Observer-Relative History, Spatial Escape, and Directional Ghost Ideals in Local Quantum Systems
Year: 2026
Type: preprint
Abstract: We formulate a static notion of observer-relative History for asymptotic families of finite local quantum systems. Starting from a norm-storage quotient and observer seminorms with independently bounded algebraic word depth and spatial radius, we define a fixed-complexity silent sector and prove that it is a closed two-sided *-ideal of the physical local corona. We then introduce a controlled CR witness cost based on projective tensor norms and define the History ideal by intersecting the silent sector with the closed ideal generated by uniformly controlled closure–residue (CR) families. For diagonal CR residues we prove an exact readout formula, ν_{N;K,R}(h_N) = ‖P_{N,R} h_N P_{N,R}‖, K ≥ 1, showing that readout depth collapses to one after a residue has returned to the diagonal sector. Consequently, nonzero diagonal History is characterized by global norm survival together with escape from every fixed observer compression. We further exhibit an explicit attenuated-shift model in which observer silence does not imply controlled CR provenance, proving, for every 0 < λ < 1, J_hist^(λ) ⊊ N_obs^(λ). The associated recovery radius therefore diverges along every subsequence on which the residue norm remains uniformly bounded away from zero. Under coarse-disjoint-union hypotheses, the physical local corona embeds isometrically into the uniform-Roe corona. Diagonal History then yields vanishing of the corresponding limit operator in the observer direction and hence membership in the associated directional ghostly ideal. Finally, under Controlled Normalizer Richness, diagonal saturation of the full History ideal is equivalent to relative geometricity, defined by density of finite-propagation History elements. The stronger relative equality with the external ghostly ideal remains an open CR-exhaustivity problem. No causal time, Lieb–Robinson dynamics, or Page-time identification is assumed in the present static theory.
Author: Tagawa, Katsuya
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221937579
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