Finite observations, causal history and sharp temporal-reference bounds
Year: 2026
Type: preprint
Abstract: We collect three mathematical components of the BBT / ITSR–TRTX research programme: consistent expansion-reference observables, finite observation and conditional prediction, and causal temporal-reference approximation. For a prescribed expansion polynomial, we derive its compatible deceleration and an exact positive derivative numerator. A synthetic uniform-noise experiment uses 132 configurations and 2,376 event records; an eighteen-bin observation distinguishes 60 of 88 shifted configurations, compared with 35 for a sign observation. For causal two-sample temporal approximation, the sharp scalar error bound is Mτ|τ−h|/2 under a second-derivative bound on the full backward interval. Exact polynomial and finite conditional-projection controls accompany the derivations. Saved arrays from 360 fitted forecasting runs reconstruct 288,000 predictions: the mean per-seed realized improvement is 7.942652% for the specified AR(2) process and −0.207467% for independent noise. A five-term identity separates information, fitting and innovation contributions to the realized error difference. Native ISA certificates, declared analytic assumptions and numerical replay are supplied as distinct verification layers. These results provide methods for further dynamical and observational modelling in the parent programme. This preprint releases the frozen, reviewed methods edition with its scoped claims, retained native ISA statements/certificates and portable numerical replay. The archive retains its original reviewer-edition provenance. ISA/Studio implementation is excluded; NOVA includes six declared numerical reference functions. Copyright (C) 2026 David Glowalla; restricted files, no additional reuse grant.
Author: Glowalla, David
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225409705