ledger_is_self_grounded
plain-language theorem explainer
The self-grounding property of the ledger asserts that the J-cost function is non-negative for every positive real number, supplying an internal existence criterion with no external substrate required. Researchers examining the Recognition Science dissolution of the simulation hypothesis cite this as the property that collapses any real-versus-simulated distinction. The definition is a direct encoding of the non-negativity condition drawn from the cost framework.
Claim. The ledger is self-grounded when $J(x)geq 0$ for all $x>0$, where $J$ is the cost function satisfying $J(x)=0$ precisely at the zero-defect state $x=1$.
background
The module IC-004 treats the simulation hypothesis as meaningless because the ledger is reality itself with no separate substrate. The J-cost function, defined in the RS-native measurement core, quantifies the recognition defect of a state $x$. Upstream results from the cost module establish that this function is non-negative, with equality only at the fixed point $x=1$ corresponding to zero defect.
proof idea
The definition directly encodes the non-negativity statement for J-cost. It serves as a one-line interface discharged by the subsequent theorem via the established non-negativity lemma from the Cost module.
why it matters
This definition supplies the key property for theorem IC-004.5 asserting ledger self-grounding and supports the module claim that the simulation hypothesis dissolves because the ledger provides its own existence criterion. It connects to the forcing chain landmarks T5 J-uniqueness and the phi fixed point, where the only zero-cost state grounds existence. The property feeds into the downstream result that RS existence holds iff J-cost vanishes.
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