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Exact SymPy certificate for the explicit rolling map φ̃(x,q) = (q₀, x+q⃗,
x−q⃗) : S²×S³ → the null quadric of Ω_W, whose bilinear is derived
in-file (Hitchin contraction = 24·b, signature (3,4)). Global immersion,
exact diagonal fibre (x,q) ~ (−x,−q), no descent to S²×SO(3). Core:
rolling direction is Ω-horizontal iff λ = −1 (both directions certified);
under the declared kinematic convention this gives ρ = 3. K = SU(2)×SU(2)
equivariance promotes plane equality globally; growth vector (2,3,5)
computed. Stabilizer Cartan decomposition certified complete (14 = 6+8);
golden-ratio boost sends e₁ to (√5/2)e₁ + (1/2)e₅. 65 exact symbolic
assertions, fully deterministic, single source of truth for the rolling
field. Incorporates three independent external reviewers' contributions.
Dependencies: Proof 22 (Ω_W), Proof 15 (γ₁ = √5/2).
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Title CCFU Script 6 — verify_explicit_rolling_map.py
Exact SymPy certificate for the explicit rolling map φ̃(x,q) = (q₀, x+q⃗,
x−q⃗) : S²×S³ → the null quadric of Ω_W, whose bilinear is derived
in-file (Hitchin contraction = 24·b, signature (3,4)). Global immersion,
exact diagonal fibre (x,q) ~ (−x,−q), no descent to S²×SO(3). Core:
rolling direction is Ω-horizontal iff λ = −1 (both directions certified);
under the declared kinematic convention this gives ρ = 3. K = SU(2)×SU(2)
equivariance promotes plane equality globally; growth vector (2,3,5)
computed. Stabilizer Cartan decomposition certified complete (14 = 6+8);
golden-ratio boost sends e₁ to (√5/2)e₁ + (1/2)e₅. 65 exact symbolic
assertions, fully deterministic, single source of truth for the rolling
field. Incorporates three independent external reviewers' contributions.
Dependencies: Proof 22 (Ω_W), Proof 15 (γ₁ = √5/2).
Work type Script
Tags captain cookie face, ccfu, script
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Registry info in Safe Creative
Identifier 2607166408688
Entry date Jul 16, 2026, 3:53 PM UTC
License All rights reserved
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Author 100.00 %. Holder Captain Cookie Face Universe. Date Jul 16, 2026.
Information available at https://www.safecreative.org/work/2607166408688-ccfu-script-6-verify_explicit_rolling_map-py
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Registration: 2607166408688
