E47 Lock
Locked E47
47 / 125 CERTIFIED
Certified collapse into a protected 47-dim subspace inside a 125-dim space
1. THE SPACE
C = C† · hermitian · spectrum locked
C eigenvalues7 distinct → 125 total
λ=0
1
λ=2
9
λ=6
25LOCKED
∈ ker
λ=12
28
λ=20
27
λ=30
22LOCKED
∈ ker
λ=42
13
DISTRIBUTION
{ 0:1, 2:9, 6:25,
12:28, 20:27,
30:22, 42:13 }
total dim125
2. THE OPERATORS IT BUILDS
K
KERNEL
ker(K) = { C=6 or 30 }
47-dim → Locked E47
Protected subspace where Γ acts as identity. Stable under C.
K²
SPECTRUM
λ111,664
λ212,544
λ319,600
λ432,400
λ5186,624
GAP
11,664
NORM
186,624
Λ
PROJECTOR
•idempotent: Λ² = Λ
•KΛ ≈ 0 · annihilates residual
•ΓΛ = Λ · stable fixed point
•[C,Λ] = 0 · commutes
rank(Λ)47
3. THE PIPELINE
Σ
state
Ψ
evolve
Γⁿ
contract
Ω
gate
Λ
project
Σ'
locked
MINIMAL recursive_step
aggregate incoming state
evolve via Ψ
contract once via Γ
project via Λ
gate on residual via Ω
FULL RUNTIME (in file)
same aggregation + Ψ, but Γ applied repeatedly until ‖K·state‖ ≤ tol (≤512×) + residual_history
Ω evaluated BEFORE Λ — non-tautological gate
M = Λ@state only if Ω=True else keep contracted state
returns pre_projection, residual, contractions, …
4. THE LOOP & CERTIFICATION
recursive_run()
Loops the full cycle, feeding Σ' back as next input. Deterministic chain: Σ→Ψ→Γⁿ→Ω→Λ→Σ'
Σ_{t+1} = Λ(Γⁿ(Ψ(Σ_t))) if Ω
reinitialize()
Inject new α each cycle. Resets aggregation weights without breaking certified subspace.
α → Σ₀ re-seed
identity_evolution(x)=x
Smoke-test Ψ. Identity map verifies contraction & projection without evolution noise.
Ψ = I · baseline check
certify_locked_e47() · EXECUTABLE PROOF
all PASS → algebra locked
C hermitianPASS
spectrum exactPASS
rank(Λ)=47PASS
Λ²=Λ error < εPASS
KΛ≈0PASS
ΓΛ=ΛPASS
[C,Λ]=0PASS
K² spectrum 5 valsPASS
gap=11664PASS
‖K‖=186624PASS
Ω_c = 47/125PASS
ε, ρ boundsPASS
ONE-SENTENCE SUMMARY
It's a deterministic Σ→Ψ→Γⁿ→Ω→Λ→Σ' loop that guarantees collapse into a certified 47/125subspace, with a residual-based certainty gate.
locked_e47_framework · certified · deterministic
QUANTUM-INSPIRED · 125 → 47 · CERTIFIED COLLAPSE
