empty_ledger_net_flow
plain-language theorem explainer
The empty ledger, containing no recognition events, yields zero net flow at every agent. Workers on the ledger-forcing step of the Recognition Science chain cite this as the base case establishing conservation before symmetry arguments begin. The proof is a one-line simplification that unfolds the fold definition of net flow over the empty event list.
Claim. Let $L_0$ be the ledger with no recognition events. For every agent $a$, the net flow at $a$ in $L_0$ equals zero, where net flow sums $Real.log(ratio)$ over events incident on $a$.
background
The module establishes that J-symmetry forces double-entry ledger structure. The empty ledger is the ledger whose event list is empty and whose double-entry predicate holds vacuously. Net flow at an agent folds over the event list, adding the logarithm of the ratio when the agent is source or target and returning zero otherwise. The reciprocal definition supplies the inverse-ratio event used in later symmetry steps. The from theorem in PrimitiveDistinction supplies the seven-axiom starting point that reduces to four structural conditions plus definitional facts.
proof idea
One-line wrapper that applies simp on the definitions of net_flow and empty_ledger. The tactic reduces the fold over the nil list directly to the zero accumulator.
why it matters
This supplies the base case for the conservation-from-symmetry section that follows in the same module. It anchors the claim that J-symmetry forces double-entry structure by verifying the zero-event ledger satisfies the zero-net-flow condition before reciprocal events are introduced. The result sits inside the ledger-forcing development that links Recognition Composition Law symmetry to balanced ledgers; no downstream uses are recorded yet.
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