The Fano brane fabric is auxetic with Poisson ratio ν = −1 (Paper XXV). Auxetic materials are shape memory materials: because lateral dimensions expand rather than contract under longitudinal loading, any deformation of the material is self- reinforcing rather than self-dissipating, and the memory of past deformations persists far longer than in conventional elastic media. We show that the ν = −1 auxetic property of the brane fabric endows spacetime with an anomalously large capacity for retaining the imprint of past cosmological events, operating at all scales above the Planck length. The mechanism is quantitative: the eective relaxation time of any metric perturbation in the auxetic brane is τeff= τrelax/|1 + ν|; at ν = −1 this diverges, making the memory retention time formally innite bounded only by the nite age of the universe and the specic damping mechanisms of each perturbation mode. Five concrete consequences follow. (1) CMB anomalies. The Axis of Evil (preferred orientation in the ℓ= 2, 3 multipoles) and the Cold Spot (anomalous −70 µK region, ∼10◦radius) are retained imprints of the initial nucleation event and the H+/H−bulk encounter (Paper XXIII) that would smooth out in conventional (ν > 0) spacetime but are preserved by auxetic shape memory. (2) Gravitational wave memory enhancement. The Christodoulou memory eect (permanent test-particle displacement after a gravitational wave passes) is enhanced in the auxetic brane: the transverse expansion locked in by the GW does not relax, giving a GW memory signal larger and more persistent than in standard GR. (3) BAO peak sharpness. Baryon acoustic oscillation peaks in the CMB power spec- trum are subject to Silk damping (∝e−l2σ2 D/r2 s). In the auxetic brane, acoustic memory is retained longer Silk damping is partially suppressed giving sharper BAO peaks at high ℓ(ℓ≳500) compared to the standard ΛCDM prediction. This is measurable by Simons Observatory, CMB-S4, and CMB-HD. (4) Entanglement decoherence suppression. The brane memory thread (Paper XXXIV) responsible for quantum en- tanglement is mechanically reinforced by the auxetic fabric. Entanglement decoherence times are enhanced by the factor 1/|1 + ν| →∞, explaining why quantum coherence in the early universe persisted long enough to generate the primordial perturbation spec- trum. (5) Holographic information retention. The black hole information paradox is resolved in the auxetic brane: information encoded as brane deformations is not lost but... Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.
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