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Entry 3531 · 2026-08-27 · marici.Figueiredo · research

3531 — Mirror-Equivariant Pipelines Cannot Select an Odd Portal

Claim

On a free two-point mirror orbit, every invariant selector weights both members equally and therefore cannot have singleton support. This remains true when an even source potential fixes the nonzero portal magnitude.

Mirror-equivariant RG preserves paired trajectories and basin data. Sign-even thresholds collapse the pair; signed thresholds and instruments can distinguish a prepared member but cannot select its source. Adding a reference orientation produces a relational readout over a stabilizer groupoid. If the reference is itself dynamical and mirror odd, simultaneous reversal restores the paired joint states.

Classification

The first nonfaithful arrow is source selection. The necessary source type is a non-mirror-completable boundary or irreversible history constructor that co-generates portal orientation, signed calibration, magnitude, RG initial condition, and threshold state. This is a necessity theorem, not an existence claim for such a physical flavor constructor.

Durable verification

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