MoralLedger
MoralLedger augments a double-entry algebra by adjoining an integer-valued agent skew map that is required to equal net flux at every vertex. Researchers extending ledger models to ethical or anthropological settings cite this structure as the substrate for the DREAM theorem on virtue-generated transformations. The declaration is a direct structural extension of DoubleEntryAlgebra that adds one field together with its defining equation.
claimLet $L$ be a double-entry algebra on $n$ vertices with antisymmetric edges and global sum zero. A moral ledger on $L$ is a map $s : [n] → ℤ$ such that $s(v)$ equals the net flux of $L$ at vertex $v$ for every $v$.
background
DoubleEntryAlgebra packages the ledger forced by the recognition composition law: every flow has a paired counterflow, global balance σ = 0 holds, and closed chains sum to zero. Its fields are a graded ledger together with the antisymmetry condition on edges and the explicit global-balance sum. MoralLedger interprets the vertices as agents and the edges as skew transfers while enforcing that the supplied skew equals the ledger's net flux at each vertex.
proof idea
This is a structure definition that extends DoubleEntryAlgebra by adjoining the agentSkew field and the single equality constraint skew_from_edges.
why it matters in Recognition Science
The structure supplies the concrete ledger model required by the DREAM theorem, which states that 14 virtues generate all σ-preserving transformations on this algebra. It realizes the double-entry consequence of J(x) = J(1/x) and the global-balance property listed in the module certificate. No downstream uses are recorded in the current graph.
scope and limits
- Does not enumerate or prove existence of the 14 virtues.
- Does not establish global balance; that is inherited from DoubleEntryAlgebra.
- Does not fix the number of agents or supply a concrete ledger instance.
- Does not reference the phi-ladder, mass formula, or T5–T8 forcing chain.
formal statement (Lean)
241structure MoralLedger extends DoubleEntryAlgebra where
242 /-- Each vertex represents an agent's moral state -/
243 agentSkew : Fin ledger.n → ℤ
244 /-- Skew is derived from edge balance -/
245 skew_from_edges : ∀ v : Fin ledger.n,
246 agentSkew v = ledger.netFlux v
247
248/-! ## §9. Summary Certificate -/
249
250/-- **LEDGER ALGEBRA CERTIFICATE**
251
252 1. Events form an abelian group (ℤ, +, 0) ✓
253 2. Conjugation e ↦ −e is involution ✓
254 3. Paired events sum to zero (double-entry) ✓
255 4. 8-window neutrality from 4 paired events ✓
256 5. Graded ledger has conservation at every vertex ✓
257 6. Net flux = 0 at all vertices ✓
258 7. Antisymmetric edges ⟹ global balance ✓
259 8. Connection to ethics (σ = 0 from ledger structure) ✓ -/