CRR Diamond — Interactive Physics Simulation

CRR PHYSICS OVERLAYS

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Thermal Micro-Ruptures

⟨u²⟩^½ ≈ 0.04 Å at 300K

Phonon-driven lattice vibrations. Each atom oscillates around equilibrium due to thermal energy. At room temperature, diamond atoms displace only ~0.04Å RMS — just 2.6% of bond length. The Debye temperature Θ_D=2230K means diamond is "frozen" into its coherence basins.

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Coherence Field C(x)

C(x,t) = ∫₀ᵗ L(x,τ) dτ

Accumulated structural stability. Bulk atoms (interior) have higher C — full tetrahedral coordination. Surface atoms have lower C — missing neighbours reduce coherence. Blue intensity = higher coherence.

Memory Weight exp(C/Ω)

W(x) = exp(C(x)/Ω)

Regeneration preference. With Ω=0.01, lattice sites have W≈e¹⁰⁰ — astronomically strong preference. This is why diamond always returns to the same structure: the memory weight at equilibrium is overwhelming.

sp³ Bond Network

θ = arccos(−1/3) = 109.47°

Tetrahedral covalent bonding. Each carbon forms 4 equivalent bonds at 109.47° — the angle maximising angular coherence for sp³ hybridisation. Bond length = 1.544Å. The network flexes with thermal vibrations when both overlays are active.

Coherence Basins

V(r) ≈ −C₀·exp(−r²/2σ²)

Potential energy wells. Each atom sits in a coherence basin — a local minimum. Basin depth ∝ exp(C/Ω): small Ω = extremely deep, narrow wells. Blue halos show the attractive region.

Regeneration Forces

F = −∇V = −(∂C/∂x)·exp(C/Ω)/Ω

Restoring forces. Coherence gradient creates restoring force scaling with exp(C/Ω)/Ω — for diamond's small Ω, forces are enormous, explaining extreme stiffness. Orange arrows show force vectors. Requires Thermal Micro-Ruptures.

CRR PARAMETERS

Ω = 0.01 · Θ_D = 2230 K · T = 300 K

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SIMULATION STATE

MACROSCOPIC

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True atoms: —

Rendered: —

Compression: —

Lattice: 3.567 Å

Bond angle: 109.47°

Bond length: 1.544 Å

Refractive idx: 2.417

REGENERATION EQUATION

R = ∫ φ(x,τ)·exp(C/Ω)·Θ(t−τ) dτ

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WHAT CRR SOLVES — THE PHYSICS OF PERSISTENCE

The Problem of Rigidity

Why does diamond always return to exactly the same structure?

Standard physics describes diamond's stiffness through spring constants and binding energies — but these are descriptions, not explanations. CRR provides the temporal mechanism: each lattice site accumulates coherence C(x,t) over time through sustained structural alignment. The exponential memory weight exp(C/Ω) with Ω=0.01 creates an astronomically deep attractor at each equilibrium position. Diamond doesn't just resist deformation — it actively regenerates its structure through overwhelming memory preference. Every thermal vibration is a micro-rupture that the system instantly resolves back to coherence.

Scale Invariance

C(x,t) = ∫₀ᵗ L(x,τ) dτ → δ(now) → R = ∫ φ·exp(C/Ω)·Θ dτ

The same C→δ→R dynamics operate at every scale: thermal phonons (femtoseconds), lattice defect healing (nanoseconds), crack propagation and arrest (microseconds), and macroscopic structural persistence (geological time). Diamond's 3.5-billion-year stability is not a different phenomenon from its picosecond thermal vibrations — it is the same CRR process operating with the same Ω across temporal scales. This is what makes CRR predictive: one parameter set explains behaviour from atomic to geological.

Ω as System Identity

Ω = 0.01 → exp(C/Ω) ≈ e¹⁰⁰ → k_eff ∝ e¹⁰⁰/Ω

Diamond's small Ω (0.01) means extremely narrow coherence basins — the lattice permits almost no deviation. This single parameter explains hardness (Mohs 10), bulk modulus (443 GPa), thermal conductivity (2200 W/m·K), and sound speed (18,000 m/s) as manifestations of one underlying property: the depth of the memory weight function. CRR unifies these disparate physical measurements through the Z₂ symmetry class, where Ω=1/π governs the coefficient of variation — matching empirical data to ~1% accuracy across independent systems.