Lnal Registers Aux5

The Aux5 register block

In computing, a register block is a fixed set of named slots that a program uses to hold working values. The Recognition Science declaration Aux5 defines one such block for the LNAL execution state, the low-level virtual machine that runs recognition computations. The block carries five fields: a rolling signed neighbor sum, an active token count, a hydration proxy, a phase-locked indicator, and one reserved slot. Each field is a plain integer except the phase indicator, which is a boolean true or false.

The block pairs with a second register block called Reg6, which holds the main recognition indices: a log-frequency index, a curvature index, a parity bit, a time-bin index, a transverse mode index, and an entanglement flag. Aux5 holds the auxiliary working state that does not fit those principal indices. The two blocks together form the complete execution state of the LNAL virtual machine.

The declaration also defines a zero value for Aux5, setting every integer field to 0 and the boolean to false, which serves as the initial state. It defines a well-formedness predicate that requires all integer fields to lie within signed 32-bit range, and it defines a parity invariant that couples the parity bit and entanglement flag from Reg6 to the phase-locked indicator in Aux5. These definitions are part of the machine-checked library of formal theorems, meaning the framework's library proves the stated properties of these structures.

What Aux5 does not claim is physics. The docstrings label the neighbor sum, hydration proxy, and reserved slot as domain-defined, which means their meaning is left to the application layer, not fixed by the declaration. Aux5 does not assert that these fields correspond to any measured physical quantity, nor does it prove that the parity invariant is actually enforced by the virtual machine's operations. It only defines the data structure and the predicates that describe its intended shape.

structure Aux5 where
  /-- Rolling signed neighbor sum (domain-defined) -/
  neighborSum : Int
  /-- Active token count (0/1 expected by invariants) -/
  tokenCt     : Int
  /-- Hydration/free-volume proxy (domain-defined) -/
  hydrationS  : Int
  /-- Phase-locked indicator (core/glassy) -/
  phaseLock   : Bool
  /-- Reserved domain-specific slot -/
  freeSlot    : Int

@[simp] def zero : Reg6 :=
  { nuPhi := 0, ell := 0, sigma := 0, tau := 0, kPerp := 0, phiE := false }

/-- Combined well-formedness for a register + auxiliary pair. -/
def WellFormed (r : Reg6) (a : Aux5) : Prop := r.inI32 ∧ a.inI32 ∧ parityInvariant r a

/-- Parity coupling: (sigma + phiE) mod 2 equals phaseLock. -/
def parityInvariant (r : Reg6) (a : Aux5) : Prop :=
  ((parity2 r.sigma + bit r.phiE) % 2) = bit a.phaseLock

What this page does not claim

Aux5 does not assign physical meaning to the domain-defined fields. Aux5 does not prove that the parity invariant is enforced by the virtual machine's operations. Aux5 does not establish any property about the recognition cost function or the forcing chain.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/LNAL/Registers.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: