IndisputableMonolith.Relativity.InformationConservation
This module establishes that total ledger information is conserved in Recognition Science because the J-cost function is defined on every state with no possible sink. Researchers deriving relativistic conservation laws or deterministic information dynamics would cite these results. The module imports the Determinism result on strict convexity of J to guarantee unique minimizers that preserve total content across updates.
claimThe ledger substrate satisfies information conservation: for any allowed update the sum of J-costs over states remains invariant, since J is defined on all states in $(0,\infty)$ and no sink exists.
background
In Recognition Science the ledger is the fundamental substrate whose total content (information) is measured by the J-cost function. The upstream Determinism module proves that J is strictly convex on $(0,\infty)$, so every constrained ledger update possesses a unique minimizer. The present module imports this determinism result together with Mathlib to organize statements that total information cannot vanish.
proof idea
This module collects the statements ledger_conservative, information_conserved, no_information_sink and their immediate consequences. Each statement follows from the unique-minimizer property imported from Determinism; the module itself supplies the structural claim that J is defined everywhere and therefore admits no sink.
why it matters in Recognition Science
The module supplies the conservation axiom required for the Relativity domain. It directly implements the structural claim in its own documentation that entries may move or transform but cannot vanish, thereby grounding later relativistic constructions on a closed ledger. No downstream theorems are yet recorded.
scope and limits
- Does not derive the explicit algebraic form of J.
- Does not treat apparent randomness or measurement.
- Does not compute numerical values for physical constants.
- Does not address multi-dimensional or curved ledger geometries.