numLedgerStates
plain-language theorem explainer
The definition fixes the cardinality of the discrete ledger state space at 256. Researchers deriving the physical Church-Turing thesis from Recognition Science ledger dynamics cite it to bound finite memory per tick. It follows immediately from the 8-phase structure by direct exponentiation in the natural numbers.
Claim. The number of possible discrete ledger states is $2^8$.
background
The module IC-003 derives the physical Church-Turing thesis from the discrete ledger structure in Recognition Science. Each ledger entry is a ratio governed by the 8-tick operator on a discrete phase space, with finite memory per tick bounded by the 8-phase structure. Transitions remain computable because the J-cost minimization maps finite states to finite states via a continuous function. Upstream results supply the collision-free property of empirical programs, the algebraic character of edge lengths from psi, the structure of mechanism design from sigma, and the explicit construction of mock theta phantoms.
proof idea
One-line definition that directly assigns the value 256 via exponentiation in the natural numbers.
why it matters
This definition supplies the finite cardinality required for the discrete state space in IC-003, ensuring that RS dynamics stay within Turing-computable bounds and inherit undecidability from the halting problem. It directly instantiates the eight-tick octave (T7) from the forcing chain, confirming that physical processes remain in BQP. No downstream uses are recorded yet, but the result closes the finite-memory step in the ledger-to-Turing reduction.
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