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NEXUS

Private research console

Formalism, certified once.

One atlas for machine-validated proofs, QuTiP simulations, and the sources they live in — GitHub Kartekeya, Drive plates, Notion city, Supabase edge, web. Duplicates collapsed to a single work with every origin attached.

Works
49
Certified
45
Simulations
7
Open
2

Casimir spectrum

5V₂ ⊕ 2V₅ = E₄₇

j=0 · λ=0
1
j=1 · λ=2
9
j=2 · λ=6
25
j=3 · λ=12
28
j=4 · λ=20
27
j=5 · λ=30
22
j=6 · λ=42
13

Kernel sectors j=2 (25) and j=5 (22) lock Ωc at 47/125. Complement 78 is the decaying filter space.

Coherence lock

47/125

47 / 125 = 0.376

K² gap
11664
K² max
186624
Operator
K = (C − 6I)(C − 30I)

Construction pipeline

  1. 01

    Σ

    State space

    V₂⊗V₂⊗V₂ · dim 125

  2. 02

    C

    Casimir

    C = Jx² + Jy² + Jz²

  3. 03

    K

    Kernel filter

    K = (C−6I)(C−30I)

  4. 04

    H

    Harmonic flow

    H = K² · gap 11664

  5. 05

    E₄₇

    Reduction

    ker K · dim 47

  6. 06

    P

    Projector

    P² = P† = P · rank 47

  7. 07

    Γ

    Contraction

    Babylonian flow → Ωc

Live machine

Reading Kartekeya…

Pinned certificates

All proofs
E47 spectral kernelE1 numeric

Finite-dimensional construction of E₄₇ = ker K on V₂⊗³. dim V = 125, dim ker K = 47, Ωc = 47/125. All kernel checks pass in the Kartekeya certificate.

proofKernel3.66e-13 annihilation
github · Kartekeya certificate
Orthogonal projector P₄₇E1 numeric

P₄₇² = P₄₇ = P₄₇†, KP₄₇ = 0, Tr P₄₇ = 47. Idempotence residual 4.91e-14. Rank and trace certified in the same machine run as the kernel.

proofKernel4.91e-14 idempotence
github · projector.py
QuTiP spectral validationE2 quantum

Deterministic QuTiP eigen-decomposition of C and K on the 125-dimensional Hilbert space. All seven checks pass: dim, ker, Ωc, gap, tensor product, kernel idempotence, Casimir clustering.

simulationQuantumexact after 5-dec rounding
github · qutip_validation.json

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