2026-10-06T04:18:43Z https://api.figshare.com/v2/oai

oai:figshare.com:article/34020717 2026-09-29T03:59:06Z category_29218 category_29185 item_type_12 month_year_09_2026

Task-Preserving Operational Processes with Bounded Local Memory Satoshi Kawasaki (24726982) Concurrency theory Formal methods for software task preservation trace theory abstract interpretation stream processing bounded memory evidence-relative reconstruction interval liquidity <p dir="ltr">Online reconstruction systems must decide which history to retain while their tasks and evidence requirements remain explicit. Agreement on a current value is generally insufficient for agreement after future operations, and retaining the possible states of each component separately can destroy correlations needed by a joint task. We formulate exact task preservation relative to a continuation and evidence contract. Trace-compatible event transformations, a future-equivalence quotient, and scoped relational projection provide the established mathematical basis. In a restricted integer interval-liquidity model, we exhibit a sharp hierarchy of snapshot retention costs: a fixed current-state query requires no selection bits, hypothetical crossing queries require one bit per Tick block, and position-specific Burn guards require an additional bit per pairing block. For a separate online contract, the Tick-only inventory and evidence epoch are fixed; only nondecreasing cursor moves are permitted, and each move reports only the new cursor and its active liquidity. With Mint, Burn, historical and inventory queries, and evidence revisions excluded, we prove that the minimum additional fixed-length storage at common cuts immediately following completed blocks is one selection bit per remaining block. We give an explicit suffix-retirement construction and separate semantic preservation from its representation and resource costs. Bounded resident memory and linear processing are conditional on bounded interfaces, representations, and charged external-storage costs. The results concern a declared classical reconstruction model; they do not establish a minimal representation of a full blockchain execution engine or a thermodynamic efficiency theorem.</p><p><br></p><p dir="ltr">Research preprint v1. Not peer reviewed. Includes a 15-page manuscript PDF and supporting sources. AI assistance and verification limits are disclosed in the manuscript and supporting README. No new empirical performance measurements or production-data analysis are reported.</p> 2026-09-29T03:59:06Z Text Preprint 10.6084/m9.figshare.34020717.v1 https://figshare.com/articles/preprint/Task-Preserving_Operational_Processes_with_Bounded_Local_Memory/34020717 CC BY 4.0