arrowOfTime
plain-language theorem explainer
J-cost minimization selects a preferred direction for time evolution under unitary dynamics. Researchers reconciling quantum reversibility with thermodynamic irreversibility would reference this when discussing the emergence of the arrow of time. The declaration is a direct string assignment encoding the Recognition Science resolution to the puzzle.
Claim. J-cost minimization selects a direction: forward evolution proceeds from low to high J-cost configurations while the reverse requires special conditions. Entropy increase corresponds to movement toward higher J-cost states and remains thermodynamic rather than fundamental.
background
The QFT unitarity module derives quantum unitarity from ledger conservation, which preserves information and forces probability conservation. J-cost is the cost of any recognition event, defined as Cost.Jcost on the state and proven non-negative in upstream observer forcing. Related upstream results include the derived cost from multiplicative recognizers and the recognition-weighted stellar assembly structure.
proof idea
This is a definition that directly assigns the string 'J-cost minimization selects a direction' as the RS answer. No lemmas are applied and no tactics are used; the body is a one-line textual anchor inside the unitarity section.
why it matters
It supplies the RS mechanism linking unitary reversibility to observed entropy increase inside the ledger-conservation derivation of unitarity. The module targets information conservation as the origin of unitarity, and this definition closes the explanatory step from reversibility to the thermodynamic arrow. It touches the open question of how ledger extension across horizons resolves information loss without violating reversibility.
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