vacuum_has_zero_mass
plain-language theorem explainer
The vacuum ledger carries zero mass under the spatial ledger mass mapping. Researchers modeling gravity as ledger curvature cite this to set the empty-space baseline before deriving strain effects. The proof is a direct reflexivity step on the mass definition applied to the vacuum ledger.
Claim. The mass computed from the vacuum ledger via the spatial ledger mapping equals zero: $m_0 = 0$.
background
The module treats gravity as ledger curvature, where mass equals ledger density (transactions per volume) and curvature equals constraint pressure. The vacuum ledger is the empty state carrying no transactions. Upstream structures supply the J-cost function (strictly convex, minimum at unity) from PhiForcingDerived and the ledger factorization from DAlembert, both of which calibrate the density-to-mass conversion used here.
proof idea
One-line wrapper that applies reflexivity directly to the mass computation on the vacuum ledger, confirming the zero value by the defining equation.
why it matters
This result supplies the zero-mass baseline required for the module's mapping of gravity to collective ledger strain. It aligns with the framework's T5 J-uniqueness and T8 three-dimensional spatial ledger, ensuring curvature appears only when density is nonzero. No downstream theorems yet reference it, leaving open its insertion into explicit curvature derivations.
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