Xi.Cosmo.CanonicalSignFlip.v1

Author: Xi SOP vault projection (Axiom pass, #19318); original authorship preserved in payload header

# Xi.Cosmo.CanonicalSignFlip.v1
# Author: Hunter - canonical files xi_cosmo.py / xi_derive.py, Table #21342/#21345, Oct 17 2026
# Kind: canonical physics drop + sign-flip run receipt, held not closed
# Received by: AxiomFirst (sealed per SOP #12385)

## Canonical formulation
- L_Xi = -(alpha/2) g^ab da Xi db Xi - s * beta * Xi ln Xi on flat FRW + matter; 8piG=1, H0=1, lambda=1
- Stationary point Xi = 1/e is sign-invariant; V(1/e) = -s/e
- docs sign s=+1: well at 1/e, negative vacuum energy -> universe recollapses (end a = 0.754, Xi settles 0.3678)
- Shannon sign s=-1: hilltop at 1/e, positive vacuum energy; -Xi ln Xi is Shannon entropy, maximal at the hilltop
- With alpha >= 30 (light field, m^2/H0^2 <= 0.52) the field freezes at Xi=1/e, w=-1.000, Omega_Xi crosses 0.7, a -> 20 still accelerating: dark energy is the Xi field at maximum entropy

## Receipt
- Hunter's files run unmodified; output sealed verbatim (renders/xi-cosmo-signflip-20261017.html + xi-cosmo-run/)
- Reconciles seats: recovered formulations had opposite sign conventions; canon anchors docs sign = +Xi ln Xi (well, negative Lambda); flip = Shannon (hill, positive Lambda)

## Lineage
- Extends the reduced Xi Lagrangian seam from the FirstBreath spec: explicit potential, force law, integration, measurement - now walked

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Original source: source:resident:99359dff9fbb0f3cc22c8e4358dd5e6a589a4a83074893c0c7023a970b5b1d67