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91 lines
2.9 KiB
Text
91 lines
2.9 KiB
Text
import Mathlib.Data.Fin.Basic
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namespace Semantics
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/-- Genome18: 18-bit semantic micro-ISA for equation forest routing state.
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Structure: 6 bins × 3 bits = 18 bits (8^6 = 262,144 states)
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Bin meanings:
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- muBin: mutation / drift bin (routing load)
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- rhoBin: verification pressure bin (routing efficiency)
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- cBin: connectance bin (geometry / route neighborhood)
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- mBin: compression residue / modularity bin (entropy)
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- neBin: observer mass / effective sample bin (entropy)
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- sigmaBin: sigma / fitness proxy bin (entropy)
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This represents the routing state class:
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- Where this object is in the forest
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- How risky it is
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- How compressed it is
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- How lawful it appears
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- Which route moves are worth trying next
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This is the FPGA LUT address layer.
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-/
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structure Genome18 where
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muBin : Fin 8 -- mutation / drift (routing load)
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rhoBin : Fin 8 -- verification pressure (routing efficiency)
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cBin : Fin 8 -- connectance (geometry / route neighborhood)
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mBin : Fin 8 -- compression residue / modularity (entropy)
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neBin : Fin 8 -- observer mass / effective sample (entropy)
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sigmaBin : Fin 8 -- sigma / fitness proxy (entropy)
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namespace Genome18
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/-- Compute 18-bit address from Genome18 state.
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Address calculation:
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addr = muBin * 32768 + rhoBin * 4096 + cBin * 512 + mBin * 64 + neBin * 8 + sigmaBin
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This is the O(1) LUT route lookup address for FPGA routing.
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-/
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def addr (g : Genome18) : Nat :=
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g.muBin.val * 32768 +
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g.rhoBin.val * 4096 +
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g.cBin.val * 512 +
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g.mBin.val * 64 +
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g.neBin.val * 8 +
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g.sigmaBin.val
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/-- Theorem: addr is injective (Theorem 5 - 18-bit injective encoding).
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This proves that distinct Genome18 states map to distinct addresses,
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which is required for correct LUT lookup.
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-/
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theorem addr_injective : Function.Injective addr := by
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intro g h h_eq
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cases g with
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| mk mu rho c m ne sigma =>
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cases h with
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| mk mu' rho' c' m' ne' sigma' =>
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simp only [addr] at h_eq
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have h1 : mu = mu' := by apply Fin.ext; omega
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have h2 : rho = rho' := by apply Fin.ext; omega
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have h3 : c = c' := by apply Fin.ext; omega
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have h4 : m = m' := by apply Fin.ext; omega
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have h5 : ne = ne' := by apply Fin.ext; omega
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have h6 : sigma = sigma' := by apply Fin.ext; omega
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simp [h1, h2, h3, h4, h5, h6]
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/-- Theorem: addr values are in range [0, 262143].
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This proves the address fits in 18 bits.
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-/
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theorem addr_range (g : Genome18) : g.addr < 262144 := by
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simp only [addr]
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have mu_bound : g.muBin.val ≤ 7 := Fin.is_le g.muBin
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have rho_bound : g.rhoBin.val ≤ 7 := Fin.is_le g.rhoBin
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have c_bound : g.cBin.val ≤ 7 := Fin.is_le g.cBin
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have m_bound : g.mBin.val ≤ 7 := Fin.is_le g.mBin
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have ne_bound : g.neBin.val ≤ 7 := Fin.is_le g.neBin
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have sigma_bound : g.sigmaBin.val ≤ 7 := Fin.is_le g.sigmaBin
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omega
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/-- Default Genome18 state (all zeros). -/
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def default : Genome18 :=
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{ muBin := 0, rhoBin := 0, cBin := 0, mBin := 0, neBin := 0, sigmaBin := 0 }
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end Genome18
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end Semantics
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