Spatial Displacement Theory · Section Paper VII · Prepared for Submission
Cosmology Without Dark Components: The Replacement Table, the Two-Component Redshift, and the Audited Open Items
Melbourne, Australia · July 2026 · Atlas Chapter Six — Cosmology
Abstract. Six adjustable parameters of the concordance model are replaced by geometry: the depth field z = ϟ/r, the bound-motion law v = c√z, and the pressure tensor P(z) = Pconv(1+z)⁴. This section paper consolidates the chapter's replacement table and its evidence classes. Redshift is two native effects and no recession — an emission depth stamp at the source and a propagation squeeze across the Clearing, quantised in octaves (1+z = 2Δn, the CMB 10.10 octaves down) — and the H₀ discrepancy is the conflation of the two into one recession variable: probes weight the components differently and land in the observed ordered spread, 67.4 through 73.0. The chapter carries its audited items on its face: the eclipse-saturation rotation model failed real photometry on direct rerun and galactic rotation stands OPEN, with the derived floor a₀ = cH₀/2π and the 8.8% cross-scale collapse as the surviving content; the (1+z)⁴ energy-density scaling is shared form with the expansion reading and cannot discriminate; the pure cubic distance model is excluded against the supernova compilation. The framework retains its registered falsifiers, including the spectral-distortion gate on the release mechanism.
Keywords: replacement table · depth stamp · propagation squeeze · octave quantisation · H₀ ordering · audited open items
1. The replacement table, with evidence classes
| Eliminated entity | SDT successor | Class |
|---|---|---|
| Dark matter | collective displacement + derived floor a₀ = cH₀/2π | floor DERIVED (C-flagged); rotation shape OPEN — stated |
| Dark energy | pressure-gradient nonlinearity (running compression coefficient) | mechanism-level; no Λ term anywhere |
| Gravitational constant | koppa ϟ = v²R/c² (Section Paper II; Paper 06) | DERIVED — G never enters |
| Quantum wavefunctions | definite tours, strobe-averaged into "clouds" | Paper 13 — earned in part, residence law owed |
| Quarks & gluons | trefoil vortex topology | Paper 02 — winding spectrum class A |
| Curved spacetime | pressure gradients in a flat medium | delay/bending from accumulated depth — Paper 06 |
2. The two-component redshift and the dissolved tension
One parameter asked to carry two mechanisms lands in a spread: 67.4 (anisotropy) → 70.0 (tip-of-giant-branch) → 71.6 (lensing time) → 73.0 (ladder). Decomposing the mechanisms dissolves the tension rather than resolving it — the spread is predicted ordering. The octave structure kills nothing quietly: it excludes the classical tired-light class (octave shifting does not compound as absorption) while preserving sharp quasar lines, and it places the CMB emission wavelength at 975 nm. Equation (2) is labelled shared form — it cannot discriminate between compression and expansion readings, and is claimed only as consistency.
3. The audited open items, on the face of the chapter
| Item | Record |
|---|---|
| Galactic rotation | eclipse-saturation model FAILED real SPARC on direct rerun (RMS 66%, BTFR slope 1.33; the earlier success was a circular mock, VOIDED). Floor and 8.8% collapse survive with a 6×-worse control; crossover shape borrowed, labelled. OPEN on the books; the superseded interactive derivation is kept on display with its verdict attached. |
| Cubic distance model | EXCLUDED against 1701 SNe (rival preferred, ΔAIC ≈ 90); the surviving content is dimensional, not a distance law. |
| H₀ structure | engine value 67.4 km/s/Mpc within 1%; the rate-equation structure is assumed pending its own derivation (GOM05) — C-flagged, stated. |
| Release-mechanism gate | pre-registered: CMB spectral distortion < 50 ppm against the interferometric spectrum; a measured distortion above the bound rules the mechanism out. |
| Cyclic extension | NOT COMMITTED — recorded as a fork, not canon. |
Estimated elapsed count since the Clearing ≈ 48 Gyr; the framework makes no claim about the antecedent state. A theory that displays its failed constructions beside its passes is doing what the falsification programme (Section Paper VIII) exists to enforce.
4. Certification
| Result | Value | Status |
|---|---|---|
| P(z), γeff = 4, freeze-out ×4 | eq. (2) | DERIVED (C); shared-form scope on (1+z)⁴ stated |
| Octaves; CMB at 10.10 | λemit = 975 nm | DERIVED (CR07); excludes tired-light class |
| H₀ ordering | 67.4 → 73.0 | PREDICTED structure |
| Rotation sector | — | OPEN — verdicts carried in full (GD05) |
| a₀ = cH₀/2π | 1.04 × 10⁻¹⁰ m/s² | DERIVED, C-flagged; wrong-floor control ×6 |
Methodological declaration. No expansion of space, no dark matter, no dark energy, no inflaton, and no concordance fit enters any derivation; the rival framework appears only as the named alternative in discriminant statements, and where it is preferred by the data (the cubic model's exclusion) that preference is printed. Shared-form results are labelled shared form and claimed as consistency only.
References
- Engine/include/sdt/laws.hpp — law_I, law_II, depth_closure.
- Investigations/07 (CR04/05/07/10/12); Investigations/08 (GD05/GD06, APS03, GOM14); Hubble/ tool suite.
- FIRAS spectrum; Planck 2018; SPARC; Pantheon+ (measured targets).
- Practice papers of this series: 06 · Gravitation; 07 · Cosmology & Redshift; 08 · Galactic Dynamics; 09 · Stellar Astrophysics.