We classify regular full-dimensional stochastic containment among binary standard semi-directed strongly tree-child level-2 phylogenetic networks under the Kimura three-parameter (K3P) model. On the principal positive Fourier domain, a directed containment germ exists if and only if the labelled reduced trees of blobs agree and corresponding complete factors are either labelled-isomorphic or ordinarily triangle-redirected, with coherent boundary transports. The same condition is equivalent to a common full-dimensional regular germ and remains exact in strict continuous time. Thus no proper one-sided containment occurs in the strong class, and the semi-directed topology is generically identifiable and exactly reconstructible outside a proper exceptional set, modulo ordinary triangle redirection. The three ordinary K3P triangle orientations have generic normalized rank 14, share the same irreducible eight-term quartic hypersurface H₁₄ in normalized three-leaf Fourier space, and meet in a common strict continuous-time smooth rank-14 germ. The bounded residue consists of fourteen four-port directed relation orbits—nine polynomially separated and five directed-rank separated—plus two separately separated sink swaps. Exact restoration and coherent one- and two-port probes extend the bounded classification to arbitrary labelled subdivision words. Strong tree-childness is sharp against weakening to weak tree-childness. For every n ≥ 3, two weakly but not strongly tree-child networks have strict continuous-time K3P images sharing a common full-dimensional regular germ of dimension 6n − 3. This is the first Zenodo/DOI-bearing archival release of version 1.0.0 of the complete K3P level-2 classification and its reproducibility evidence. It contains the article, reader supplement, compile-complete source archives, canonical full proof archive, compact verifier, independent-referee replay package, exact manifest, checksums, citation metadata, and a file-level license notice. The deposited bytes correspond to immutable Git commit 0b76dd8e38f262ebe9ba8c1d23281853e334fef2, annotated tag k3p-level2-identifiability-v1.0.0 resolving to that commit, and full-archive SHA-256 4f84417f40b4e5ddae80b36d87dc7bb6d00389a573a58d0b82a2592c9f7c6403. The archive includes the previously completed all-producer regeneration evidence bound to unchanged mathematical inputs, together with successful exact and independently implemented replays, rigorous interval arithmetic where required, and fail-closed mutation tests. The present release changes bibliography, nonmathematical administrative/public-release prose, and release engineering only; unchanged multi-hour mathematical producers were not rerun during this dependency-scoped reseal. No empirical data set is used. Preprint; not peer reviewed by a journal. Generative-AI assistance and its verification workflow are disclosed in the article. Article, supplement, figures, documentation, and mathematical certificate data are licensed under CC BY 4.0; original verifier and build code are licensed under MIT, as mapped in LICENSES.md. No specific funding supported this work. The author declares no competing interests.
Alec Kriebel· Zenodo (CERN European Organi...· 0 citations
We classify regular full-dimensional stochastic containment among binary standard semi-directed strongly tree-child level-2 phylogenetic networks under the Kimura two-parameter (K2P) model. On the principal positive Fourier domain D₊ = {(s,g): 02s−1}, a directed containment germ exists if and only if the two labelled networks are isomorphic after independently redirecting ordinary three-cycle factors. The same condition is equivalent to a common full-dimensional regular germ; in particular, no proper one-sided containment occurs. It follows that the semi-directed topology is generically identifiable modulo ordinary triangle redirection, and that its structural triangle class is exactly reconstructible away from a proper algebraic exceptional set. The proof combines displayed-quartet inequalities and exact whole-map identities, an exact two-sector bridge-fibre theorem, physical marginal submersions, localization, and a bounded graph-to-algebra classification of cycle and theta factors. The bounded classification is computer-assisted: every directed primitive relation, rank exclusion, restoration parent, transport, and one-/two-port probe is represented by an exact certificate with independent replay and mutation evidence. The classification transfers to the strict continuous-time domain 0<s<1, s²<g<1. For every n≥3, two weakly but not strongly tree-child level-2 networks have continuous-time K2P images sharing a regular germ of dimension 4n−3, proving sharpness of strong tree-childness. This record is the complete v1.0.5-r1 priority and reproducibility package: the 26-page article, 24-page reader supplement, compile-complete five-file source archive, deterministic 495-member referee/verifier archive, external archive-qualification report, checksum sidecars, and dual-license notice. The manuscript source is v1.0.5; revision r1 repairs only an auxiliary probe-current semantic binding and changes neither the theorem, manuscript, PDFs, nor frozen classification. The clean verifier replay passed 41/41 layers, and the focused semantic mutation suite rejected 20/20 attacks. Exact source bindings: package tag k2p-same-referee-package-v1.0.5-r1; annotated tag object 6c9c89d38f4f4cdc9c328d8bb1237458c617136d; commit e2f6e32e6fe885e90c8e83a8c5b00785e663a4ae; referee archive SHA-256 4564cd1f8cd95f670a2e0d9619babaf3c343762cfd8ceeb190cd17df72802889. Article, supplement, and certificate data are licensed under CC BY 4.0; verifier and build code are licensed under MIT. No specific funding supported this work. The author declares no competing interests. Generative-AI assistance and its verification workflow are disclosed in the article. No mixed-sign K2P classification is claimed.r
Alec Kriebel· Zenodo (CERN European Organi...· 0 citations
We classify regular full-dimensional stochastic containment among binary standard semi-directed strongly tree-child level-2 phylogenetic networks under the Kimura two-parameter (K2P) model. On the principal positive Fourier domain D₊ = {(s,g): 02s−1}, a directed containment germ exists if and only if the two labelled networks are isomorphic after independently redirecting ordinary three-cycle factors. The same condition is equivalent to a common full-dimensional regular germ; in particular, no proper one-sided containment occurs. It follows that the semi-directed topology is generically identifiable modulo ordinary triangle redirection, and that its structural triangle class is exactly reconstructible away from a proper algebraic exceptional set. The proof combines displayed-quartet inequalities and exact whole-map identities, an exact two-sector bridge-fibre theorem, physical marginal submersions, localization, and a bounded graph-to-algebra classification of cycle and theta factors. The bounded classification is computer-assisted: every directed primitive relation, rank exclusion, restoration parent, transport, and one-/two-port probe is represented by an exact certificate with independent replay and mutation evidence. The classification transfers to the strict continuous-time domain 0<s<1, s²<g<1. For every n≥3, two weakly but not strongly tree-child level-2 networks have continuous-time K2P images sharing a regular germ of dimension 4n−3, proving sharpness of strong tree-childness. This record is the complete v1.0.5-r1 priority and reproducibility package: the 26-page article, 24-page reader supplement, compile-complete five-file source archive, deterministic 495-member referee/verifier archive, external archive-qualification report, checksum sidecars, and dual-license notice. The manuscript source is v1.0.5; revision r1 repairs only an auxiliary probe-current semantic binding and changes neither the theorem, manuscript, PDFs, nor frozen classification. The clean verifier replay passed 41/41 layers, and the focused semantic mutation suite rejected 20/20 attacks. Exact source bindings: package tag k2p-same-referee-package-v1.0.5-r1; annotated tag object 6c9c89d38f4f4cdc9c328d8bb1237458c617136d; commit e2f6e32e6fe885e90c8e83a8c5b00785e663a4ae; referee archive SHA-256 4564cd1f8cd95f670a2e0d9619babaf3c343762cfd8ceeb190cd17df72802889. Article, supplement, and certificate data are licensed under CC BY 4.0; verifier and build code are licensed under MIT. No specific funding supported this work. The author declares no competing interests. Generative-AI assistance and its verification workflow are disclosed in the article. No mixed-sign K2P classification is claimed.r
Alec Kriebel· Zenodo (CERN European Organi...· 2 citations