IndisputableMonolith.Verification.UnitsFromAnchorsRescaleCert
Certificate module showing that rescaling a pair of anchors by a positive factor s leaves the derived units data unchanged up to the built-in units rescaling. Consistency of the zero pattern is automatic: if a1 vanishes then a2 vanishes, and the same holds after multiplying by s. Downstream audit certificates cite it to obtain speed and units-equivalence invariance without redoing the ratio algebra.
claimGiven anchors $(a_1,a_2)$ and a scale $s$, form rescaled anchors $(s a_1, s a_2)$. The zero-consistency implication $a_1=0\Rightarrow a_2=0$ is preserved, the speed extracted from the anchors is invariant under this rescaling, and the units package built from the anchors equals the units package of the original anchors after the standard units rescaling by $s$.
background
In the Recognition Spec layer, physical units are not free parameters; they are reconstructed from a pair of anchor quantities $(a_1,a_2)$ together with a consistency constraint that forbids a nonzero second anchor when the first vanishes. From those anchors one extracts a characteristic speed and a full units package used by later verification certificates.
This module sits in the Verification domain and packages the elementary scaling facts about that reconstruction. The only external dependency is the RecogSpec specification module, which supplies the anchor and units types and the maps that turn anchors into speed and units data.
The intended regime is positive (or at least nonzero) scale factors $s$, so that the geometric content of the anchors is unchanged and only the overall unit choice moves.
proof idea
The module is a small certificate bundle, not a deep derivation. It defines the pointwise rescaling of anchors, then records three facts: consistency of the zero pattern under multiplication by $s$; invariance of the speed extracted from anchors; and equality of the units package of the rescaled anchors with the units-rescaled package of the original anchors. Each step is elementary algebra on the Spec constructors, packaged so downstream certificates can import a single named object rather than rebuild the scaling lemmas.
why it matters in Recognition Science
The immediate consumer is the Anchors-Rescaling Equivalence Certificate, which records that rescaling anchors by a positive $s$ does not change their units-equivalence class under the speed equivalence on anchors. That certificate deliberately avoids re-proving ratio algebra: it derives speed invariance from the already-certified facts in this module, then lifts them to the quotient.
In the broader Recognition verification stack this closes a units-gauge loophole: any two anchor pairs that differ only by an overall scale must yield the same physical units class, so later claims about constants, speeds, and ladder normalizations cannot depend on an arbitrary choice of anchor magnitude.
scope and limits
- Does not define the anchor or units types; those come from RecogSpec.Spec.
- Does not prove full anchors-equivalence on the quotient; that is left to AnchorsRescaleEqvCert.
- Does not address non-constant or spacetime-dependent rescalings.
- Does not derive numerical values of c, hbar, or G from anchors.
- Does not treat s = 0 as a physically meaningful gauge move.