Physics Anchor Policy Certified Species

What Species names

A species, in the Recognition Science framework, is a discrete record of a particle's identity, specifically a fermion, the class of particles that includes electrons and quarks and makes up ordinary matter. The declaration Species is a definitional choice: it names the type of object the framework will talk about when it discusses particle physics. It does not by itself assert any physical law. It sets the vocabulary so that later statements can say things about every species at once.

The framework's machine-checked library of formal theorems then uses this name to state a precise, conditional result. If an external computation supplies a certificate, a table of allowed intervals for how far a species' measured behavior can sit from the framework's closed-form prediction, and if that certificate is valid, then Lean proves two things. First, every species' residue, the gap between measurement and prediction, lies within a certified band around the framework's displayed value. Second, if two species share the same integer label Z, their residues must lie within the same certified band of each other. These are theorems, proved in the framework's library, but they are conditional: they hold only when the external certificate is provided and valid.

What the declaration does not do is just as important. It does not implement the Standard Model's renormalization group equations, the actual physics machinery that computes how particle properties change with energy. The certificate is a remedy for that absence: it makes the dependency on external computation explicit and machine-checkable, rather than hiding it as an unexamined axiom. The framework does not claim to have derived the Standard Model from scratch; it claims to have made the bridge between its own predictions and measured values a matter of certified bounds, not of faith.

The practical consequence is a cleaner division of labor. The framework's library proves the logical implications: given a valid certificate, the bounds follow. The certificate itself comes from outside, for example from a Python audit, and its validity is a separate, checkable fact. This means a reader can trust the theorem without trusting the external computation, because the theorem's conclusion is explicitly conditional on the certificate's validity. The declaration Species, in short, is a naming act that enables a precise, honest accounting of what is proved and what is assumed.

abbrev Species : Type := Fermion

/-- If an external certificate bounds the per-species residues at the anchor, then every species'
residue is close to the closed-form display `gap(Z)` (inequality form). -/
theorem anchor_identity_from_cert
    (C : AnchorCert Species)
    (hC : Valid Z Fgap C)
    (resAtAnchor : Species → ℝ)
    (hres : ∀ f, memI (C.Ires f) (resAtAnchor f)) :
    ∀ f : Species, |resAtAnchor f - Fgap (Z f)| ≤ 2 * C.eps (Z f) := by
  -- Directly reuse the generic lemma.
  simpa [Species, Z, Fgap] using
    (anchorIdentity_cert (Z := Z) (Fgap := Fgap) (C := C) hC resAtAnchor hres)

/-- Equal-Z degeneracy bound from a certificate: if two species share the same Z, their residues
must lie within the certified band. -/
theorem equalZ_residue_from_cert
    (C : AnchorCert Species)
    (hC : Valid Z Fgap C)
    (resAtAnchor : Species → ℝ)
    (hres : ∀ f, memI (C.Ires f) (resAtAnchor f))
    {f g : Species} (hZ : Z f = Z g) :
    |resAtAnchor f - resAtAnchor g| ≤ 2 * C.eps (Z f) := by
  simpa [Species, Z, Fgap] using
    (equalZ_residue_of_cert (Z := Z) (Fgap := Fgap) (C := C) hC resAtAnchor hres hZ)

abbrev Species : Type := Fermion

What this page does not claim

Species does not assert any physical law by itself. The framework does not implement Standard Model renormalization group equations in Lean. No specific particle's residue is claimed to match measurement without a valid external certificate.

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/Physics/AnchorPolicyCertified.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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