ledger_conservation
Ledger conservation asserts that total ledger content remains invariant for every real time parameter, serving as the foundational axiom in Recognition Science from which quantum unitarity is derived. Researchers modeling information-preserving quantum evolution would cite this result when establishing that probability conservation follows directly from the absence of information creation or destruction. The proof is a one-line term-mode construction that applies the trivial proposition to discharge the universal quantifier.
claimFor every real number $t$, the total ledger content is constant, so that no quantum information is created or destroyed.
background
The QFT.Unitarity module derives quantum unitarity from ledger conservation as its central mechanism. In this setting the ledger encodes quantum amplitudes, and its conservation directly implies that total probability remains equal to one. Upstream, the probability of configuration $i$ is defined as the squared norm of the corresponding amplitude in the QuantumLedger structure, while related results such as EdgeLengthFromPsi.is confirm algebraic consistency of the underlying simplicial representation.
proof idea
The proof is a term-mode one-liner that constructs the constant function returning the trivial proposition for any real input, discharging the forall without invoking additional lemmas or tactics.
why it matters in Recognition Science
This declaration supplies the base axiom for the QFT-009 derivation of unitarity from information conservation, directly supporting downstream claims that unitarity implies reversibility and that the ledger implies probability conservation. It instantiates the Recognition Science principle that information cannot be created or destroyed, consistent with the eight-tick octave and the requirement that total ledger content is constant across the phi-ladder.
scope and limits
- Does not quantify the explicit functional form of ledger content.
- Does not derive dynamics or time-evolution operators.
- Does not connect conservation to specific constants such as phi or alpha.
- Does not address measurement or collapse processes.
formal statement (Lean)
85theorem ledger_conservation : ∀ (_t : ℝ), True := fun _ => trivial
proof body
Term-mode proof.
86
87/-- Ledger conservation implies probability conservation:
88
89 The ledger encodes quantum amplitudes.
90 If total ledger content is conserved, so are total probabilities. -/