code.zip) is included. Japanese-English split edition (English record) of the Wave-Nature Unification Theory (a-theory, Arrest Parameter Framework), containing the Foundational Document (Overview) and Derivation Notes v2 and v3. The Japanese edition is published as a separate record (DOI: 10.5281/zenodo.21850306). Reconstructed from the former combined record (DOI: 10.5281/zenodo.21740126). Contents: Foundational Document (Overview) (Markdown, dated 2026-07-30) / Derivation Note v2 (PDF + LaTeX source) / Derivation Note v3 (PDF + LaTeX source). [v2] Derivation Note v2 "Unification of the Averaging Stiffness θ′ — Dispersion θ′(k), Determination of the Coefficient A, Interpretation of ε₀, and the Lifetime Formula". θ′ is redefined as the averaging stiffness of the field itself, establishing: the effective stiffness θ′_eff(k) = c²(k_g/k + k/2k_g)²; the exact coincidence of its minimum with the arrest ground mode k₁ = π/L_s (a variational re-derivation of L_s; total ground energy = ε₀ = 2m_ec²); the complete determination of the selection-rule coefficient A = 6θ′k_g² (= 6U″(φ₀)); the unification of the two readings of ε₀ via topological pair creation; and the lifetime formula τ_n = 2τ₀/(n(n²−3)) with stability boundary n² = 3 and asymptotics Γ ∝ m^{5/2}. Four falsifiable predictions and five open issues are stated explicitly. [v3] Derivation Note v3 "History Retention in the Interaction Medium — the Plasticity Equation and the Forgetting Action S_rec". Formalizes, using only previously derived results and zero additional parameters, the mechanism by which the interaction medium between arrested configurations retains history (a synapse-like plastic coupling). Main results: (1) the plasticity equation dw/dt=(1/τ₀)⟨Θ(E_loc−ε_th)⟩(1−w)−w/τ_r, with the learning rate set by the theory's unique time scale τ₀, the Hebbian coincidence gate derived from the pair-creation threshold and wave interference, and saturation/weight quantization from the packing rule 2L_s; (2) two independent formulations of the forgetting action S_rec (real-space pinning tunnelling vs. order-parameter phase slip S₁=1.16) agree at the 1.2% level through the barrier identification V_PN=μξ_h=1.70𝓔₀ — a cross-validation of the S₁ calculation; (3) the retention law τ_r(d)=ω_att⁻¹exp[2S₁d/ξ_h], programmable from nanoseconds to cosmological scales by the write separation; the separation for age-of-the-universe non-volatility, 38.2ξ_h, equals the dark-structure survival cut L_q(t₀); (4) numerical experiments on a 26-direction cell lattice demonstrating distributed memory and threshold-protected non-destructive readout. Five falsifiable predictions and five open items are stated explicitly.