BCT Exploratory Package (Level-3): White-Rabbit Suppression, Predictor Rigidity, Open Proof Obligations, and the Selection Problem

Working / exploratory package (Level-3). Not part of the current BCT Canon set. Phase taxonomy (for clarity). In BCT, Phase 1 denotes the initial exploratory stage, and Phase 2 denotes the Axiom0-anchored operational/canonical stage. Level-3 is not a new phase: it is an exploratory theoretical layer built on Phase-2 commitments, currently focused on typicality, coherence-selection, white-rabbit suppression, and the broader selection problem for observer-coherent histories. What is included. This package contains two linked texts: a revised integrated Level-3 working draft, with: a record-based V0 formalization, a quantitative Occam-suppression result for generic single-step glitches under explicit local assumptions, a sparse-irregular-step control result extracted from the V0 coherence budget, a most-time generic suppression corollary outside a controlled exceptional set, a conditional simple-glitch route via predictor rigidity, and a sharpened list of open proof obligations; a companion philosophical/programmatic note, Why Coherent Histories?, which isolates the selection problem in informational and branching ontologies and situates BCT Level-3 as a disciplined partial candidate framework for addressing it. Current status. This is an exploratory research package, not a completed derivation of law-like reality. It combines: a genuine partial mathematical suppression result, an extracted intermediate consequence from the coherence budget, and a broader conceptual note explaining why the underlying selection problem should be treated explicitly rather than absorbed into measurement, probability, or objectivity debates. What remains conditional / open. The simple-glitch case still depends on predictor rigidity, which is stated precisely but not yet proved in the desired generality. Adversarial-time local closure, reference-machine robustness, and natural-family counting in the strongest form remain open. Collaboration invite (targeted). I welcome focused input on: predictor-rigidity proofs (or counterexamples) for restricted computable MDL / CTW-style predictor classes, adversarial-time local regularity closure, natural-family counting bounds and entropy-gap formulations, computable approximations to Kolmogorov / MDL-based weighting schemes, and conceptual critiques of the selection-problem framing across Everettian, relational, Darwinian, or computational ontologies. Background: independent researcher. Shared for critique, refinement, and collaboration. Email: batoritranslation@gmail.comWeb site: bit-collapse-theory.netlify.appMain DOI: 10.5281/zenodo.18496128 Abstract This Level-3 BCT package explores a record-based route to typicality, coherence-selection, and white-rabbit suppression, together with the broader foundational problem of why coherent observer-histories should dominate over arbitrary continuations. It is explicitly exploratory and not part of the current BCT Canon (Phase-2 / Axiom0) set. The main working draft formalizes a V0 layer based on record-chains, a coherence functional, and coherence-filtered Occam weighting, and proves a partial quantitative result: generic high-complexity single-step deviations are exponentially suppressed under a frozen-version setup and explicit local assumptions. It also extracts a weaker but rigorous intermediate consequence from the V0 coherence budget: sufficiently irregular steps must remain sparse, yielding a most-time form of generic suppression outside a controlled exceptional set. The simple-glitch case is not claimed as solved; it is reduced to a stated predictor-rigidity condition, which remains an open proof obligation. The package also includes a companion programmatic note on the selection problem in informational and branching ontologies, arguing that this problem should be named explicitly and treated as a foundational issue in its own right. The goal is not to overclaim, but to expose a structured mathematical and conceptual research program with clear limits, clear bottlenecks, and clear next steps. Keywords quantum foundations; selection problem; typicality; white rabbits; record-chains; coherence filtering; Kolmogorov complexity; MDL; predictor rigidity; branching ontologies