conservation_is_unconditional
plain-language theorem explainer
Any topological charge on an N-entry ledger is invariant under a single variational step from one configuration to its successor. Researchers deriving charge conservation from topology in Recognition Science cite this to establish that quantization and exact preservation follow directly from the integer-valued linking definition. The proof is a one-line application of the conserved property built into the TopologicalCharge structure.
Claim. Let $N$ be a natural number. Let $Q$ be a topological charge, that is an integer-valued function on configurations of $N$ entries that is invariant under variational dynamics. For any two configurations $c$ and $c'$ such that $c'$ is a variational successor of $c$, the value of $Q$ at $c'$ equals its value at $c$.
background
TopologicalCharge is the structure whose value map sends each Configuration to an integer and whose conserved field asserts invariance under any IsVariationalSuccessor step. Configuration itself is the record of N positive real entries representing ledger ratios. The module sets the local setting as F-012, where conservation arises from linking numbers in D = 3 rather than from continuous symmetries, making charges integer-valued by construction and exactly preserved along trajectories.
proof idea
The proof is a one-line wrapper that applies the conserved field of the TopologicalCharge structure directly to the given successor hypothesis.
why it matters
This theorem supplies the unconditional conservation step required by the F-012 certificate in the module summary. It feeds the claim that three charges (electric, baryon, lepton) arise only in D = 3 via face-pair linking and are stronger than Noether charges because they are integer-valued and symmetry-independent. It closes the gap left by DimensionForcing by showing that topological invariance replaces symmetry assumptions in the ledger dynamics.
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