IndisputableMonolith.Verification.AnchorsRescaleEqvCert
Verification module certifying that two anchor packs related by a positive rescaling factor induce equivalent RS unit systems (with c held fixed). Auditors of the units-from-anchors surface cite it to confirm scale invariance is an equivalence, not a one-way map. The module packages the equivalence certificate around the existing units-rescaled relation.
claimRescaling recognition anchors by any $s > 0$ yields $RSUnits$ packs related by the units-rescaled equivalence (speed of light $c$ fixed), so physical predictions are invariant under anchor scale.
background
Recognition Science fixes dimensionless structure (phi-ladder, J-cost, eight-tick period) while dimensionful units are read off from chosen anchors. The certified surface therefore must treat units as defined only up to scale.
The upstream units-from-anchors rescaling certificate records that multiplying anchors by a positive factor $s$ produces a UnitsRescaled relation between the resulting $RSUnits$ packs, with $c$ held fixed. That makes the invariance explicit as a directed certificate.
This module sits in the Verification domain and imports the RecogSpec specification together with that rescaling certificate, so the equivalence form of the same invariance can be stated on the audit surface.
proof idea
Definition and certificate packaging module rather than a deep proof development. It wraps the upstream units-from-anchors rescaling certificate into an equivalence-shaped audit object: rescaling anchors by $s > 0$ and the inverse rescaling witness the two directions of the units-rescaled relation between $RSUnits$ packs. No independent analytic argument beyond that packaging.
why it matters in Recognition Science
Closes the scale-invariance story on the certified surface: units derived from anchors are not merely rescalable one way, but equivalent under positive rescalings. That is required for any claim that RS predictions are anchor-scale independent while $c$ stays fixed.
Downstream consumers of the verification layer use this when discharging audit obligations that mention units-up-to-scale. It complements the directed Units-from-Anchors Rescaling Certificate by presenting the same fact as an equivalence certificate named for anchors-rescale.
No further used-by edges are recorded in the graph snapshot; the module is a leaf audit artifact rather than a lemma feeding the forcing chain (T0–T8).
scope and limits
- Does not derive the numerical values of c, hbar, or G from first principles.
- Does not alter dimensionless RS constants (phi, alpha band, mass rungs).
- Does not prove uniqueness of anchors, only equivalence under positive rescaling.
- Does not address time-varying or non-global rescaling factors.
- Does not feed the T0–T8 forcing chain directly.