Pattern Persistence Across Boundary Dissolution: The Afterlife Theorem under Recognition‑Science Invariants
Recognition Physics Institute — Austin, Texas, USA
Summary
We formalize persistence of a recognition pattern across boundary dissolution (“death”) in RS: the integer invariant \(Z\) is conserved and the light‑memory state is cost‑minimal with \(J(1)=0\). Under explicit availability assumptions (substrate suitability and an arrival process with rate \(\lambda\) and acceptance \(p\)), pattern reformation occurs with expected waiting time \(\mathbb{E}[T]=1/(\lambda p)\). Core conservation/minimality statements are mechanically verified in Lean; recurrence/timing results are conditional and paired with falsifiers and preregistered audits.
Abstract
We prove: (i) \(Z\) is conserved across boundary dissolution, and (ii) the post‑dissolution light‑memory state is cost‑minimal with \(J(1)=0\). Given a suitability predicate on substrates and an arrival process with rate \(\lambda\) and acceptance probability \(p\), we further obtain pattern reformation and the timing law \(\mathbb{E}[T]=1/(\lambda p)\). Lean‑verified components cover conservation/minimality; recurrence/timing use stated hypotheses and include falsifiers and preregistered empirical protocols (NDE motifs; timing/clustering in reincarnation datasets).
Key Points
- Conservation: \(Z\) persists through boundary dissolution.
- Light‑memory: cost‑minimal state with \(J(1)=0\).
- Conditional recurrence with \(\mathbb{E}[T]=1/(\lambda p)\) under availability assumptions.
- Lean‑verified invariants; preregistered falsifiers for conditional claims.