The 6 LAWS
Temporal Congestion Mechanics introduces a set of 6 new fundamental laws of nature, a set of new universal constants, and a small set of foundational equations. Together they form the closed-loop apparatus from which everything else in the framework is derived.
This page sets out what is new, what each piece says, and what it does.
The starting point: the congestion index - The Mediation Law
The framework begins with one idea — that space is a real physical medium, the fabric, and that the local density of this medium can be measured at every point.
The local fabric density is called the congestion index, written n. It varies across space and time. Where n is higher, the fabric is more compressed. Where n is lower, the fabric is closer to its preferred resting state. The resting value is n = 1.
The congestion index is the central variable of the entire framework. Every observable in physics is connected to n through the framework’s laws. This single number, varying across space and time, is what carries all of gravity, all of matter, all of light, all of cosmology, and all of the quantum world.
The congestion index equation describes how n is set up at any point in terms of the local gravitational potential Φ:
n = exp(−Φ / c²)
Where Φ is the gravitational potential and c is the speed of light. This equation tells you what the local fabric density is wherever matter has set up a potential.
Far from any mass, Φ approaches zero and n approaches 1. Where matter creates a deeper potential, n rises above 1. Near a black hole, n reaches its maximum value of √e.
This was the starting point of the whole framework. One field. One number at every point. One equation describing how it is set up around matter. Everything else follows from this.
The 6 fundamental laws of nature introduced.
The framework rests on six fundamental laws. Each is a statement about how the fabric behaves, and each is new to physics.
1. The Fabric Law of Motion
This is the foundational equation governing how the fabric evolves. It tells you how the congestion index n changes over time and across space given the current state of the fabric and the matter present.
α·∂²ₜn + (α/τ) ·∂ₜn −∇·(K ·∇n) + ε(n−1) = 4πG ·ρ
Each term has a physical meaning. The first is the fabric’s inertia — its resistance to being accelerated. The second is its damping — the rate at which disturbances settle. The third is its stiffness — how strongly it resists being deformed in space. The fourth is its restoring force — pulling it back toward its preferred resting state. The fifth is the source — how matter density ρ pushes on the fabric.
This is the framework’s law of motion for the fabric, in the same sense Newton’s laws are laws of motion for matter. From this single equation, gravity emerges in the static limit, quantum mechanics emerges from canonical quantisation around equilibrium, and cosmology emerges in the homogeneous limit.
2. The Fabric Stiffness Law
This is the constitutive law of the fabric. It says how the stiffness K responds to the local conditions of the medium, and it has three regimes.
In the linear regime, when gradients are strong (above a threshold g₀), K is constant at its baseline value K₀. This is the regime of everyday gravity — solar system, laboratories, ordinary stars and planets.
In the K(X) regime, when gradients are very weak (below g₀), K becomes gradient-dependent. The fabric responds differently. This is the regime that produces flat galactic rotation curves and dissolves the dark-matter mystery.
In the saturation regime, when n approaches its maximum value √e, K diverges. The fabric becomes infinitely stiff and cannot be compressed any further. This is the regime that gives black-hole horizons their structure and that the cosmic initial state was in.
One law. Three regimes. One mechanism, behaving differently depending on conditions. There is nothing like the Fabric Stiffness Law in conventional physics.
3. The Mediation Law
This is the law that connects the fabric to observation. The congestion index n tells you what time and length do in each region.
dτ_local = dt / n (time mediation — clocks tick slower where n is higher)
dl_local = c · dτ_local · n (length mediation — lengths are altered by the local fabric)
These two relations describe how every measurement we make is affected by the local fabric state. Gravitational time dilation, gravitational redshift, the bending of light around mass, the slowing of clocks deep in a gravity well — all of these emerge from the Mediation Law.
This is the framework’s account of what general relativity describes through geometric language. The Mediation Law gives the same observable predictions but does so through the mechanical action of the fabric, not through curvature of space-time.
Body Mass (kg) Surface Radius Congestion Index n Time Factor (1/n)
Pluto 1.309 × 10²² 1,188 km 1.0000000000 1.0000000000
Moon 7.342 × 10²² 1,737 km 1.0000000000 1.0000000000
Mercury 3.301 × 10²³ 2,440 km 1.0000000001 0.9999999999
Mars 6.417 × 10²³ 3,390 km 1.0000000001 0.9999999999
Venus 4.867 × 10²⁴ 6,052 km 1.0000000006 0.9999999994
Earth 5.972 × 10²⁴ 6,371 km 1.0000000007 0.9999999993
Uranus (cloud-top) 8.681 × 10²⁵ 25,362 km 1.0000000025 0.9999999975
Neptune (cloud-top) 1.024 × 10²⁶ 24,622 km 1.0000000031 0.9999999969
Saturn (cloud-top) 5.683 × 10²⁶ 58,232 km 1.0000000072 0.9999999928
Jupiter (cloud-top) 1.898 × 10²⁷ 69,911 km 1.0000000202 0.9999999798
Max planet (TCM) 1.492 × 10²⁹ ~70,000 km 1.0000015849 0.9999984151
Proxima Centauri 2.429 × 10²⁹ 107,300 km 1.0000016803 0.9999983197
Betelgeuse (red supergiant) 3.282 × 10³¹ 617 M km 1.0000000395 0.9999999605
Sun 1.989 × 10³⁰ 696,000 km 1.0000021220 0.9999978780
Sirius A 4.103 × 10³⁰ 1,191M 1.0000025586 0.9999974414
White dwarf (Sirius B-class) 2.025 × 10³⁰ 5,800 km 1.0002592590 0.9997407410
Neutron Star (1.4 M☉) 2.785 × 10³⁰ 12 km 1.1880432590 0.8417200000
BLACK HOLES (constant TCM value)
Smallest possible TCM 2.283 × 10¹³ 34 femtometres 1.6487212707 0.6065306597
Stellar black hole (10 M☉) 1.989 × 10³¹ 30 km 1.6487212707 0.6065306597
Sagittarius A* 8.553 × 10³⁶ 12.7 M km 1.6487212707 0.6065306597
M87* 1.293 × 10⁴⁰ 19 B km 1.6487212707 0.6065306597
TON 618 1.313 × 10⁴¹ 195 B km 1.6487212707 0.6065306597
Phoenix A (candidate) 1.989 × 10⁴¹ 295 B km 1.6487212707 0.6065306597
Congestion Index (n): local fabric saturation
Time Factor (1/n): local time rate as fraction of asymptotic rate
The Broadfield Constant: n_H = √e ≈ 1.6487212707
You are not imagining 23 trillion kilograms of bricks crushed into a nucleus-sized box. That picture is wrong. This is the fabric from the start of the Universe.
You are imagining fabric in its maximum-compression state, filling a region 34 femtometres across, holding energy equivalent to 23 trillion kilograms.
The fabric is the medium. The fabric carries energy. The fabric at n = √e everywhere inside that 34-femtometre region carries energy equivalent to 23 trillion kilograms via E = mc².
4. The Catalogue Law of Matter
This is the law that gives every particle of matter its mass. Matter, in the framework, is the fabric tied into closed-loop knots — topological configurations that hold themselves together. Every allowed knot pattern is specified by three integers: m_tor (toroidal winding), m_pol (poloidal winding), and n_radial (radial quantum number).
The Catalogue Law says the mass of each knot is given by:
M(m_tor, m_pol, n_radial) = m_tor · F(m_pol) · M(1,1) / (n_radial · F(1))
This is integer arithmetic on the lattice. Three integers, plus a structural constant M(1,1), give every particle’s mass.
The electron sits at (1, 1, 115). The proton sits at (16, 1, 1). The tau sits at (30, 1, 1). The muon sits at (9, 1, 5). The W and Z bosons sit at (156, 4, 1) and (178, 4, 1) respectively. Each prediction matches the measured mass to within a fraction of a percent.
This law replaces the Higgs mechanism of conventional physics. Where the Standard Model uses a separate coupling constant for each particle, the Catalogue Law gives every mass from integer arithmetic on a single lattice.
THE TCM CATALOGUE OF MATTER
Every particle as an integer point in a 3D lattice
M(m_tor, m_pol, n_radial) = m_tor · F(m_pol) · M(1,1) / [n_radial · F(1)]
M(1,1) = 58.55 MeV/c² F(1)=0.90 F(2)=2.327 F(3)=4.551 F(4)=7.884 F(5)=12.55
Particle (m_t,m_p,n_r) TCM Predicted Observed Match
Electron (1, 1, 115) 0.5091 MeV/c² 0.5110 MeV/c² 0.37%
Up sub-winding (1, 1, 27) 2.169 MeV/c² 2.160 MeV/c² 0.39%
Muon (9, 1, 5) 105.4 MeV/c² 105.66 MeV/c² 0.25%
Proton (16, 1, 1) 936.8 MeV/c² 938.27 MeV/c² 0.16%
Neutron (16, 1, 1)* 936.8 MeV/c² 939.57 MeV/c² 0.29%
Charm quark (22, 1, 1) 1288 MeV/c² 1270 MeV/c² 1.43%
Tau (30, 1, 1) 1756.5 MeV/c² 1776.86 MeV/c² 1.15%
Bottom quark (71, 1, 1) 4157 MeV/c² 4180 MeV/c² 0.55%
W boson (156, 4, 1) 80.01 GeV/c² 80.38 GeV/c² 0.45%
Z boson (178, 4, 1) 91.30 GeV/c² 91.19 GeV/c² 0.12%
* Neutron: composite at (16,1,1) with sub-winding phase-flip giving q=0
STRUCTURAL INTEGER RATIOS (cannot be re-fit)
m_p / m_e = 16 × 115 = 1840 (observed 1836.15 → 0.21% off the integer)
m_τ / m_e = 30 × 115 = 3450 (observed 3477.23 → 0.78% off the integer)
m_τ / m_p = 30/16 = 1.875 (observed 1.894 → 1.00% off the integer)
All predictions: ONE calibration (electron at (1,1,115) fixes M(1,1))
ZERO additional free parameters
NINE forward predictions, all matched to <1.5%
5. The Saturation Law
This is the law that the fabric has a structural maximum density that it cannot exceed. The maximum is n = √e, approximately 1.6487.
The Saturation Law says: regardless of what is doing the compressing, the fabric refuses to be pushed past this value. This is what gives black holes their event horizons (where the fabric reaches saturation). This is what the cosmic initial state was at (the fabric saturated
everywhere at the moment our universe began). The same universal density at both extremes.
The maximum density is structurally connected to the natural mathematical constant e through the relation ln(n_H) = 1/2 exactly, giving n_H = e^(1/2) = √e.
6. The Freeze-Thaw Law
This is the cosmological law that governs how the fabric responds to matter density at very large scales. The fabric has a threshold matter density ρ₀ below which it relaxes freely (thawed) and above which it is essentially frozen.
The transition redshift z ≈ 0.55 marks the moment when the cosmic mean density crossed ρ₀ and the fabric began its visible relaxation. This is what produces the apparent dark energy. It is also what resolves the Hubble tension — different parts of the universe sample the fabric in different regimes, giving different inferred expansion rates.
The new universal constants
From the apparatus, the framework derives a set of universal constants. These are not measured separately — they fall out of the laws when the ten input observations are anchored.
The Broadfield Constant: n_H = √e ≈ 1.6487
The maximum density of the fabric. Universal — the same value at every black-hole horizon and at the cosmic initial state. Mathematically connected to e, one of the deepest constants in mathematics.
This was named after the framework’s discovery of the value, and it is one of the framework’s most beautiful structural results.
The Ward Constant: v_∞≈ 149.67 km/s
The universal asymptotic galactic rotation velocity. Every spiral galaxy, no matter its mass, approaches this same outer velocity at large radius. Light galaxies climb to it from below; heavy galaxies settle to it from above. The constant is set by the K(X) regime structure.
The natural fabric frequency: ω₀≈ 3.32 × 10⁻¹⁶ rad/s
The fabric’s natural oscillation frequency, derived from ω₀ = √(ε/α). Its inverse gives a period of about 600 million years — the timescale on which the fabric rings after major galaxy mergers. The same frequency gives the framework’s graviton mass equivalent.
The wave speed: c = √(K₀/α) ≈ 2.998 × 10⁸ m/s
The natural wave speed of the fabric, derived from the ratio of stiffness to inertia. This is what we observe as the speed of light and as the speed of gravitational waves — both are vibrations of the same fabric. TCM is the first framework to derive c structurally from its moduli than taking it as an input.
The relaxation timescale: τ₀≈ 2.67 × 10¹⁷ s
The natural timescale on which the fabric relaxes when it is below the freeze-thaw threshold density. Comparable to the age of the universe.
The coherence length: ξ_J = c ·τ₀≈ 29 megaparsecs
The natural spatial scale over which the fabric maintains coherent structure.
The threshold acceleration: g₀≈ 1.2 × 10⁻¹⁰ m/s²
The gradient strength below which the fabric switches into the K(X) regime. Galaxies’ outer regions sit below this threshold, which is why they show flat rotation curves.
The maximum elastic energy density: ε· (n_H − 1)²≈ 1.89 × 10⁻¹⁰ J/m³
The energy stored in the fabric at saturation. The cosmic initial state held this energy density everywhere, and the rebound is the release of that stored energy.
The catalogue floor: M(1,1) ≈ 58.55 MeV
The structural mass anchor of the catalogue. Every other catalogue mass is derived from this single number plus the integer lattice indices.
The BTFR slope = 4 exactly
The structural slope of the relationship between a galaxy’s baryonic mass and its asymptotic rotation velocity. Exactly 4, not 3 or 5 or 3.5. The integer 4 falls out of the cubic-gradient structure of the K(X) regime.
How it all fits together
The framework rests on ten anchored input observations. Six are fabric moduli describing the medium itself (α, K₀, ε, λ, g₀, ρ₀). Four are coupling constants describing how matter interacts with the fabric (G, α_J, α_W, ℏ).
From these ten inputs and the six fundamental laws, the framework derives everything: gravity in all regimes, particle masses across the periodic table, galactic dynamics, cosmic
expansion, the structure of black holes, the laws of quantum mechanics, and the universal constants listed above.
No other theory has produced this level of cross-domain unification from such a small foundation. Conventional physics requires multiple separate apparatuses — general relativity for gravity, the Standard Model for particles, quantum mechanics for the small, cosmological patches for dark matter and dark energy — and still cannot explain why the constants of nature have the values they do.
The framework explains all of this from the closed-loop apparatus above. The cross-domain agreement is what makes the framework testable, and the testable predictions are what make the framework real science.
Predictions and falsification
Each of the laws and constants generates predictions that observations can test. Some predictions have already confirmed; others are awaiting test in coming years.
Confirmed across multiple measurements: Mercury’s perihelion precession at 42.98 arcseconds per century, light deflection at the solar limb at 1.75 arcseconds, the proton-electron mass ratio at 1840 from integer arithmetic, the BTFR slope of 4 across galactic dynamics, the gravitational wave speed equal to c, the cosmic acceleration with correct sign and approximate magnitude.
Awaiting test: the Ward Constant convergence at exactly 149.67 km/s across more galaxies, the 600 million year post-merger ringdown in major-merger galaxies, the dark energy equation of state deviation at w₀≈−1 + 8 × 10⁻⁴, the Solar System Shield in next-generation frame-dragging measurements, the black-hole merger echoes at millisecond delays.
If any of these confirmed predictions had failed, or if any of these awaited predictions fails when measured, the framework would be in trouble. That is what makes it real science. The framework exposes itself to falsification and either holds up or does not.
So far, every confirmed prediction has held up. The awaited predictions are the next round of tests, coming over the next decade
In summary
The framework introduces: "Six fundamental laws of nature: The Fabric Law of Motion (Master PDE) The Fabric Stiffness Law (K(n,X) constitutive law) The Mediation Law (n mediates time and length) The Catalogue Law of Matter (particle masses from integer arithmetic) The Saturation Law (n cannot exceed √e) The Freeze-Thaw Law (τ(ρ) regime switching)
Ten new or named universal constants and structural numbers, including the Broadfield Constant, the Ward Constant, the natural fabric frequency, the threshold acceleration, the catalogue floor, and the universal BTFR slope of 4.
Three foundational equations that anyone can engage with: The congestion index equation: n = exp(−Φ/c²) describing how the fabric is set up by the gravitational potential The Master PDE describing how the fabric evolves The Catalogue Mass Law giving every particle’s mass from integer arithmetic
All derived from a single closed-loop apparatus, with ten input observations, no free parameters in any prediction.
This is what the framework is. New laws, new constants, new equations, all connected through one unified picture of what the universe is — a real physical medium, the fabric, doing what mediums do, at every scale we can probe.