KSCCN VOLUME III · 31 AUGUST 2026 Observable Shapes of a Persian-Rug Substrate What multi-sector quantum geometry looks like from inside the apparatus

Syed Muntasir Mamun

Published Aug 31, 2026• 0 citations

Abstract

Volumes I and II defined a rug substrate and computed a holonomy residual on a six-site chain (Mamun, 2026a; 2026b). The present volume asks a different question: if that space is real, what shapes can an observer record? Shape is not a picture of a manifold. It is the image of a finite list of maps from laboratory paths into numbers, curves and flags. Five observable shapes are classified. (S1) The occupancy constellation: the image of Λ in a four-dimensional ledger. (S2) The wall complex: the arrangement of regime crossings in control space. (S3) The holonomy curve: ΔF as a function of knot angle and winding. (S4) The theme flag: an invariant that stays put under legal walls and drops under detectors. (S5) The measure and echo shapes: correlator profiles, revival envelopes, and a finite-N singularity spectrum. On the Volume II toy these shapes are already distinct. The constellation separates in the (gap, lT) plane and crowds in the (IPR, d2) plane. The holonomy curve is monotone in ε, with an identity-wall intercept of 0.020. The theme flag is binary at legal knots and leaks to we = 0.882 at a detector. Echo envelopes and connected ZZ profiles are sector-specific; d2 is not. The laboratory translation is a short menu: report the shape, not only the fidelity to a target computational state. A single exponential T2, a single Berry phase on one Bloch sphere, and a single Lindblad rate are the shapes this ontology predicts one will not see once walls are present. C S Also available on Academia.edu: https://www.academia.edu/attachments/134081814/download_file?s=portfolio

DOI: 10.5281/zenodo.22990198

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