CRR — HOW EACH ASPECT IS SOLVED
Ω(r) = v/r · v ≈ 220 km/s flat → SO(2), Ω_scale=3
Dark matter sets Ω for the entire disk. The flat rotation curve means every radius shares the same coherence capacity. CRR agent: highest Ω, slowest cycle, most stable — you cannot see it but you feel it as sub-bass drone at D1 (36.7 Hz).
Z&sub2;, Ω_scale=0.4 · M = 4.15×10&sup6; MⓈ
The supermassive black hole has the lowest Ω — most rigid, frequent micro-ruptures reconstituting the same pattern. CRR explains why it’s the gravitational anchor: exp(C/Ω) is peaked, accessing only recent coherence. Musical: D0 sub-bass rumble (18.35 Hz), felt not heard.
SPIRAL ARMS = COHERENCE WAVES
Ω_pattern ≠ Ω_star → arms are NOT material
Density waves are C accumulating as gas enters the arm. When C reaches Jeans threshold (C = Ω), it ruptures into star formation δ(now). CRR agent: Z&sub2;, Ω_scale=1.2 — periodic compression-rupture cycles. Musical: strings pad = the density wave field itself.
Ω_star = Ω_pattern at r ≈ 8 kpc (the Sun)
At corotation, C = Ω permanently — maximum resonance. This is where we live. CRR predicts this as the point of maximum coherent memory access. Musical: piano represents our perspective — the listener standing at the galaxy’s resonance peak.
Chandrasekhar threshold: C = Ω at ~1.4 MⓈ → catastrophic rupture
A supernova IS the ultimate δ(now). Nuclear fusion accumulates C until the Chandrasekhar limit. The explosion enriches the ISM with heavy elements — R(memory) for the next generation. Every element heavier than iron was forged in a δ(now).
R = ∫φ(x,τ)exp(C/Ω)Θ(...)dτ
Regeneration weights stellar memory by significance. exp(C/Ω) determines which past coherence moments are accessible: high-coherence supernova products are preferentially incorporated into new stars. Musical: reverb delay = temporal memory weighting.
BOWED GUITAR = MAGNETIC COHERENCE
B ≈ 2–10 μG sustained along spiral arms
The Milky Way’s large-scale magnetic field follows arm structure — sustained coherence that accumulates along arms and ruptures at reconnection events. The ebow synthesis = continuous, shimmering, slowly evolving. Two detuned sawtooths + triangle, long attack. Pure Sigur Rós bloom.
FALSETTO = STELLAR POPULATIONS
Hopelandic: meaning from harmonic relationship, not words
Each voice = a stellar population. Shared harmonics = constructive coherence. exp(C/Ω) weights which populations dominate. Triangle wave: 1/n² harmonic decay → coherence dominated by fundamentals. We hear HARMONY not TIMBRE — Hopelandic as the language of stars.
VOID → COLLAPSE → FIRST LIGHT → SPIRAL → ROTATION → COROTATION → RUPTURE → REGENERATION → STILLNESS
The entire composition IS one C→δ→R cycle. Post-rock crescendo = coherence accumulation. Wall of sound = C approaching Ω. Silence = δ(now). The rebuild = R(memory). At 72 BPM, 12 beats = one galactic breath — π² ≈ 10 seconds.
CRR AGENTS IN COMPOSITION
7 concurrent CRR agents driving all dynamics
Sgr A* · Z&sub2;, Ωs=0.4 · rigid
Dark matter · SO(2), Ωs=3 · stable
Disk rotation · SO(2), Ωs=1.5
Density wave · Z&sub2;, Ωs=1.2 · periodic
Star formation · Z&sub2;, Ωs=0.8
Composition · φ, Ωs=2 · macro
Phrase · SO(2), Ωs=1.5 · musical
Alexander Sabine · CRR Framework · temporalgrammar.ai