Masses Mass Genesis T10 Posted Load Scale

Posted load scale

In the Recognition Science account of how particles get their masses, the T10 posted-load scale is a theorem about the size of a ledger, a discrete record of events. The framework models a particle's mass as a settlement, a difference between two ledger entries. The T10 result says that when the ledger's occupation is Boolean, meaning each entry is simply on or off, the settlement amplitude is forced to be exactly 1. A settled anchor, a reference point whose window equals that Boolean difference, cannot carry a doubled scale of 2. The theorem is proved in the framework's machine-checked library of formal theorems, with no unproved assumptions added.

The proof works by showing that a Boolean difference settlement window, where every entry is 0, 1, or -1, forces the window amplitude to be 1 whenever it is positive. This holds for settled anchors directly, and also for emitted photon states, where the window is read as a settled pattern. The library proves that a doubled scale of 2 is incompatible with a Boolean window, and that the same unit-scale law applies to emitted states. These are the theorem's positive results: unit scale is forced, doubled scale is rejected.

The T10 module also constructs a specific counterexample, a worldline pattern with a gap-one two-phase mode. This pattern is a settled Boolean unit seed, meaning it satisfies the conditions for unit scale, yet its load topology ratio is not equal to 1. The exact residual proposition, called SettledLoadIsPostedLoad, states that unit Boolean posting forces the load topology ratio to be 1. The library proves this proposition is false, so the wall stands: the residual claim remains open as a forcing parent. The module therefore establishes a precise boundary, what is forced and what is not, rather than claiming a complete derivation.

/-- **Boolean unit-scale law.** A positive settled anchor whose anchor window
is Boolean-valued must post at amplitude `1`. -/
theorem settledAnchor_boolean_forces_unitAmplitude
    {a : ℝ} {ψ : LightPattern (Fin 8)}
    (hwin : SettledAnchorWindow a ψ)
    (hbool : BooleanDifferenceSettlementWindow (ψ.window 0))
    (ha : 0 < a) : a = 1 := by
  have hphase0 := settledAnchor_phase0 hwin
  have hb : IsBooleanPostingAmplitude (ψ.window 0 0) := hbool 0
  rw [hphase0] at hb
  exact ofReal_eq_one_of_boolean_pos ha hb

/-- **Doubled-scale decoy.** `SettledAnchorWindow 2` is never Boolean-valued:
its commit entry is `2`, outside `{0,±1}`. -/
theorem settledAnchorWindow_two_not_boolean
    {ψ : LightPattern (Fin 8)}
    (hwin : SettledAnchorWindow 2 ψ) :
    ¬ BooleanDifferenceSettlementWindow (ψ.window 0) := by
  intro hbool
  have hunit :=
    settledAnchor_boolean_forces_unitAmplitude hwin hbool (by norm_num)
  norm_num at hunit

/-- **CONSTRAINT+WITNESS wall.** Unit Boolean posted settlement does not force
`loadTopologyRatio = 1`. The gap-one worldline is the discriminating decoy
against treating Boolean unit scale as topology-matched load. -/
theorem settledLoadIsPostedLoad_wall :
    ¬ SettledLoadIsPostedLoad := by
  intro hall
  obtain ⟨ψ, hcarrier, hunit, hbool, hratio⟩ :=
    exists_unitBooleanSettled_loadTopologyRatio_ne_one
  exact hratio (hall ψ hcarrier hunit hbool)

What this page does not claim

This answer does not claim that the T10 module derives any particle mass value. This answer does not claim that unit Boolean posting alone forces the load topology ratio to be 1. This answer does not claim that the framework's mass law is a theorem of conventional physics.

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/Masses/MassGenesis/T10PostedLoadScale.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: