Temporal Congestion Mechanics — Predictions Catalogue
The 166 predictions as published. Beneath each: its category and a plain-language description of what it means.
1. Ward Constant v_∞ = c²/√(2πGλ) ≈ 149.67 km/s as the universal asymptotic galactic velocity.
Two-stage prediction. Stage 1 (intermediate r): the K(X)-regime BTFR slope-4 V_flat = (G·M_bar·g₀)^(1/4) governs. [DERIVED, CONFIRMED]
Unique to TCM
Every spiral galaxy, whatever its size, settles to the same outer rotation speed — 149.67 km/s — set purely by the fabric's own constants. Standard physics has no reason to expect a single universal speed across all galaxies; here it falls straight out of the fabric moduli.
2. Ward attractor 1/r profile in outer halos at r > r_knee.
Outside the BTFR knee radius r_knee = √(GM_baryon/g₀), galactic gravity follows the K(X)-regime 1/r attractor rather than Newtonian 1/r². Filament lensing, tidal streams, cluster lensing at r > r_knee follow the same attractor. [DERIVED]
Distinctive prediction
In the outer reaches of galaxies, gravity falls off as 1/r instead of the usual 1/r². This is a different force law from Newton's in exactly the region where 'dark matter' is normally invoked.
3. Ward Constant convergence from above and below establishes the universal asymptote.
Galaxies with M_baryon < M× approach v_∞ from below (NGC 3198, V_outer = 149.6 km/s); galaxies with M_baryon > M× approach from above (NGC 0801, V_outer = 216.2 km/s, declining at −0.22 km/s/kpc). [DERIVED, CONFIRMED]
Distinctive prediction
Galaxies lighter than the reference mass (3.15×10¹⁰ M☉) drift up to the universal 149.67 km/s from below; heavier ones drift down to it from above. The direction of approach depends on mass in a specific, checkable way that standard halos don't predict.
4. Universal Broadfield Constant n_H = e^(1/2) at every static saturation surface.
n_H = exp(1/2) ≈ 1.6487, from the n-index equation at r_s. The same constant sets the cosmological initial state and the fabric saturation — one constant across twelve orders of magnitude. [DERIVED, covariant]
Unique to TCM
Every fully-collapsed surface (a black-hole equivalent) reaches the exact same maximum fabric compression, n_H = e^(1/2) ≈ 1.6487 — a fixed universal number. No standard theory has such a ceiling.
5. Big Rebound: cosmic initial state at n = n_H.
Maximum elastic energy density ρ_rebound·c² = ½ε·(n_H−1)² ≈ 1.89×10⁻¹⁰ J·m⁻³. Cosmic history is one continuous relaxation toward n = 1. [DERIVED]
Unique to TCM
The universe began not at a singular point but at that same maximum compression (energy density ½ε(n_H−1)² ≈ 1.89×10⁻¹⁰ J/m³), then started relaxing. The 'Big Bang' is a rebound from the fabric's stretch limit, not an infinite-density origin.
6. BTFR slope = 4 exactly from K(X)-regime flux conservation.
V_flat⁴ = G·M_bar·g₀ from closed-surface flux integration of the Master PDE. Slope 4 structural; α cancels. Reference mass M× ≈ 3.15×10¹⁰ M☉. [DERIVED]
Distinctive prediction
The relationship between a galaxy's visible mass and its rotation speed follows an exact fourth-power law, with no adjustable knobs. Standard dark-matter models fit this; TCM forces it exactly.
7. Baryonic Faber-Jackson: σ⁴ = G·M_bar·g₀ for pressure-supported spheroidals.
Dispersion-supported analog of BTFR. Slope 4 exactly; α cancels. Testable against ATLAS³D / SAMI / MaNGA. [DERIVED]
Distinctive prediction
The same fourth-power mass-speed law applies to blob-shaped galaxies (ellipticals) using their internal star motions instead of rotation. A parameter-free version of a known scaling relation.
8. Geometric universality of slope-4 BTFR.
V_flat⁴ ∝ G·M·g₀ across thin disks, thick disks, barred spirals, spheroidals; slope fixed at 4. Geometry affects only the transition kernel near r_knee. [DERIVED]
Distinctive prediction
That fourth-power law holds identically across every galaxy shape — thin disks, fat disks, barred, spheroidal. Geometry doesn't change it, which is a stronger claim than standard fits make.
9. BTFR slope = 4 exactly from action.
v_char = (G·M_bar·g₀)^(1/4) gives M_bar ∝ v⁴. Predicted normalisation ~14% near V_flat = 100 km/s. [DERIVED, CONFIRMED]
Recovers known physics
Recovers the observed mass-rotation relation of galaxies (the Tully-Fisher relation) with the correct normalisation, from the fabric's constitutive law rather than from fitted dark matter.
10. Cosmic acceleration is transient, not eternal.
As n → 1 globally, elastic energy exhausts; w(z) → 0, coasting expansion not de Sitter. [DERIVED — preliminary confirmation 2025: Lee, Son & Chung MNRAS supernova analysis finds present-epoch deceleration onset; full confirmation pending Vera Rubin]
Distinctive prediction
Cosmic acceleration is temporary — it will fade as the fabric finishes relaxing, ending in coasting expansion rather than eternal speed-up. Standard dark energy accelerates forever.
11. Late-time equation of state w₀ = −1 + 8×10⁻⁴ from elastic relaxation.
w₀ = −1 + 18·(H₀/ω₀)². Current data consistent at ~10⁻² sensitivity; precision test pending Euclid/Roman. [DERIVED]
Distinctive prediction
Dark energy isn't a constant: its equation of state sits at w₀ = −1 + 8×10⁻⁴, just above −1 by eight parts in ten thousand. A specific, tiny, measurable departure from a pure cosmological constant.
12. Thawing dw/dz > 0 unconditional.
Sign fixed by H increasing with z; independent of ε or τ(ρ). [DERIVED — preliminary confirmation 2025: DESI DR2 + Pantheon+ + ACT/Planck prefer thawing-class behaviour]
Distinctive prediction
That dark-energy departure always evolves in one direction (thawing) as you look back in time — a sign fixed by the framework, not a free choice. Distinguishes TCM from a constant Λ.
13. Freeze-thaw transition at z_t = 0.55.
z_t = (ρ₀/ρ_m,0)^(1/3) − 1, ρ₀/ρ_m,0 ≈ 3.72. [DERIVED — preliminary confirmation 2025: DESI indicates dark-energy deviations from constant w at low redshift]
Distinctive prediction
There's a specific cosmic moment — redshift z_t = 0.55 — where the fabric transitions from frozen to thawing. A datable event standard cosmology doesn't feature.
14. Specific thawing functional form w(z) = −1 + 18·(H(z)/ω₀)².
Distinct from CPL / w0wa / step parametrisations. [DERIVED — precision test pending Euclid/Roman/DESI at <10⁻³ near z ≈ 0.5]
Distinctive prediction
Dark energy follows one specific formula, w(z) = −1 + 18(H/ω₀)², different in shape from every standard parametrisation. Precision surveys can tell it apart.
15. No-phantom theorem w(z) ≥ −1 unconditional.
Sign-fixed by α > 0 and ε > 0. [DERIVED, exact — preliminary confirmation 2025: DESI BAO + Pantheon+ prefer w > −1]
Distinctive prediction
Dark energy can never cross below −1 (no 'phantom' behaviour) — an absolute floor forced by the fabric having positive stiffness. Some rival models allow crossing; TCM forbids it.
16. Black holes finite everywhere.
K(n) → ∞ at n = n_H forbids infinite density. Interior is a physical medium with information in elastic strain n(x,t). [DERIVED]
Distinctive prediction
Black holes have no infinite-density centre — the fabric stiffens to a stop. Inside is a real physical medium storing information in its compression, not a singularity.
17. Finite congestion throughout any rotating saturation surface.
Fabric reaches maximum n = √e and stops; the surface absorbs all anisotropy under harmonic linearisation. [DERIVED]
Distinctive prediction
Even spinning black holes stay finite everywhere inside; the fabric maxes out and halts. Differs from the singular interior of standard rotating black holes.
18. GW echoes from saturation surface.
Echo delay Δt = 2r_s/c = 4GM/c³. M = 10 M☉ → 0.20 ms; 30 M☉ → 0.59 ms; 62 M☉ → 1.22 ms. Amplitude Γ = 0.5–1. [DERIVED]
Distinctive prediction
A black-hole merger should produce faint repeating echoes after the main signal, delayed by Δt = 4GM/c³ — 0.20 ms for 10 solar masses, 0.59 ms for 30, 1.22 ms for 62. A specific, testable deviation from clean ringdown.
19. Test-particle radial-confinement structure on the rotating saturation surface.
Static (a*=0): radially-confined trajectories for all r > r_m = 4.700 GM/c² = 2.350 r_s. [DERIVED, TCM-internal — verified by two independent stability calculations; reproduced this review from eqs 37+40 → 4.7026 GM/c²]
Distinctive prediction
Around a spinning collapsed surface there's an innermost stable orbit at r_m = 4.700 GM/c² = 2.350 times the horizon radius — against general relativity's 3.0. Directly falsifiable.
20. Saturation Brake on frame-dragging.
Frame-drag slip δ(r) < 0 uniformly for all r > r_s. [DERIVED, TCM-internal]
Distinctive prediction
The frame-dragging (twisting of space by a spinning mass) is always slightly braked compared to the standard prediction — a uniform, one-directional difference.
21. Closed-form rotating saturation-surface profile via harmonic linearisation.
n_K(r) = n_H − (n_H−1)·[(r−r_+)/(r−r_−)]^β_K. Non-linear constitutive equation reduces to □f = 0 under f = −ln[(n_H−n)/(n_H−1)]. [DERIVED]
Unique to TCM
A clean closed-form shape for the fabric around a spinning collapsed surface, obtained by a mathematical trick unique to the fabric's equation. No standard-theory analogue.
22. Saturation-surface interior screened-wave structure.
With K_sat ≫ K₀: ∇²n − μ_int²(n−n_H) = 0, μ_int² = ε/K_sat. [DERIVED, conditional on K_sat]
Distinctive prediction
Inside the collapsed surface, disturbances behave like screened waves that die off over a set distance — a specific interior structure standard black holes don't have.
23. Saturation-surface entropy area law S = A/(4ℓ_P²).
From fabric mode counting at the surface. Exact 1/4 prefactor pending explicit TCM mode-counting. [DERIVED via correspondence — prefactor pending]
Recovers known physics
Recovers the black-hole entropy area law (entropy proportional to surface area) from counting fabric vibration modes, matching the known result.
24. Saturation-surface relaxation timescale τ_BH ~ τ₀·(M/m_P)².
M² scaling from area-law mode counting. For 1 M☉: τ_BH ~ 10⁷⁷ Gyr ≫ τ₀. [DERIVED — leading M² scaling]
Distinctive prediction
A collapsed surface relaxes on a timescale growing as mass-squared, τ_BH ~ τ₀·(M/m_P)². For one solar mass this is ~10⁷⁷ Gyr — a different scaling from standard evaporation.
25. Solar System Shield 8πGα/c² = 1.523×10⁻⁴.
Structurally-fixed frame-dragging coefficient. Below LAGEOS by ~2.8 orders, below Gravity Probe B by ~3.1 orders. [DERIVED, covariant]
Unique to TCM
A fixed, tiny frame-dragging strength of 8πGα/c² = 1.523×10⁻⁴ set by the fabric constants — below LAGEOS by ~2.8 orders and Gravity Probe B by ~3.1 orders, a specific number to aim at.
26. Post-merger rotation curve ringdown at ω₀ — period 600 Myr.
Major mergers excite the fabric mode at ω₀; ε(n−1) drives oscillatory recovery of the outer rotation curve. [DERIVED — mechanism established; amplitude open]
Distinctive prediction
After a major galaxy merger, the rotation curve should 'ring' — oscillate with a 600-million-year period (the fabric frequency ω₀) as it recovers. A distinctive transient signal.
27. ISW stiffness-scale suppression at ℓ ≈ 72 in CMB-LSS cross-correlation.
Stiffness transition at z_t = 0.55 imprints suppression at ℓ_ISW = k_J × D_C(z_t) ≈ 72. [DERIVED — angular location]
Distinctive prediction
A specific suppression in the cross-correlation of the cosmic microwave background with galaxy maps, at angular scale ℓ ≈ 72, from the fabric's freeze-thaw transition at z_t = 0.55.
28. Primordial CMB feature at ℓ ≈ 476.
Elastic rebound excites ω₀ at last scattering. ℓ = k_J × D_C(z_CMB) ≈ 476, distinct from standard acoustic peaks. [DERIVED — angular location]
Distinctive prediction
A specific extra feature in the cosmic microwave background at angular scale ℓ ≈ 476, separate from the standard acoustic peaks, from the fabric's rebound at last scattering.
29. GW speed = c exactly.
Single-field action propagates one mode at c = √(K₀/α). [DERIVED, CONFIRMED]
Recovers known physics
Recovers the observed fact that gravitational waves travel at exactly the speed of light — here because both are the same fabric moving, not two separate things tuned to match.
30. Solar System tests pass exactly in the linear-stiffness regime.
K = K₀ for a ≫ g₀. Mercury 42.98″/century, Cassini residuals at 2×10⁻⁵. [DERIVED, CONFIRMED]
Recovers known physics
Recovers all the classic Solar-System gravity tests exactly — Mercury's orbit shift, the Cassini probe timing — in the regime where the fabric behaves stiffly and normally.
31. Black hole shadows match linear-stiffness regime signature.
Shadow imaging within 10⁻⁴ fractional of the linear-stiffness value, ~300–2000× below current precision. [DERIVED, CONFIRMED]
Recovers known physics
Recovers the observed sizes of black-hole shadows (as imaged by the Event Horizon Telescope) to well within current precision.
32. GW memory amplitude τ-dependent.
Residual strain ∝ local τ. Larger in voids, smaller in clusters. [DERIVED — sign structural]
Distinctive prediction
The permanent spacetime shift left after a gravitational wave passes depends on the local fabric relaxation time — larger in cosmic voids, smaller in clusters. An environmental dependence.
33. Fabric Frequency ω₀ = 3.32×10⁻¹⁶ rad/s.
ω₀ = √(ε/α), period ≈ 600 Myr. [DERIVED]
Unique to TCM
The fabric has its own natural vibration frequency, ω₀ = √(ε/α) = 3.32×10⁻¹⁶ per second — a 600-million-year period. A fundamental clock rate with no standard counterpart.
34. Graviton effective mass m_g = 2.18×10⁻³¹ eV/c².
m_g = ℏω₀/c² from the mass-gap term ε(n−1). [DERIVED — TCM-internal cross-check open]
Distinctive prediction
Gravity's carrier behaves as if it has a minuscule mass, m_g = ℏω₀/c² = 2.18×10⁻³¹ eV. Most gravity theories assume exactly zero; TCM gives a specific tiny value.
35. Linear-stiffness saturation acceleration a_sat ≈ 539·g₀ ≈ 6.45×10⁻⁸ m/s² near SMBHs.
Within ~3.0 pc of SMBHs the fabric enters K(X)-saturation. Observable via VLBI tracking of S-stars near Sgr A*. [DERIVED]
Distinctive prediction
Very close to supermassive black holes (within ~3.0 pc), the fabric enters its special regime and produces a specific acceleration scale, a_sat ≈ 539·g₀ ≈ 6.45×10⁻⁸ m/s² — trackable by watching stars orbit the galactic centre.
36. Knee radius r_knee = √(GM_baryon/g₀) exactly.
Linear-stiffness to K(X) transition radius. Zero free parameters. [DERIVED]
Unique to TCM
Each galaxy has a precise 'knee' radius where gravity switches from normal to the fabric's 1/r regime, set with no free parameters. A structural feature unique to the model.
37. Cosmological-scale K(X) crossover wavenumber k_×^cosmo.
Same constitutive law suppresses late-universe clustering at k > k_×^cosmo where perturbation acceleration crosses g₀. [DERIVED — structural; numerical integration open]
Distinctive prediction
The same fabric law that flattens rotation curves also suppresses clustering in the late universe above a certain scale — a specific cosmological signature.
38. No extra galactic substructure beyond the baryonic catalogue.
Derrick scaling forbids static topological matter; the only matter sector is the closed-ring catalogue. Substructure follows from baryonic distribution. [DERIVED]
Distinctive prediction
There is no invisible substructure beyond the visible matter — the framework forbids extra static matter, so all structure traces the ordinary catalogue of particles. Opposite to dark-matter substructure.
39. Filament lensing follows 1/r Ward attractor.
Filaments are baryonic; outside r_knee gravity follows the attractor. [DERIVED — qualitative]
Distinctive prediction
Lensing by cosmic filaments follows the fabric's 1/r law in their outskirts, not the standard profile.
40. Cluster lensing follows 1/r at r > r_knee.
Beyond the cluster knee, lensing tracks the attractor not the inner profile. [DERIVED]
Distinctive prediction
Cluster lensing in the outer regions follows the fabric's 1/r attractor rather than the inner mass profile.
41. Tidal streams follow 1/r Ward attractor.
Stream orbits at r > r_knee follow the 1/r attractor. [DERIVED]
Distinctive prediction
Stellar streams orbiting a galaxy trace the fabric's 1/r law in the outer regions.
42. Void lensing scales with n ≈ 1.
Voids: fabric near resting state, lensing structurally weak. [DERIVED — qualitative]
Distinctive prediction
Cosmic voids, where the fabric sits near its resting state, lens light very weakly — a specific expectation from the fabric being nearly undisturbed there.
43. Void galaxies sit above the BTFR.
Softer void fabric → stronger self-sourcing per unit baryonic mass. [DERIVED — depends on τ(ρ)]
Distinctive prediction
Galaxies in voids sit slightly above the standard mass-speed relation because the softer void fabric responds more strongly per unit mass.
44. Bounded fabric rest-state energy density.
ρ_rest ≤ ½ε·(n_H−1)² ≈ 1.89×10⁻¹⁰ J·m⁻³. Saturation forbids unbounded contributions. [DERIVED]
Unique to TCM
There's a hard ceiling on the fabric's resting energy density, ½ε(n_H−1)² ≈ 1.89×10⁻¹⁰ J/m³, set by the stretch limit. No standard analogue to this cap.
45. G_eff(k) = G·[1 + (4πGα/c²)·(n₀−1)/(1+(k/k_J)²)] sub-stiffness-scale.
Deviation 1.5×10⁻⁹ — below Solar-System bounds, possibly within next-gen precision cosmology. [DERIVED]
Distinctive prediction
Gravity's effective strength varies very slightly with scale — a deviation of 1.5×10⁻⁹ — potentially within reach of next-generation precision cosmology.
46. G consistency from fabric moduli to 0.04%.
G_TCM = c⁴/(2πλ·v_∞²) = 6.674×10⁻¹¹ to 0.04%. With λ anchored from v_∞, a self-consistency check. [DERIVED — self-consistency]
Recovers known physics
Recovers Newton's gravitational constant from the fabric moduli, G_TCM = c⁴/(2πλv_∞²) = 6.674×10⁻¹¹, to 0.04% — a self-consistency check of the framework.
47. ρ₀ from galaxies matches z_t.
Same ρ₀ governing galactic rotation sets z_t = 0.55. Cross-scale consistency. [DERIVED]
Distinctive prediction
The same fabric density that governs galaxy rotation also fixes the cosmic freeze-thaw redshift of 0.55 — one quantity tying two very different scales together.
48. Smooth rotation-curve knee.
K(X) changes continuously through r_knee; no sharp kink. [DERIVED]
Distinctive prediction
The transition at a galaxy's knee radius is smooth, not a sudden kink — a specific, checkable shape standard models don't require.
49. HSB galaxies Newtonian to larger radii.
Higher surface density keeps fabric stiff further out. [DERIVED]
Distinctive prediction
Denser (high-surface-brightness) galaxies stay in the normal-gravity regime out to larger radii — a specific trend tied to surface density.
50. BTFR scatter is baryonic only.
No environmental or merger-history dependence; scatter correlates only with baryonic M/L and finite-r convergence. [DERIVED]
Distinctive prediction
Scatter in the mass-speed relation comes only from the visible matter, with no dependence on environment or merger history — a stronger claim than standard fits.
51. BTFR slope as universal g₀ measurement.
Deviations from slope 4 constrain g₀ or systematic M/L shifts. [DERIVED — methodological]
Distinctive prediction
Deviations from the exact fourth-power law can be used to measure the fabric's baseline acceleration g₀ directly — turning the relation into a measuring tool.
52. No halo assembly delay in early-galaxy population.
No extra structure-formation timescale; high-z bright galaxies form as soon as baryons condense. [DERIVED — qualitative]
Distinctive prediction
Bright galaxies can appear very early in cosmic history, because there's no extra delay waiting for invisible halos to assemble. Differs from standard structure-formation timing.
53. Finite maximum redshift z_max.
K(n) → ∞ as n → n_H forbids infinite density; a finite z_max exists structurally. [DERIVED — existence; value open]
Distinctive prediction
There's a hard maximum redshift beyond which nothing can be seen, because the fabric can't compress past its limit. A finite edge standard cosmology doesn't impose this way.
54. CMB high-ℓ damping has TCM signature.
Viscoelastic damping modifies the tail via Rayleigh dissipation. [CONJECTURED — pending]
Distinctive prediction
The fine detail at the smallest angular scales of the cosmic microwave background carries a fabric-viscosity fingerprint from internal damping.
55. BAO scale modified near z_t.
K(ρ) modifies effective sound speed near ρ₀, shifting BAO near freeze-thaw. [CONJECTURED — magnitude pending]
Distinctive prediction
The cosmic 'sound horizon' scale (used as a cosmic ruler) shifts slightly near the freeze-thaw redshift, because the fabric changes the effective sound speed there.
56. Constant GW speed, environment-dependent amplitude.
v_gw = c everywhere; amplitude carries weak environmental damping via τ(ρ). [DERIVED]
Recovers known physics
Recovers that gravitational waves travel at light speed everywhere, while adding that their strength carries a faint environmental damping from the fabric.
57. Mild GW attenuation in voids.
(α/τ)·∂ₜn produces slight attenuation in long-τ regions. [CONJECTURED — depends on τ(ρ)]
Distinctive prediction
Gravitational waves are attenuated very slightly in cosmic voids, where the fabric's long relaxation time lets it sap a little energy.
58. GW amplitude attenuation in dense regions.
(α/τ)·∂ₜn implies additional attenuation at high density. [CONJECTURED — depends on τ(ρ)]
Distinctive prediction
Gravitational waves are attenuated slightly in dense regions too, from the same fabric-damping term — a specific environmental effect.
59. Viscosity correction to binary orbital decay.
Decay rate carries correction ∝ 1/τ(ρ) from Rayleigh dissipation. [CONJECTURED — conditional on τ(ρ)]
Distinctive prediction
Binary orbits decay with a tiny extra correction from fabric viscosity, on top of the standard gravitational-wave energy loss.
60. Cluster merger offsets scale with collision velocity.
Δx ≈ v_collision × τ_cluster; a fabric-relaxation effect. [CONFIRMED — see companion Bullet Cluster paper, DOI 10.5281/zenodo.20410639, five-cluster validation]
Distinctive prediction
When galaxy clusters collide, the offset between visible gas and the lensing mass scales with collision speed times the fabric relaxation time — a specific prediction confirmed across five clusters.
61. Galaxy bar slowdown rate set by Rayleigh dissipation.
Bars slow at the rate set by the (α/τ)·∂ₜn term. [CONJECTURED]
Distinctive prediction
Galactic bars slow their spin at a rate set by the fabric's internal friction — a specific, measurable braking mechanism.
62. Outer halo stellar orbits more circular.
Rayleigh dissipation circularises eccentric orbits over Hubble time. [CONJECTURED]
Distinctive prediction
Stars in the outer halo have their orbits gradually rounded out by fabric friction over cosmic time — a subtle circularising trend.
63. Transition-zone width correlates with surface density.
Compact galaxies narrow transition; diffuse galaxies broad. [DERIVED — qualitative]
Distinctive prediction
The width of the transition zone at a galaxy's knee depends on how compact the galaxy is — narrow for dense, broad for diffuse.
64. Isolated dwarfs σ-hotter than hosted dwarfs.
Longer environmental τ for isolated systems. [CONJECTURED — depends on environmental τ]
Distinctive prediction
Isolated dwarf galaxies run internally 'hotter' (faster random star motions) than dwarfs near big galaxies, because their fabric relaxation time is longer.
65. Local H₀ measurements addressable through environmental τ.
H₀^void > H₀^filament: longer τ in voids → locally higher H₀. [DERIVED — mechanism; quantitative resolution open]
Distinctive prediction
The disagreement over the universe's expansion rate (the Hubble tension) can be addressed through the fabric: voids give a locally higher rate than filaments. A specific mechanism for a real puzzle.
66. Fabric horizon scale ~ Hubble radius.
λ_fabric = c·τ₀ ≈ 2590 Mpc ≈ 0.6·c/H₀. [DERIVED]
Unique to TCM
The fabric has a natural horizon scale λ_fabric = c·τ₀ ≈ 2590 Mpc — roughly the observable universe's size, about 0.6·c/H₀ — emerging from its own relaxation time. No standard counterpart.
67. Inertial mass slightly anisotropic.
Galactic congestion gradient creates a preferred direction; inertia differs at ~10⁻⁸. [CONJECTURED — magnitude]
Distinctive prediction
Inertia is very slightly direction-dependent, at the ~10⁻⁸ level, because the galaxy's fabric gradient sets a preferred direction. A tiny measurable anisotropy.
68. No gravitational repulsion.
n = exp(−Φ/c²) monotonic in Φ; gravity attractive everywhere. [DERIVED]
Recovers known physics
Recovers that gravity is always attractive — never repulsive — because the fabric's compression response is one-directional.
69. No superluminal propagation in any sector.
c = √(K₀/α) sets the universal limit; both regimes propagate at most at c. [DERIVED]
Recovers known physics
Recovers the universal speed limit: nothing, in any sector of the theory, travels faster than light, because that speed is set by the fabric's stiffness and inertia.
70. Galactic K(X) fabric self-scattering σ_KX ~ (αc⁴/g₀)²·k⁴.
Direct fabric self-interaction in K(X), observable on galactic scales independent of matter-coupling closure. [DERIVED]
Unique to TCM
The fabric can scatter off itself directly on galactic scales, with a specific strength — a self-interaction with no standard-physics counterpart.
71. m_p/m_e = 16·115 = 1840 (clean integer).
Proton (16,1,1), electron (1,1,115). Ratio purely integer, m_pol cancels. Observed 1836.15 — 0.21%. [DERIVED]
Unique to TCM
The proton is exactly 16×115 = 1840 times heavier than the electron — a clean whole-number ratio from their lattice positions (proton (16,1,1), electron (1,1,115)). Observed 1836.15, within 0.21%. No standard theory predicts integer mass ratios.
72. m_τ/m_e = 30·115 = 3450 (clean integer).
Tau (30,1,1), electron (1,1,115). Observed 3477.23 — 0.78%. [DERIVED]
Unique to TCM
The tau lepton is exactly 30×115 = 3450 times the electron mass — another clean integer ratio (tau (30,1,1), electron (1,1,115)). Observed 3477.23, within 0.78%. Unique to the catalogue structure.
73. Catalogue mass formula on a 3D integer lattice (m_tor, m_pol, n_radial).
M = m_tor·F(m_pol)·M(1,1)/[n_radial·F(1)], M(1,1) = 58.55 MeV/c². Three integers from H₁(T²) = ℤ×ℤ plus radial quantisation. [DERIVED]
Unique to TCM
Every particle's mass comes from one formula, M = m_tor·F(m_pol)·M(1,1)/[n_radial·F(1)] with floor M(1,1) = 58.55 MeV, on a 3D grid of whole numbers. Masses aren't free inputs but lattice positions. Nothing standard works this way.
74. TCM soliton lifetime floor τ ≥ ℏ/[2(Mc²−ℏω₀)] universally respected.
τ ≥ ℏ/(2Mc²) for any catalogue point. Tested π⁰ to neutron — margin 21× to 10²⁷×. [DERIVED, CONFIRMED]
Distinctive prediction
Every particle has a minimum possible lifetime set by its mass — a floor no particle can undercut. Confirmed from the neutral pion to the neutron. A structural bound standard physics doesn't state.
75. Integer charges from m_tor topology.
Single-valuedness of the toroidal phase forces m_tor ∈ ℤ. No separate confinement mechanism. [DERIVED]
Unique to TCM
Electric charge comes out as whole numbers automatically, from how the particle's loop winds around itself. No separate rule needed. Charge quantisation is built in.
76. Spin-½ from framing self-linking SL = ±½.
Closed rings carry an automatic framing; canonical quantisation gives half-integer ℏ. Spin-½ structural, not postulated. [DERIVED]
Unique to TCM
A particle's spin of one-half arises automatically from the twisting of its closed loop — spin isn't assumed, it's a geometric consequence. Distinctive origin for a known quantity.
77. Pauli exclusion from spin-statistics.
Lorentz invariance + microcausality + positive-energy spin-statistics gives anti-symmetrisation. [DERIVED]
Recovers known physics
Recovers the Pauli exclusion principle (why matter particles can't overlap) from the standard spin-statistics connection applied to the fabric loops.
78. Born rule from coupling.
Fermi's Golden Rule on fabric mode + detector coupled by 4πG̃·ρ_d·(n−1) gives Γ_d ∝ |ψ_mode(x_d)|². [DERIVED]
Recovers known physics
Recovers the Born rule — the recipe for turning quantum amplitudes into probabilities — from how a fabric wave couples to a detector. A derivation of a normally-postulated rule.
79. Bell singlet correlation E(θ_A,θ_B) = −cos(θ_A−θ_B).
From SU(2) framing-rotation + Born rule on two entangled framings. CHSH ≤ 2√2. Non-local realist. [DERIVED, CONFIRMED]
Recovers known physics
Recovers the exact quantum correlations of entangled particles (the −cos θ law behind Bell tests), from the fabric's loop-orientation coupling. Reproduces confirmed quantum results.
80. Heisenberg uncertainty Δx·Δp ≥ ℏ/2.
Direct from canonical commutator [φ̂,π̂] = iℏδ³. [DERIVED]
Recovers known physics
Recovers Heisenberg's uncertainty principle directly from the fabric's basic commutation relation. A known result from the framework's own structure.
81. CPT.
Lorentz invariance + microcausality + positive-definite energy give Lüders-Pauli. [DERIVED]
Recovers known physics
Recovers CPT symmetry (the deep matter-antimatter/space/time mirror symmetry) from the framework's core properties.
82. Phase-sign reversal as the structural origin of anti-soliton states.
Φ_matter admits (ω,m_pol,m_tor) → (−ω,−m_pol,−m_tor) at the same n_radial. [DERIVED]
Unique to TCM
Antiparticles are the same fabric loop with its phase run backwards — a specific structural origin for antimatter. Distinctive to the model.
83. α_J channel J → −J symmetry across eight precision tests at parts-per-billion.
α_J·J^μJ_μ quadratic in J → symmetric under J → −J. Sign-paired solitons: identical mass, opposite charge, opposite moments, equal lifetimes, equal gravity. [DERIVED, CONFIRMED at listed precisions]
Distinctive prediction
Matter and antimatter match in mass, lifetime, and gravity to extreme precision, because the coupling is symmetric under phase reversal — confirmed across eight precision tests.
84. Parity violation from framing self-linking chirality.
Framing orientation inherited from SL = ±½; chiral couplings distinguish handedness. Topological. [DERIVED]
Unique to TCM
The universe's handedness (why nature distinguishes left from right in some interactions) comes from the chirality of the loop's twist. A topological origin.
85. α_W channel parity-violating asymmetry under phase-sign reversal in narrow weak channels.
Framing current ∂γ flips; the parity-violating ∂γ·∂γ vertex gives asymmetric response between sign-paired solitons. [DERIVED]
Distinctive prediction
In certain narrow interaction channels, matter and antimatter show a specific mirror-asymmetry from the parity-violating coupling — a structural, testable difference.
86. Fabric radiative mode mass scale ω₀·ℏ/c² ≈ 2.2×10⁻³¹ eV/c².
Dispersion floor ω₀ = 3.32×10⁻¹⁶ rad/s. ~30 orders below tritium β-decay endpoint bound. [DERIVED, CONFIRMED]
Recovers known physics
Recovers the extremely tight experimental bound on any mass for the fabric's radiative mode — floor ω₀ = 3.32×10⁻¹⁶ rad/s, giving ~2.2×10⁻³¹ eV/c², about 30 orders below the tritium β-decay endpoint bound.
87. Three correlation classes from three lepton-soliton framing topologies.
The three 'flavors' are three lepton catalogue points: e (1,1,115), μ (9,1,5), τ-equivalent. [DERIVED]
Unique to TCM
The three 'families' of leptons (electron, muon, tau types) are just three positions on the fabric loop catalogue — not a mystery, but three catalogue entries. Distinctive framing.
88. Distance-dependent correlation change as α_W vertex phase evolution.
A mode emitted at a transition vertex carries non-orthogonal overlap with all three lepton framing classes. [DERIVED]
Distinctive prediction
How particle-identity correlations change with distance comes from the phase evolving along the fabric mode — a specific structural account of a measured effect.
89. n−p mass splitting +1.29 MeV with correct sign.
J·J self-energy +0.86 MeV plus K(X) internal-structure +2.15 MeV nets +1.29 MeV. Matches at leading order. [DERIVED structurally]
Distinctive prediction
The neutron is heavier than the proton by exactly +1.29 MeV with the correct sign — the J·J self-energy (+0.86 MeV) plus internal K(X) structure (+2.15 MeV) netting +1.29 MeV. A specific number matched at leading order.
90. Proton/neutron magnetic moment ratio framework.
m_tor = 16 partition (4,4,8) derived; Picture B forced by prime-knot topology; sign of μ_p/μ_n negative. [DERIVED — partition/Picture B/sign; precise value pending]
Distinctive prediction
The proton and neutron magnetic-moment ratio comes out with the right structure and sign from the loop's internal partition — a specific, checkable framework result.
91. Pion lifetimes order-of-magnitude framework.
τ(π⁰) ≈ 3.4×10⁻¹⁷ s vs 8.4×10⁻¹⁷ (×2.5); τ(π±) ≈ 5×10⁻⁸ vs 2.6×10⁻⁸ (×1.9). Within 2–3×. [CONJECTURED]
Distinctive prediction
Pion lifetimes come out to the right order of magnitude (within 2–3×) from the fabric decay mechanism — a structural estimate.
92. Electron at canonical catalogue point (1,1,115) with no ad-hoc factor.
A_★ continuous + n_radial = 115 quantisation. 1/115 = m_e/M(1,1) from the radial spectrum. [DERIVED]
Unique to TCM
The electron sits at the specific catalogue point (1,1,115) with no fudge factor — its 1/115 mass ratio to the floor drops out of the loop's radial quantisation. Unique lattice result.
93. F(m_pol) cross-section solution.
F(1)=0.90, F(2)=2.327, F(3)=4.551, F(4)=7.884, F(5)=12.55, from the constitutive cross-section EL equation by relaxation. (m_pol^(π/2) is a large-m_pol asymptote only, not valid at these integers; solver values are primary.) [DERIVED]
Unique to TCM
A specific set of scaling factors F(1) through F(5), computed by solving the fabric's cross-section equation numerically. These shape the particle masses and have no standard analogue.
94. Self-limited amplitude A_★_n = A_max·n_radial^(−1/3).
Canonical quantisation of A_★ on [0,A_max] gives discrete eigenvalues; n_radial structural. [DERIVED]
Unique to TCM
A particle's loop amplitude self-limits in a specific way as its radial number grows — a structural feature of the fabric quantisation.
95. Soliton decay rate framework Γ ~ α_J·m_tor²·ΔE³/(ℏ·M²·c⁴).
Phase-current coupling gives the leading decay channel; structural form derived. [DERIVED conditional on closure]
Distinctive prediction
Particle decay rates follow a specific formula from the phase-current coupling — a structural prediction for how fast unstable particles decay.
96. W and Z phenomenology = catalogue points (156,4,1) ≈ 80 GeV and (178,4,1) ≈ 91 GeV.
High-(m_tor,m_pol) catalogue points excited via the α_W framing-current vertex. [DERIVED]
Distinctive prediction
The W and Z particles are specific high catalogue points, (156,4,1) ≈ 80 GeV and (178,4,1) ≈ 91 GeV, excited via the framing-current vertex. A structural identification of known particles.
97. Photon-equivalent identified as fabric radiative-mode component carrying J^μ correlations.
The 'photon' is the radiative-mode component of n carrying J^μ correlations between source and detector. [DERIVED]
Unique to TCM
What we call the photon is the radiative-mode component of the fabric carrying correlations between source and detector — not a separate entity. A distinctive re-identification.
98. Conventional gluon-mediated dynamics = framing-current ∂γ·∂γ on multi-soliton configurations.
Multi-nucleon dynamics correspond to the framing-current coupling on multi-soliton bound configurations. [DERIVED]
Unique to TCM
The strong-force gluon dynamics correspond to the fabric's framing-current coupling on multi-loop configurations — a structural re-identification with no separate field.
99. Pair production threshold = 2Mc² exactly with two-quantum back-to-back final state.
A mode with energy ≥ 2Mc² produces a pair at sign-paired lattice points (net J^μ = 0, net charge = 0). [DERIVED]
Recovers known physics
Recovers the pair-production threshold (energy needed to create a particle-antiparticle pair, exactly twice the rest energy) with the correct back-to-back final state.
100. Left-handed helicity dominance from α_W ∂γ·∂γ parity violation.
The parity-violating α_W vertex gives an emitted mode a parity-asymmetric helicity correlation. [DERIVED]
Distinctive prediction
Emitted radiation from weak processes carries a specific left-handed helicity preference, from the parity-violating fabric coupling. A structural asymmetry.
101. Cross-section ~10⁻⁴⁴ cm² at MeV energies from α_W² × small overlap.
σ ~ α_W²×|⟨γ_target|Φ_mode|γ_source⟩|²×overlap, α_W ≈ 0.42. [DERIVED]
Distinctive prediction
Weak-interaction cross-sections come out around 10⁻⁴⁴ cm² at MeV energies from the framing-current coupling strength α_W ≈ 0.42 — a specific structural magnitude.
102. Negligible cosmological mass-density contribution from fabric radiative modes.
m ≈ 2.2×10⁻³¹ eV/c², n ~336/cm³ → ~10⁻³⁰ eV/cm³, far below bounds. [DERIVED]
Recovers known physics
Recovers that the fabric's radiative modes contribute negligibly to the cosmic energy budget, consistent with observational bounds.
103. Casimir force has fabric signature.
½K|∇n|² gives a sub-100 nm correction, dominant at small separations. [CONJECTURED — coefficient pending]
Distinctive prediction
The Casimir force (attraction between close plates) gets a specific fabric correction that dominates below 100 nanometres — a testable deviation.
104. Casimir resonance at ω₀ wavelength.
½ε(n−1)² implies a resonance at the fabric-mode separation. [CONJECTURED]
Distinctive prediction
There should be a Casimir-type resonance at the fabric mode's wavelength — a specific extra feature.
105. K(X) breakdown of superposition at extreme gradients.
Hydrogen-like levels deviate near saturation surfaces by ∝ (|∇n|/(g₀/c²))². No analogue in linear QM. [DERIVED]
Distinctive prediction
Quantum superposition breaks down in a specific way near collapsed surfaces, where fabric gradients are extreme — an effect with no analogue in ordinary quantum mechanics.
106. No extra fabric mode channels beyond the single linearised n-perturbation.
One field, one mode at c with mass-gap ω₀. No additional propagating sectors. [DERIVED]
Distinctive prediction
There are no hidden extra force-carrier channels beyond the single fabric mode — one field, one propagating disturbance. A constraint standard physics doesn't share.
107. Marginal coupling and structural finiteness.
Matter-fabric coupling finite by saturation; no separate UV regulator beyond K(X) crossover. [DERIVED]
Unique to TCM
The matter-fabric coupling is automatically finite — the fabric's stiffening acts as a built-in regulator, so no separate infinity-removal is needed. Distinctive structural finiteness.
108. Next-order coupling bound |ξ₂| < 2.3×10⁻⁴.
Solar-System timing bound on next-order matter-fabric coupling. [DERIVED]
Distinctive prediction
A specific bound (below 2.3×10⁻⁴) on the next-order matter-fabric coupling, from Solar-System timing data.
109. α_J·(m_P/m_e)² ≈ 4.2×10⁴² at electron mass — matter-coupling hierarchy.
39-order gravity/atomic-binding gap reduces to α_J ≈ 1/137. (m_P/m_e)² to 0.8%. [DERIVED conditional on α_J calibration]
Distinctive prediction
The 39-order-of-magnitude gap between gravity and atomic binding reduces to the single number α_J ≈ 1/137: α_J·(m_P/m_e)² ≈ 4.2×10⁴², with (m_P/m_e)² matched to 0.8%. A specific structural relationship.
110. Phase-current 1/r potential U_{J·J}(r) = α_J·m_tor·m_tor'·ℏc/r.
Integer charges from m_tor topology; mediator is the fabric n, no separate field. [DERIVED]
Distinctive prediction
The force between charged particles is a 1/r potential, U = α_J·m_tor·m_tor'·ℏc/r, carried by the fabric with integer charges — recovering the Coulomb form but from the fabric, screened at 1/κ ≈ 9×10²³ m.
111. Framing-current coupling with parity violation.
α_W·(∂_μγ)·(∂^μγ)·n contact coupling. Chirality from framing self-linking; left-right asymmetry topological. [DERIVED]
Unique to TCM
The weak force's parity-violating coupling is a specific fabric contact term with chirality from the loop twist — a distinctive structural origin.
112. Catalogue selection rules under J·J closure: Δm_tor = 0.
Charge conservation from topology; allowed transitions preserve toroidal winding. [DERIVED conditional on closure]
Distinctive prediction
Allowed particle transitions must conserve the toroidal winding number — a specific selection rule from topology.
113. Particle masses are self-energies of closed-ring solitons.
The 125 GeV scalar is a high-(m_tor,m_pol,n_radial) catalogue point; formula at m_pol = 4 requires m_tor·F(m_pol) ≈ 1370 for ≈ 125 GeV. [DERIVED — specific lattice point pending]
Distinctive prediction
The 125 GeV Higgs-like particle is a specific high-number catalogue point — a structural identification (exact lattice slot still being pinned down).
114. Cosmic asymmetry of soliton populations is an initial-condition observation.
Relative populations at sign-paired points and the ~10⁹:1 mode-to-soliton density ratio are calibrated, not derived. [Stated as input]
Distinctive prediction
The cosmic imbalance of matter over antimatter is treated as an initial condition to be observed, not derived — stated honestly as an input, not a prediction.
115. α_W-only carriers identified as fabric radiative modes, not solitons.
Carriers of missing energy in nuclear transitions are the existing fabric radiative modes â†(k)|0⟩ with energy ℏω(k). [DERIVED]
Unique to TCM
The carriers of 'missing energy' in nuclear decays are the fabric's own radiative modes — not a separate neutrino field, but existing fabric quanta. A distinctive re-identification.
116. Conserved current + integer charges as a global U(1) structural ingredient.
Available for promotion to gauged coupling; the source structure of the matter sector. [DERIVED]
Distinctive prediction
The framework carries a conserved current with integer charges — the structural ingredient a gauge coupling would be built from.
117. Multi-soliton bound configurations require no new structural input.
N closed rings bind via existing channels: α_J, α_W, Pauli, canonical quantisation. [DERIVED]
Distinctive prediction
Multi-particle bound systems (nuclei, atoms) need no new ingredients — they bind through the channels already in the theory. A structural economy claim.
118. Element-specific atomic spectra from multi-body Master PDE solutions.
Each (Z protons, N neutrons, Z electrons) has a unique discrete spectrum from canonical quantisation. [Structure]
Distinctive prediction
Each atom's unique light spectrum comes from solving the fabric equation for its specific proton/neutron/electron loops — a structural account of atomic spectra.
119. Aston curve binding-energy peak ~7.6 MeV at iron-56.
Multi-nucleon α_W binding follows the Aston curve; peak near mass-56 before α_J inter-proton repulsion (∝ Z²) dominates. [Structure]
Distinctive prediction
Nuclear binding energy peaks near iron-56, following the Aston curve, from the balance of framing-current binding against charge repulsion. A structural reproduction of a known curve.
120. Magic numbers (2,8,20,28,50,82,126) from Pauli occupancy of nucleon framing shells.
Pauli on nucleon framing quantum numbers gives closed shells. [STRUCTURE DERIVED — magic numbers open]
Distinctive prediction
The nuclear 'magic numbers' (2,8,20,28,50,82,126 — extra-stable configurations) come from Pauli filling of nucleon shells in the fabric. Structure derived; exact numbers a work in progress.
121. Ionization energy shell pattern from 2(2ℓ+1) Pauli occupancy.
Pauli on electron solitons in α_J-bound states gives 2(2ℓ+1) per shell. [STRUCTURE DERIVED — specific energies open]
Distinctive prediction
The pattern of atomic ionisation energies (the 2(2ℓ+1) shell filling) comes from Pauli occupancy of electron loops in fabric-bound states.
122. Chemical stoichiometry from outer-electron-soliton overlap integrals.
Molecules are local minima of multi-soliton α_J binding; overlap integrals set stable configurations. [Structure]
Distinctive prediction
Which molecules form and their proportions come from overlap of outer-electron loops — a structural basis for chemistry.
123. Crystal lattice geometries from extended-array α_J + α_W minimisation.
Solids minimise total α_J + α_W binding; geometry reflects inter-atomic α_J directionality. [STRUCTURE DERIVED — specific lattices open]
Distinctive prediction
Crystal structures arise from minimising the total fabric binding across atomic arrays — a structural origin for solid-state geometry.
124. Periodic chemical behavior from identical outer-shell occupancy.
Identical outer-shell occupancy → identical α_J inter-atomic coupling; periodic-table columns reflect this. [DERIVED]
Distinctive prediction
The periodic table's repeating chemistry comes from identical outer-shell occupancy giving identical inter-atomic coupling — a structural account.
125. Spectral line splitting in external fields (Zeeman, Stark) at leading order.
External α_J fields / α_W gradients shift bound-soliton levels via the same vertices. [DERIVED at leading order]
Recovers known physics
Recovers the splitting of spectral lines in magnetic and electric fields (Zeeman and Stark effects) at leading order, from the same fabric couplings.
126. Path integral Z = ∫Dn·exp(iS_TCM/ℏ) canonically equivalent to Heisenberg/Schrödinger.
Schrödinger / Heisenberg / Feynman triple from canonical quantisation of the fabric. [DERIVED]
Recovers known physics
Recovers the equivalence of the three great formulations of quantum mechanics (Schrödinger, Heisenberg, Feynman) from quantising the fabric — a known result reproduced.
127. Classical correspondence: ℏ → 0 recovers the classical Master PDE.
Stationary phase of the path integral; Ehrenfest and WKB follow. [DERIVED]
Recovers known physics
Recovers classical physics in the limit where Planck's constant goes to zero — the fabric's master equation re-emerges. Standard correspondence, from the framework.
128. Universal mass-coupling 4πG̃·ρ·(n−1) recovers the Newtonian limit at all sub-cosmological scales.
Produces an inter-matter potential e^(−κr)/r with 1/κ = ξ_J ≈ 9×10²³ m. [DERIVED]
Recovers known physics
Recovers Newton's gravity at all sub-cosmological scales from the universal mass-fabric coupling 4πG̃·ρ(n−1), giving a screened potential e^(−κr)/r with cutoff 1/κ ≈ 9×10²³ m.
129. QHO Fourier mode structure for fabric.
Each linear mode is a quantum harmonic oscillator; coherent states are classical waves; thermal states give Bose-Einstein occupation. [DERIVED]
Recovers known physics
Recovers the standard quantum-harmonic-oscillator structure of field modes, giving classical waves as coherent states and thermal radiation as mode occupation.
130. Quantum Zeno effect from Fermi-rule coupling.
High-rate detector coupling freezes a fabric mode in a measurement eigenstate. [DERIVED]
Recovers known physics
Recovers the quantum Zeno effect (a watched quantum state freezes) from the fabric-detector coupling. A known effect from the framework.
131. Aharonov-Bohm analog from fabric phase.
Phase-winding topology produces A-B-like effects; gated by phase-current closure. [DERIVED conditional on closure]
Distinctive prediction
Recovers Aharonov-Bohm-type effects from the fabric's phase-winding topology — gated by the phase-current structure.
132. Berry/geometric phase γ = ∮⟨ψ|i∂_λ|ψ⟩dλ.
From canonical quantisation + collective coordinates. [DERIVED]
Recovers known physics
Recovers the geometric (Berry) phase that a quantum state picks up under slow cyclic change, from the framework's collective coordinates.
133. Unitary time evolution U(t) = exp(−iĤt/ℏ).
Hamiltonian real and positive-definite; U(t) unitary by construction. [DERIVED]
Recovers known physics
Recovers unitary time evolution (probability-preserving quantum dynamics) because the framework's energy is real and bounded below.
134. Angular momentum SU(2) algebra [Ĵ_i,Ĵ_j] = iℏε_ijk Ĵ_k.
Canonical quantisation of framing rotation as SO(3). Eigenstates |j,m⟩, j ∈ {0,½,1,…}. [DERIVED]
Recovers known physics
Recovers the full angular-momentum algebra and its allowed spin values from quantising the loop's framing rotation.
135. Density-matrix formalism for mixed fabric states.
ρ̂ = Σ p_i|ψ_i⟩⟨ψ_i| with Bose-Einstein occupation and reduced-density-matrix structure. [DERIVED]
Recovers known physics
Recovers the density-matrix description of mixed and open quantum systems, with the correct thermal occupation, from the fabric modes.
136. Adiabatic theorem and TCM lifetime floor.
Slowly-varying Hamiltonians evolve adiabatically; ΔE·τ_MT ≥ ℏ/2 from the commutator and bounded H. [DERIVED]
Recovers known physics
Recovers the adiabatic theorem (slowly-changing systems stay in their state) alongside the framework's own lifetime floor.
137. Decoherence from fabric-mode propagation.
Environmental dispersal via fabric-mode propagation; ~10³⁹× gravity at lab scales, self-consistent with atomic binding. [DERIVED conditional on closure]
Distinctive prediction
Recovers quantum decoherence (why big systems look classical) from fabric-mode dispersal — with a specific strength ~10³⁹ times gravity at laboratory scales, self-consistent with atomic binding.
138. Scattering-matrix structure with three TCM sectors.
Fabric self-scattering (K(X)); fabric-on-matter (gravitational); matter-matter via fabric exchange. [DERIVED]
Distinctive prediction
The full scattering theory splits cleanly into three fabric sectors — self-scattering, gravity, and matter-matter exchange. A structural organisation.
139. No static topological matter — Derrick scaling.
Derrick's theorem forbids static spherical solitons; matter must be dynamical (closed-ring ansatz). [DERIVED]
Unique to TCM
Matter must be dynamic loops, not static blobs — a mathematical theorem (Derrick's) forbids static stable matter in the single field. This forces the whole closed-ring picture. Distinctive foundation.
140. Particle sizes from closed-ring topology.
For n_radial = 1: R = m_tor·ℏ/(Mc), a = m_pol·ℏ/(Mc), r = √(m_tor·m_pol)·ℏ/(Mc). [DERIVED]
Unique to TCM
Every particle's physical size comes from its loop winding numbers and mass — a specific geometric formula. No standard analogue for particle 'size' like this.
141. Fabric mode thermal scale T₀ = ℏω₀/k_B ≈ 2.53×10⁻²⁷ K.
Temperature of the lowest fabric mode; intrinsic thermal scale of resting fabric. [DERIVED]
Unique to TCM
The resting fabric has its own temperature floor, T₀ = ℏω₀/k_B ≈ 2.53×10⁻²⁷ K — the coldest possible fabric vibration. A fundamental thermal scale unique to the model.
142. Saturation-cap thermal scale T_sat ≈ 26.58 K.
Fabric-mode temperature at which thermal population reaches ½ε(n_H−1)². [DERIVED]
Unique to TCM
A specific temperature, T_sat ≈ 26.58 K, at which fabric vibrations fill up to the stretch-energy limit ½ε(n_H−1)². A structural thermal threshold.
143. Freeze-thaw thermal threshold T_FT ≈ 39.24 K.
Corresponds to ρ₀·c². Above T_FT the relaxation timescale grows without bound; below, τ finite. [DERIVED]
Unique to TCM
A specific temperature, T_FT ≈ 39.24 K, marking the freeze-thaw boundary, above which the fabric's relaxation time grows without bound. Unique thermal marker.
144. Saturation surface temperature T_H = ℏλv_∞²/(4M·k_B·c) per mass M.
M_min ~5.4×10⁹ K; 1 M☉ ~6.2×10⁻⁸ K; Sgr A* ~1.5×10⁻¹⁴ K; M87* ~9.5×10⁻¹⁸ K; TON 618 ~9.3×10⁻¹⁹ K. [DERIVED]
Unique to TCM
Every collapsed surface has a specific temperature T_H = ℏλv_∞²/(4Mk_Bc) set by its mass — ~5.4×10⁹ K at the minimum mass, ~6.2×10⁻⁸ K for one solar mass, ~1.5×10⁻¹⁴ K for Sgr A*, ~9.3×10⁻¹⁹ K for TON 618. A distinctive mass-temperature ladder.
145. Critical mass for saturation-surface radiative equilibrium M_eq ≈ 4.5×10²² kg.
Mass at which T_H equals the measured cosmic radiation temperature 2.725 K. [DERIVED]
Unique to TCM
A specific critical mass, M_eq ≈ 4.5×10²² kg, at which a collapsed surface's temperature equals the measured cosmic background temperature of 2.725 K. A structural crossover.
146. Catalogue characteristic thermal scales T_cat = m_X·c²/k_B for each catalogue point.
Each point has a thermal scale where modes carry energy comparable to its rest energy. [DERIVED]
Unique to TCM
Each catalogue particle has a characteristic temperature where thermal energy matches its rest energy — a structural thermal scale per particle.
147. Universe today sits below T_FT, T_sat, and all catalogue thermal scales.
2.725 K places the present universe in the thawed, sub-saturation, stable-catalogue regime. [Structure]
Distinctive prediction
The present-day universe sits below all these thermal thresholds — in the thawed, sub-saturation, stable-matter regime. A structural placement of 'now.'
148. Present-day cosmic radiation temperature T_CMB = 2.725 K.
From canonical quantisation of the linearised Master PDE: T = (15ℏ³c³u_rad/(π²k_B⁴))^(1/4), σ_TCM matching Stefan-Boltzmann. [DERIVED via radiation-law apparatus; deeper derivation is quest Q-T1]
Distinctive prediction
The cosmic background temperature of 2.725 K is derived from quantising the fabric's radiation law, T = (15ℏ³c³u_rad/π²k_B⁴)^(1/4) — reproducing the observed value from the framework's own radiation apparatus.
149. Wide-binary velocity plateau at 422 m/s for solar-mass pairs.
V_flat(binary) = (G·M_total·g₀)^(1/4) ≈ 422 m/s, a factor 2^(1/4) above the single-Sun 355 m/s. Testable with Gaia. [DERIVED — NEW]
Unique to TCM
Two sun-like stars in a wide pair should show a flat relative velocity of V_flat = (G·M_total·g₀)^(1/4) ≈ 422 m/s at large separation — a factor 2^(1/4) above the single-Sun 355 m/s. Gaia-testable, with no standard-gravity counterpart.
150. Wide-binary K(X) threshold separation s_KX = 7030 AU for solar pairs.
s_KX = √(G·M_partner/g₀) ≈ 7030 AU — same expression as the single-source Solar-System crossover, two-body case. [DERIVED — NEW]
Unique to TCM
Wide stellar pairs enter the fabric's special regime beyond s_KX = √(G·M_partner/g₀) ≈ 7030 AU separation for solar masses — a specific threshold testable with Gaia data.
151. Wide-binary mass-scaling: s_KX ∝ √M_partner, V_flat ∝ M_total^(1/4).
A specific s_KX(M) and V_flat(M) curve across the stellar mass spectrum. Falsifiable by population analyses. [DERIVED — NEW]
Unique to TCM
The wide-pair threshold and plateau speed scale with stellar mass in a specific way — a whole predicted curve across the mass range, falsifiable by population studies. NEW.
152. Galactic match radius transcendental closure with prefactor 1.0383.
r_match³·[ln(r_match/r_knee) − 1/3] = 6·V_flat²·ξ_J²/g₀, prefactor 1.0383 at M×, no free parameter. [DERIVED]
Unique to TCM
A precise transcendental formula for the galactic match radius, r_match³·[ln(r_match/r_knee) − 1/3] = 6·V_flat²·ξ_J²/g₀, with fixed coefficient 1.0383 and no free parameters. A distinctive structural closure.
153. Unified perturbation asymptote r·δp → (v_∞² − V_flat²)/c².
Both SPARC branches from the sign of one expression; a single integration constant, not two mechanisms. [DERIVED]
Unique to TCM
Both branches of galaxy rotation behaviour come from the sign of a single expression — one integration constant, not two separate mechanisms. A unifying structural result.
154. Solar System equalizer baseline r_match,⊙ = 23.72 kpc.
The Sun's latent match radius, embedded within the Milky Way K(X) regime so never an isolated observable. [DERIVED]
Distinctive prediction
The Sun's own match radius is r_match,⊙ = 23.72 kpc — but it sits embedded within the Milky Way's K(X) regime, so it's never seen in isolation. A specific structural value.
155. The √2 non-linear lensing suppression on the cluster symmetry plane.
Between two equal-mass sources, the K(X) regime suppresses the combined gradient by exactly √2 ≈ 1.414 below linear superposition. Parameter-free, from the cubic-gradient flux conservation. [DERIVED — NEW]
Unique to TCM
Between two equal-mass lensing sources, the K(X) regime suppresses the combined gradient by exactly √2 ≈ 1.414 below simple superposition — a parameter-free signature of the non-linear regime.
156. 29.3% apparent symmetry-plane mass deficit for cluster pairs.
Standard linear inversion finds an apparent deficit 1 − 1/√2 ≈ 29.3% along the symmetry plane — a signature of the non-linear K(X) regime, testable with weak-lensing surveys of cluster pairs. [DERIVED — NEW]
Unique to TCM
Standard lens analysis of a cluster pair will show an apparent mass deficit of 1 − 1/√2 ≈ 29.3% along the symmetry plane — a specific fingerprint of the fabric's non-linear regime, testable in weak-lensing surveys of cluster pairs.
157. Cluster-pair far-field lensing scales as 1/b with κ = γ_t.
Past the pair, convergence and tangential shear both scale as 1/b — not 1/b² or exponential. κ = γ_t from the constitutive law. [DERIVED]
Distinctive prediction
Far from a cluster pair, both lensing quantities fall off as 1/b (not 1/b² or exponential), with a specific relationship between them. A distinctive far-field law.
158. Saddle-point plane-polarised shear (γ₁ ≠ 0, γ₂ = 0).
Near the saddle line, galaxies shear into ellipses aligned along the cluster-to-cluster axis, not tangentially. [DERIVED]
Unique to TCM
Near the saddle point between two clusters, galaxies shear into ellipses aligned along the cluster-to-cluster axis rather than tangentially — a distinctive, unusual lensing pattern.
159. Saddle-point intra-cluster gas pressure plateau.
Where the field gradient vanishes at the saddle, the gas pressure gradient vanishes, flattening the profile along the dipole axis. [DERIVED]
Distinctive prediction
At the saddle point between clusters, the gas pressure flattens into a plateau where the field gradient vanishes — a specific, observable gas signature.
160. Ψ-flux linearity theorem for exact multi-source cluster fields.
With Ψ ≡ K(n,X)·∇n, the static K(X) Master PDE reduces to ∇·Ψ = 4πG̃·ρ_bar, linear in Ψ, permitting exact multi-source treatment. [DERIVED]
Unique to TCM
An exact mathematical theorem letting multiple lensing sources be combined precisely in the fabric's non-linear regime — a structural tool with no standard analogue.
161. Closed-form elliptic-integral aperture kernel F(x).
F(x) = (1/π)·[(1−x)·K(k²) + (1+x)·E(k²)]; limits F(0)=1, F(1)=2/π, F(∞)→1/(2x). [DERIVED]
Unique to TCM
A specific closed-form lensing formula built from elliptic integrals, with defined limits — a distinctive exact result.
162. The κ̄·R scaling law and matter-density column equivalent.
κ̄(<R)·R independent of aperture for a coherent K(X) far-field source: M_bar(<R) = (κ̄·R·c²)²/(4π²·D_l²·G·g₀). [DERIVED]
Unique to TCM
A specific scaling law relating the averaged lensing signal to the enclosed visible mass, independent of aperture — a structural relationship for measuring cluster mass.
163. Five-cluster Bullet Cluster validation with no parameter adjustment.
Bullet, Abell 1689, El Gordo, MACS J0717.5+3745, Abell 1835 matched within ratio 0.72–1.27 across an order of magnitude in mass, z = 0.18–0.87, four morphologies, no parameter adjustment. [DERIVED, CONFIRMED]
Distinctive prediction
Five different cluster collisions — Bullet, Abell 1689, El Gordo, MACS J0717, Abell 1835 — all matched within ratio 0.72–1.27 with no parameter adjustment, across an order of magnitude in mass, redshift 0.18–0.87, and four morphologies. A confirmed multi-system test.
164. Quadruple cross-domain ω₀ consistency.
One anchored ω₀ = √(ε/α) fixes four domains: galactic Wardonian-to-Relaxonian handover, 600 Myr post-merger ringdown, cluster-scale screening length, dark-energy w deviation. Failure of any one falsifies the shared ω₀. [DERIVED]
Unique to TCM
One fabric frequency ties together four completely different phenomena — galaxy rotation handover, merger ringdown, cluster lensing scale, and dark energy. If any one fails, the shared frequency is falsified. A distinctive cross-domain lock.
165. Primordial tensor-to-scalar ratio r = 0 at leading order.
The framework has only one field — the fabric n — and the cosmic initial state (the saturation surface n = n_H) is structurally isotropic, so the leading-order tensor-to-scalar ratio is zero by rotational invariance (equation 49, §12.5). A sharp, distinctive, falsifiable prediction for the primordial gravitational-wave background, directly testable by BICEP/Keck, LiteBIRD, and CMB-S4. [DERIVED — §12.5; not previously catalogued]
Distinctive prediction
The primordial gravitational-wave signal is predicted to be exactly zero at leading order, because the framework has only one field and an isotropic starting state. A sharp, distinctive target for LiteBIRD and CMB-S4. NEW.
166. Scalar spectral tilt n_s − 1 = 2η_sr − 6ε_sr, red (n_s < 1).
The relaxation away from n_H toward n = 1 sources linear fabric perturbations with spectrum set by the asymptotic-relaxation potential V(u) = ½ε(e^u − 1)². The slow-roll parameters give a small negative n_s − 1 — a red primordial tilt (equation 50, §12.5). Planck measures n_s ≈ 0.965, robustly below 1; the framework's sign matches existing data. [DERIVED — §12.5; not previously catalogued]
Distinctive prediction
The primordial density ripples are predicted to tilt 'red' — n_s − 1 = 2η_sr − 6ε_sr, slightly below 1 — matching the observed Planck value of n_s ≈ 0.965. A specific sign the framework forces.