Act I as a Problem: Record of File PF-0 — Statement, Exact Lemmas, Classical No-Go Theorem, Shape Filter, Withdrawals and Open Questions
This note is a record, not a results paper. It fixes the state of File PF-0 on Act I of RCD (Radial Coherential Dynamics) as of October 7, 2026: what is proved, what is calibrated, what was withdrawn and why, and what remains open. New in v0.4: a no-go theorem. In the generic Rideout–Sorkin branch of classical sequential growth with fixed weights (t₀ = 1), exact projective consistency under uniform thinning forces t_k = 0 for all k ≥ 1; the only fixed point of that class is the antichain. The proof solves the consistency equations N = 3→2 (t₂ = t₁²/2) and N = 4→3 symbolically and extends to all k by induction. The t₀ = 0 branch and the total chain are recorded separately; the theorem does not imply a quantum fixed point. Also proved: the partial order is born from heredity without time (Order Lemma); the count of differentiations is an intrinsic measure (Measure Lemma); and in the classical sequential-growth family the weight of a differentiation does not increase with the number of maximal elements of its past (Monotonicity Lemma). Calibrated: a shape filter that receives no forbidden input — the number of direct links against the size of the past — grows in Minkowski sprinklings with the known exponent (d−2)/d and stays flat in every growth candidate tested. Exact at small size: the growth measure propagated up to N = 8 shows that none of four t_k families exceeds percolation in maximal elements per past size. Withdrawn, with reasons: a plateau at γ = 3/4 (finite-size crossover), an L ∝ v (artifact of a non-mixing sampler), a dimension reader D_link, a uniqueness of Poisson wrongly attributed to a theorem, I₃ = 0 as a constraint, a naive self-similarity, and a projective consistency of percolation. Open: which class to enlarge beyond fixed weights (scale-running couplings, another classical dynamics, or later a phase); the quantum version stays closed until that is stated. Files: English version, Spanish version (reference text), and the Python code that reproduces every figure and the symbolic algebra. Developed at the Panel Cerezo with cross-checking among AI tools (Claude, ChatGPT, Grok); authorship of each contribution is stated in the note.
Authors
- Arturo Cerezo García (ORCID: https://orcid.org/0009-0007-4739-4990)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-10-08
- DOI
- https://doi.org/10.5281/zenodo.23201184
- Primary Topic
- Stochastic processes and statistical mechanics
- Type
- preprint