information_is_physical
plain-language theorem explainer
Landauer's principle is recorded as the claim that information has thermodynamic, hence physical, consequences; Recognition Science strengthens this to identity (ledger entries are reality). Cite it as the named conceptual marker in the INFO-004 Landauer module, not as a quantitative bound. The proof is the trivial inhabitant of True.
Claim. Information is physical: erasing a bit has a thermodynamic energy cost, and in Recognition Science ledger entries constitute physical reality. Formally the asserted proposition is $\top$.
background
Module INFO-004 targets the Landauer bound from Recognition Science's fundamental timescale $\tau_0$. Classically, erasing one bit costs at least $E_{\min} = k_B T \ln 2$: the initial bit is uncertain, the final state is fixed, one bit ($\ln 2$ nats) is lost, entropy rises by $\Delta S = k_B \ln 2$, and heat $Q = T\Delta S$ is dissipated.
In the RS reading, erasure is recognition-then-forgetting and therefore carries a $J$-cost; $\tau_0$ sets the rate at which that cost is paid. Sibling declarations in the module package $k_B$, room temperature, landauerEnergy, positivity, the room-temp numerical value, a $\tau_0$-linked quantum energy, minimum erasure power, and the claim that the erasure $J$-cost matches the thermodynamic expression.
Upstream entropy hooks (configuration defect entropy, Boltzmann/partition-function entropy, horizon microstate entropy) supply the ambient language that information loss is entropy increase. They are not invoked in this particular proof.
proof idea
Term-mode proof of True by trivial. No lemmas are applied; no Landauer identity, $\tau_0$ relation, or entropy definition is unfolded. The declaration is a named propositional marker, not a derivation.
why it matters
Marks the philosophical endpoint of the Landauer thread in Recognition Science: not merely that information has physical consequences (Landauer 1961), but that information is the ledger and the ledger is reality. It sits beside the quantitative siblings that actually build $E_{\min}$, room-temp values, and $J$-cost matching, and beside the module's stated applications (ultra-low-power design, DNA and neural efficiency limits, quantum power budgets).
No downstream theorems currently depend on it (used_by is empty), so it does not feed a parent forcing-chain step (T0–T8), the RCL, or the $\phi$-ladder mass formula. Its role is documentary closure for INFO-004's claim that the Landauer bound emerges from $\tau_0$ and $J$-cost, pending the non-trivial equalities in the sibling layer.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.