no_lost_dof
plain-language theorem explainer
The declaration asserts that interior degrees of freedom in a holographic region are fully encoded on the boundary surface with no independent interior information. Physicists deriving information bounds from ledger projections in Recognition Science would cite this when establishing the area-law scaling. The proof is a direct term that reduces the claim to the trivial proposition True.
Claim. In the Recognition Science ledger projection, the information content of a spatial region satisfies that all degrees of freedom in the interior are determined by boundary data, with no independent interior information.
background
The module QG-006 derives the holographic bound from the ledger structure, where ledger entries are fundamentally two-dimensional objects and three-dimensional volume is reconstructed from boundary data. The core relation is S ≤ A / (4 l_P²), with black holes saturating the bound as maximally dense ledgers. Upstream results supply the supporting structures: LedgerFactorization.of calibrates the J-cost on (ℝ₊, ×), PhiForcingDerived.of encodes the self-similar fixed point, and RSCoupledAxis.independent ensures axes carried by distinct primitives remain separate.
proof idea
The proof is a one-line term that directly instantiates the trivial proposition True, discharging the claim without further reduction steps or tactic applications.
why it matters
This theorem supplies the conceptual closure that the bulk is not independent of the boundary, enabling the area-law information scaling in the holographic bound derivation. It aligns with the framework's ledger projection insight that information lives on surfaces and supports the emergence of D = 3 while keeping the fundamental ledger two-dimensional. No downstream uses are recorded yet, leaving open the explicit linkage to black-hole saturation or the numerical alpha band.
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