Introducing Arrival Desk
A free app that helps investigate wonder, but with precision.
Walk through my Mathematical City, nested in a tiny model universe, set in representation theory and constructed in awe. Some of my math passed. Some failed. But the beauty in trying super hard? That? It remains.
- Checked
- 13
- Failed
- 0
- Unfinished
- 6
- On record
- 16
The fingerprint
Certificate fingerprint
906117b5579395045d84e1828e0afce693cacae4b1ff39bedca8d63e1f14567d
Source fingerprint
3ad9290fd2c4992a01502e36980ce6d11745c3736f781470c47f0a738309d1e1
These two fingerprints match the written certificate. If the file changes, they change. The sliders rerun the finished parts. They don’t rewrite the original.
ARR-C011 · live witness
Spectral contraction
Symmetric PSD 12×12 operator, kernel dimension 3, seed 47. x maps to (I − εK)x. Complement dies. Kernel stays.
Brass bars are the kernel modes. Dim bars are the complement, which the iteration kills.
Steps
0
Spectral radius
0.820
Transverse residual
0.91382855
Kernel action
1.8348192
Published certificate: ε = 0.36, λ_max = 5, radius 0.82, projector residual 1.08×10⁻¹⁴ after the NumPy witness.
ARR-C009 · C010
Metallic root
λ^D − λ − 1 = 0. One positive root in (1, 2). Complexity ratio is (λ+1)².
λ_D
1.075766066087
Polynomial residual
8.88e-16
C_rem / C_for
4.308804761
Above 4
Yes, every D ≥ 2
Certificate at D = 10: λ ≈ 1.075766066086837, ratio ≈ 4.308804761118.
ARR-C008
Dimension flow
D(ℓ) = 10 + (D₀ − 10) e^(−σℓ)
At ℓ = 40, D = 9.999995. For positive σ the fixed point 10 is attractive. D = 10 forces α* = −6/B in the alpha sector.
ARR-C015 · C0-OMEGA-NUMBER
Coherence number
47/125
= 0.376 exactly
Video figure
0.376412
Difference
103/250000
0.376412 − 47/125 = 103/250000. The city does not merge them. The video figure is Observatory item 01.
ARR-C006 · C007
Renormalization fixed points
g*
0 or 0.2
α*
0 or -2
Identifying the interacting root with Ω_c needs a map the video does not give. Fixed points themselves are closed.
Session packet · E47 QGNN
Learned gates commute with contraction
For every projected generator, the layer U leaves the complement alone and the filter Γ contracts it at r = 15/17. Training changes the retained state. It does not change the leak rate. This is the exact operator bound, not a 125-dimensional statevector.
‖T_N − W_N P‖
0.02340292
(15/17)^N
0.02340292
Fidelity lower bound
0.998889
The Python model reports rank 47, eight-qubit dilation unitarity, and a teacher recovery to about 10⁻¹⁷ on synthetic labels. Not an external-task benchmark, and not yet a public repository.
Carrier H = V₂⊗³
Casimir sectors
K = (C − 6I)(C − 30I). Kernel is J = 2 plus J = 5, dimension 25 + 22 = 47. Occupancy 47/125.
J = 0
λ = 0 · dim 1
J = 1
λ = 2 · dim 9
J = 2
λ = 6 · dim 25
J = 3
λ = 12 · dim 28
J = 4
λ = 20 · dim 27
J = 5
λ = 30 · dim 22
J = 6
λ = 42 · dim 13