Spatial Displacement Theory · Paper 12 · Prepared for Submission

Collective Vortices in One Medium: Conduction as Occlusion Drag, the Native Compression Wave, and Phase-Locked Condensates — A Programme Specification

J. C. Harvey

Melbourne, Australia · July 2026 · Domain 12 — Condensed Matter Physics

Abstract. Condensed matter is the collective behaviour of many vortices co-resident in the relay substrate. No second medium exists: the same lattice that carries gravitation (g = v²/R) and the handed occlusion force also carries conduction, magnetism, sound in solids, and the condensate phases. A conduction electron is a drifting W = 1 vortex; resistance is occlusion drag converting organised throughput into disordered throughput (heat); the solid-state quantum of lattice vibration is the native compression wave of Paper 10, requiring no field operator; a magnet is aligned wake circulation. Superconductivity is specified as phase-locking of vortex pairs through the compression wave — a defect-blind collective mode with zero drag and swirl expulsion; superfluidity as the same phase lock in the neutral sector, whose circulation quantum κ = h/m is already recovered to 0.02%. This domain is a SPEC-status programme: mechanisms and falsifiable targets are fixed and pre-registered here; except where a result is imported from an executed domain, no target below is claimed as achieved.

Keywords: occlusion drag · drifting vortex · compression wave · phase lock · condensate · native metrology

1. One medium, restated for solids

conduction e⁻ = drifting W = 1 vortex; resistance = occlusion drag → heat(1)

Drift velocity is the balance of the driving push against disorder occlusion; dissipation is organised throughput dumped into the disordered channel of Paper 11. The conductivity assumes the observed form σ = ne²τ/m with τ the drag time — the form is the convergence target; the mechanism (occlusion, not scattering amplitudes) is the SDT content. Metallic resistivity rising with temperature follows from drag on thermal lattice agitation.

2. The native vibration quantum

"phonon" ≡ FD05 compression relay wave; c_s = relay stiffness(2)

Solid-state heat capacity follows from mode counting of compression waves in a bounded box: the high-temperature 3R plateau and the low-temperature T³ regime are counting consequences, with the characteristic temperature set by c_s — no quantised field is introduced, and the mode-content caveat of Paper 11 (ε = hν asserted) is inherited and disclosed.

3. Condensate phases as macroscopic phase lock

superconductor: vortex pairs locked via the compression wave ⟹ R = 0; flux count Φ₀ = h/2e(3)

superfluid: neutral phase-locked condensate; κ = h/m — recovered to 0.02% (FD02, executed)(4)

Pair-locking makes the collective mode defect-blind: drag vanishes not because carriers avoid obstacles but because the locked mode has no channel into disorder. Swirl expulsion from the locked bulk is the expulsion phenomenon; the flux count h/2e is a native winding count (two carriers per locked pair). The isotope shift of the transition temperature (T_c ∝ M^−½) follows from the compression-wave mediator. Of these, only (4)'s circulation quantum is presently earned (imported from the executed fluid suite); the rest are pre-registered targets.

4. Band ordering, the Hall staircase, and native metrology

Conductor/semiconductor/insulator ordering is specified from lattice-packing occlusion gaps (the same packing geometry as the atomic k-factor radii), not from delocalised wave states. The quantised Hall resistance and the frequency–voltage relation are specified as lattice-topology counts — R_K = h/e² and K_J = 2e/h as winding arithmetic — which would ground the practical resistance and voltage units natively (experiment specs E86 and E85). Ferromagnetism is aligned wake circulation with exchange as wake co-rotation energy; its entire quantitative programme is committed to native wake-circulation units — magnetons are forbidden on the face of the spec.

5. Certification

Item	Target	Status
Occlusion-drag conduction	σ form; ρ(T) sign; Joule channel	SPEC — pre-registered target
Compression-wave heat capacity	3R plateau; T³ law	SPEC — inherits ε = hν caveat
Superconductivity as pair lock	R = 0; Φ₀ = h/2e; T_c ∝ M^−½	SPEC (seed written)
Superfluid circulation quantum	κ = h/m	EARNED at 0.02% — imported from executed FD02
Hall / frequency–voltage counts	R_K, K_J native	SPEC — E85/E86
Ferromagnetism in native units	Curie point; hysteresis	SPEC — magnetons forbidden

Methodological declaration. The forbidden imports of this domain are named in its constitution: no pair-potential gap function, no delocalised wave states, no symmetry-breaking ontology, no electron clouds, and no field-operator vibration quanta — all are convergence targets, not machinery. This paper distinguishes throughout between EARNED results (imported from executed domains with their classes) and SPEC targets (pre-registered, unclaimed). Nothing in SPEC status is presented as achieved.

References

Investigations/12_Condensed_Matter_Physics — CM01–CM07 programme constitution and seeds.
Investigations/10_Fluid_Dynamics — FD02 (κ = h/m, executed), FD05 (compression wave).
Engine/include/sdt/laws.hpp — law_III (occlusion), law_VI::traction and topology (winding counts), bridge (native g).
Experiments/E85.md, E86.md — native voltage and resistance specifications.
Papers 03, 10, 11, 14 of this series.