Constants Fine Structure Constant Alpha Lock In Unit Interval

A misnamed lock

The fine-structure constant α is the dimensionless number, about 1/137, that sets the strength of electromagnetic interactions. It is one of the most precisely measured quantities in physics. The Recognition Science library contains a declaration named alphaLock_in_unit_interval, and its name invites a guess: that it pins down α itself. That guess is wrong, and the library's own documentation corrects it in the first lines of the module.

The declaration proves a narrow analytical fact. It states that a certain quantity, written α_lock, lies strictly between 0 and 1. A companion theorem gives the explicit form: α_lock = (1 − 1/φ)/2, where φ is the golden ratio, about 1.618. Numerically, α_lock is about 0.19. The proof is a short chain of inequalities, and the fact is a theorem in the machine-checked library of formal theorems, meaning a computer verified every step.

What α_lock is not: it is not the electromagnetic fine-structure constant. The library says so without ambiguity. α_lock is the information-limited-gravity kernel exponent, a parameter in a different part of the framework. The value 0.19 is nowhere near 1/137, and no conversion between the two exists in the repository. The module header records that an earlier claim, that α_lock resolves the question of what determines α, has been retracted.

The honest position on the real α sits in a different module, Constants.AlphaGenesis. There, the exact value of α⁻¹ at zero energy is described as a free boundary datum within the framework, and the first-order construction value is excluded by measurement. The lesson a reader can carry away: a name in a formal library is a label, not a proof. The declaration proves a small, true fact about a different number, and the framework's own files are the ones drawing the line.

/-- α_lock lies in the open unit interval. -/
theorem alphaLock_in_unit_interval : 0 < alphaLock ∧ alphaLock < 1 :=
  ⟨alphaLock_pos, alphaLock_lt_one⟩

/-- α_lock structure: `alphaLock = (1 − 1/φ)/2` with unit-interval bounds.
    This is a φ-structural fact about the ILG kernel exponent. It does NOT
    determine the EM fine-structure constant; see the module header. -/
theorem alphaLock_structure :
    0 < alphaLock ∧ alphaLock < 1 ∧
    alphaLock = (1 - 1 / phi) / 2 :=
  ⟨alphaLock_pos, alphaLock_lt_one, rfl⟩

@[deprecated alphaLock_structure (since := "2026-07-06")]
alias fine_structure_derived := alphaLock_structure

/-- α_lock structure: `alphaLock = (1 − 1/φ)/2` with unit-interval bounds.
    This is a φ-structural fact about the ILG kernel exponent. It does NOT
    determine the EM fine-structure constant; see the module header. -/
theorem alphaLock_structure :
    0 < alphaLock ∧ alphaLock < 1 ∧
    alphaLock = (1 - 1 / phi) / 2 :=
  ⟨alphaLock_pos, alphaLock_lt_one, rfl⟩

@[deprecated alphaLock_structure (since := "2026-07-06")]
alias fine_structure_derived := alphaLock_structure

What this page does not claim

This answer does not claim that α_lock equals the fine-structure constant or that any conversion between them exists. This answer does not claim that the exact value of α is determined anywhere in the framework.

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/Constants/FineStructureConstant.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.

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