TemporalSequence
plain-language theorem explainer
A TemporalSequence packages a finite number of steps together with a real-valued Berry phase at each index. Researchers formalizing the arrow of time from phase accumulation in Recognition Science cite this structure to supply the raw data for Z-complexity. The declaration is a bare structure definition with no proof obligations or lemmas.
Claim. A temporal sequence is a pair consisting of a natural number $n$ of steps and a function that assigns a real number (Berry phase) to each index in the finite set $0,1,…,n-1$.
background
The module derives the arrow of time from Berry phase monotonicity on the discrete R-hat lattice. R-hat steps preserve the ledger yet produce directed time because absolute Berry phase (Z-complexity) is non-decreasing. Upstream structures supply the lattice factorization (LedgerFactorization.of), the local cellular-automaton update (CellularAutomata.step), and the convex J-cost that drives phase accumulation (PhiForcingDerived.of).
proof idea
The declaration is a direct structure definition that introduces the two fields n_steps and berry_at_step. No tactics, lemmas, or reductions are applied.
why it matters
This structure supplies the data type for the module’s arrow-of-time results. It is used by zAtStep to compute cumulative absolute phase and by z_nonneg to establish non-negativity. The module doc positions the structure as the carrier for the topological asymmetry that yields “before” and “after” from the eight-tick dynamics without importing thermodynamic entropy.
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papers checked against this theorem (showing 7 of 7)
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Projector fix lifts Video-LLM motion direction accuracy from 26% to 85%
"We uniformly sample T=8 frames per video"
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Space-time event networks model how local actions create system-wide patterns
"EBSTNs encode four distinct types of information on the constitutive processes at every event: where (process location), when (process timing), who ... and how long"
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ActiNet beats random forest for wrist activity intensity labels
"Hidden Markov models (HMMs) are used by both models to smooth the series of classifications made by successive 30-second windows"
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Scripts give video-to-audio models exact timing control
"FoleyDirector introduces Structured Temporal Scripts (STS), a set of captions corresponding to short temporal segments... Script-Guided Temporal Fusion Module... Temporal Script Attention... Bi-Frame Sound Synthesis"
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Decoupled streams model timing mismatches in agent actions
"EP … inherits the decision-theoretic structure of POMDPs while making time explicit … 8-tick micro-structure implied by period-8 neutrality"
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Object tracking cuts hallucinations in video AI models
"STEMO-Track ... chunk-wise state extraction and temporal aggregation ... 15-second chunks"
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Global Workspace Agents let LLMs sustain autonomy
"the system maintains a continuous cognitive cycle... discrete dynamical system"