Coherence Attractor Theorem

A keep-set exists. A shrink rule sends everything else toward it. If the gap is clean, the ending is unique. HARs, in this model, change how fast a developmental network falls in — not the size of the keep-set.

Axioms

1. 01

   Information is fundamental

   Whatever a brain, a genome, or a circuit is made of, what persists is pattern — who talks to whom, and which patterns survive noise.

2. 02

   Coherence is the variational principle

   Systems tend to keep what still fits together and drop what fights itself. That is not mysticism — it is the same idea as water finding a basin.

3. 03

   Recursion is the mechanism

   Nothing interesting happens in one shot. The genome, the brain, and the math all work by repeating a simple rule until only the stable part remains.

4. 04

   The kernel is invariant

   Some patterns are invisible to the rule that erases everything else. Those patterns are the ones that last.

5. 05

   A positive spectral gap implies convergence

   If there is a clean gap between 'keep' and 'drop,' the drop happens exponentially fast. No gap, no clean ending.

Core identities

• Selector

  K = (C − 6I)(C − 30I)

  A filter that keeps two special families of patterns and rejects the rest.

• Dissipation

  A = K†K = K² ≥ 0

  Turn the filter into a one-way shrink rule. Only the keep-set is untouched.

• Step

  Γ_ε = I − ε A, 0 < ε < 2 / λ_max(A)

  Each round multiplies the leftovers by a number smaller than one.

• Limit

  lim Γ_εⁿ = P₄₇

  After enough rounds you are looking only at the keep-set.

• Invariant

  Ω_c = dim E₄₇ / dim V = 47/125 = 0.376

  The fraction that remains. On this carrier it is exact, not fitted.

Proof steps

1. 01

   Existence of the kernel

   The keep-set is not empty. The algebra names it: forty-seven dimensions that the eraser cannot see.

2. 02

   Contraction on the complement

   Everything outside the keep-set shrinks each round — like echoes dying in a canyon.

3. 03

   Convergence to the attractor

   Repeat the shrink step. The leftovers approach the keep-set and stay there.

4. 04

   Variational optimality

   Among nearby patterns, the keep-set is the one that costs the least to maintain.

5. 05

   Levinthal-type folding corollary

   A protein does not try every shape. If folding is a contraction toward a basin, the search is polynomial, not cosmic.

6. 06

   HAR modulation of the gap

   Human-accelerated switches do not change the keep-fraction. They can change how fast a developmental network falls into its stable pattern.

Machine certificate

nicholaskouns-create/E47-Kartekeya

dim V

125

dim E₄₇

47

gap(K²)

11664

λ_max

186624

Tr P₄₇

47

Ω_c

0.376

‖Γⁿ−P‖

9.84e-11

QuTiP

pass

A public Python package rebuilds the operators and checks every identity above. The numbers are not decorations.

Boundaries

• What is certified

  The 125-dimensional algebra, the 47-dimensional keep-set, the shrink rule, and the certificates in the public code repository.

• What is a map, not a proof

  Saying HARs 'are' the keep-set is a translation, not a theorem. The genome is not a 125-dimensional spin cube unless we build that dictionary and test it.

• HARs themselves

  HARs are real: short, mostly noncoding, human-accelerated DNA, enriched near brain-development genes. They are not a diagnosis and not destiny.

• QEGT is a statistical operator first

  The mixing-board math says cheaper programs get more weight. That is a softmax, not a proof that developing brains are quantum computers, and not a proof that 47/125 is a cognition cutoff.