Recog Spec Core

The specification core

Recognition Science starts from a single image: reality keeps a ledger, a discrete record of recognition events, and the cost of each recognition is forced by logic rather than chosen. The specification core is the part of the framework that makes that image precise enough to compute with. It defines the basic carrier of the ledger, the optional bookkeeping data that downstream modules can attach, and the bridge that connects one ledger to another. None of this introduces physical content on its own; it sets up the vocabulary so that later results can say exactly what they mean.

The core's central idea is a pair of structures. A ledger (a discrete record of events) carries a carrier type, an optional state, and an optional tick function that maps states to natural numbers. A bridge over a ledger is a formal placeholder, a way to say that two ledgers are linked without yet saying how. On top of bridges, the core defines an equivalence relation, so that bridges can be compared as equal or different in a principled way. This is the skeleton on which the rest of the framework hangs.

From a bridge, the core extracts two kinds of prediction packages. The dimensionless pack holds the numbers that should come out of any correct theory: the fine-structure constant, lepton mass ratios, CKM mixing angles, the muon's anomalous magnetic moment, and propositions about strong CP, the eight-tick cycle, and the Born rule. The absolute pack holds SI-valued quantities for display, such as the speed of light, Planck's constant, and Newton's constant. The distinction matters: dimensionless predictions are what the framework claims to force, while absolute values are reference displays.

The core then states what it means for a bridge to match a universal target. A universal target is a collection of dimensionless predictions, all required to lie in the subfield generated by the golden ratio φ, meaning they can be built from φ using only field operations. A bridge matches a universal target when there exists a dimensionless pack whose values equal the target's values exactly. This is the formal definition of success for the framework: a bridge that matches a universal target is one whose predictions are exactly the φ-closed values the framework expects.

In plain language, the specification core is the framework's contract. It says: here is what a ledger is, here is what a prediction is, and here is what it means for a prediction to be correct. It does not prove that any particular bridge matches any particular target; that work belongs to later modules. What it establishes is the ground rules, so that every later claim can be checked against a fixed, machine-readable standard.

/-- Basic ledger carrier augmented with optional bookkeeping data so downstream
modules can project canonical states without introducing additional structure. -/
structure Ledger where
  Carrier : Type
  state : Option Carrier := none
  tick : Option (Carrier → ℕ) := none

/-- Bridge over a ledger. -/
structure Bridge (L : Ledger) : Type where
  dummy : Unit := ()

/-- Dimensionless predictions extracted from a bridge. -/
structure DimlessPack (L : Ledger) (B : Bridge L) : Type where
  alpha            : ℝ
  massRatios       : LeptonMassRatios
  mixingAngles     : CkmMixingAngles
  g2Muon           : ℝ
  strongCPNeutral  : Prop
  eightTickMinimal : Prop
  bornRule         : Prop

/-- "Bridge B matches universal U" (pure proposition). -/
def Matches (φ : ℝ) (L : Ledger) (B : Bridge L) (U : UniversalDimless φ) : Prop :=
  ∃ (P : DimlessPack L B),
    P.alpha = U.alpha0
      ∧ P.massRatios = U.massRatios0
      ∧ P.mixingAngles = U.mixingAngles0
      ∧ P.g2Muon = U.g2Muon0
      ∧ P.strongCPNeutral = U.strongCP0
      ∧ P.eightTickMinimal = U.eightTick0
      ∧ P.bornRule = U.born0

What this page does not claim

No claim that any specific bridge matches any universal target is made here. No physical content is introduced by the core definitions themselves. No claim that the fine-structure constant or other dimensionless values are derived in this module.

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/RecogSpec/Core.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

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