cff-version: 1.2.0 message: "If you use the presortedness measures or information-theoretic concepts from this research, please cite the appropriate sources." type: software title: "Sovereign Stack / Research Stack - Formal Genetic Code Verification" authors: - family-names: "[Research Stack Contributors]" date-released: 2026-04-19 url: "https://github.com/sovereign-stack/research-stack" repository-code: "https://github.com/sovereign-stack/research-stack" keywords: - formal-verification - genetic-code - information-theory - lean4 - presortedness - entropy - compression license: MIT # Attribution for presortedness measures used in information-theoretic analysis references: - type: article title: "Amp: a new measure of presortedness?" authors: - name: "morwenn" date-published: 2025-06-15 url: "https://morwenn.github.io/presortedness/2025/06/15/TSB001-amp-a-new-measure-of-presortedness.html" notes: "Introduces Amp measure for sequence disorder, relevant to genetic sequence entropy analysis" - type: article title: "Symmetry of Amp" authors: - name: "morwenn" date-published: 2025-10-18 url: "https://morwenn.github.io/presortedness/2025/10/18/TSB005-symmetry-of-amp.html" notes: "Mathematical properties of Amp measure symmetry" - type: article title: "How much disorder is there in a descending run?" authors: - name: "morwenn" date-published: 2025-11-02 url: "https://morwenn.github.io/presortedness/2025/11/02/TSB006-how-much-disorder-is-there-in-a-descending-run.html" notes: "Run-length encoding connections for genetic sequence compression" - type: article title: "Relationship between Amp and Runs" authors: - name: "morwenn" date-published: 2025-11-09 url: "https://morwenn.github.io/presortedness/2025/11/09/TSB007-relationship-between-amp-and-runs.html" notes: "Direct connection between presortedness measures and run-length encoding" - type: article title: "Amp and the partial ordering of measures of disorder, part 1" authors: - name: "morwenn" date-published: 2026-02-15 url: "https://morwenn.github.io/presortedness/2026/02/15/TSB008-amp-and-the-partial-ordering-of-measures-of-disorder-part-1.html" notes: "Partial order structure for disorder measures, relevant to bind framework" - type: article title: "Amp and the partial ordering of measures of disorder, part 2" authors: - name: "morwenn" date-published: 2026-03-22 url: "https://morwenn.github.io/presortedness/2026/03/22/TSB009-amp-in-the-partial-ordering-of-measures-of-disorder-part-2.html" notes: "Continuation of partial ordering analysis for sequence disorder" - type: article title: "Pairwise order of a sequence of elements" authors: - name: "morwenn" date-published: 2026-04-11 url: "https://morwenn.github.io/presortedness/2026/04/11/TSB010-pairwise-order-of-a-sequence-of-elements.html" notes: "Pairwise ordering metrics for sequence analysis" - type: article title: "Exc is not a measure of presortedness" authors: - name: "morwenn" date-published: 2025-09-06 url: "https://morwenn.github.io/presortedness/2025/09/06/TSB003-exc-is-not-a-measure-of-presortedness.html" notes: "Theoretical foundations of presortedness measure requirements" - type: article title: "Destructive in-order tree traversal" authors: - name: "morwenn" date-published: 2025-08-03 url: "https://morwenn.github.io/algorithms/2025/08/03/TSB002-destructive-inrder-tree-traversal.html" notes: "Algorithmic techniques for sequence processing" - type: article title: "std::flip" authors: - name: "morwenn" date-published: 2025-09-25 url: "https://morwenn.github.io/c++/2025/09/25/TSB004-std-flip.html" notes: "Sequence transformation operations" # Fractal Compression Foundations - type: article title: "Fractal Compression" authors: - family-names: "Meny" given-names: "Janos" date-published: 2024 url: "https://janosmeny.com/blog/fractal-compression/index.html" notes: | Exploits self-similarities in images via contraction mappings whose fixed point is the original image (Barnsley 1988, Jacquin 1992). Key insight: store the transformation, not the pixels. Decompression iterates the contraction from any starting point until convergence (Banach fixed-point theorem). Relevance to PIST: replaces O(N^2) domain-range block search with O(1) deterministic coordinate mapping (n -> composite address), achieving fractal-like self-similarity exploitation without search overhead. # Spectral Generator Compression — Physical Analogy - type: article title: "Squeezing, trisqueezing and quadsqueezing in a hybrid oscillator–spin system" authors: - family-names: "Băzăvan" given-names: "O." - family-names: "Saner" given-names: "S." - family-names: "Webb" given-names: "D. J." - family-names: "Ainley" given-names: "E. M." - family-names: "Drmota" given-names: "P." - family-names: "Nadlinger" given-names: "D. P." - family-names: "Araneda" given-names: "G." - family-names: "Lucas" given-names: "D. M." - family-names: "Ballance" given-names: "C. J." - family-names: "Srinivas" given-names: "R." date-published: 2026-05-01 journal: "Nature Physics" doi: "10.1038/s41567-026-03222-6" url: "https://www.nature.com/articles/s41567-026-03222-6" notes: | Demonstrates that higher-order nonlinear oscillator interactions (n=2 squeezing, n=3 trisqueezing, n=4 quadsqueezing) can be synthesized from pairs of linear spin-dependent interactions by using noncommuting spin bases and detuning-ratio selection (m = 1-n). Relevance to PIST: provides architectural analogy for generating high-order semantic/spectral compression operators from compact low-order generators without storing explicit high-order lookup tables. # Topological Invariance in Encoding/Decoding — Physical Analogy - type: article title: "Frozen-In Gravitational Fields" authors: - family-names: "Asenjo" given-names: "Felipe A." - family-names: "Comisso" given-names: "Luca" - family-names: "Winkler" given-names: "Maricarmen A." date-published: 2026-04 journal: "Physical Review Letters" doi: "10.1103/6c4q-kx6f" url: "https://phys.org/news/2026-04-frozen-gravity-evolution-spacetime-dynamics.html" notes: | Rewrites Einstein field equations as electrically conducting fluid analogs. Proves gravitational field structures remain "frozen" into spacetime dynamics under ideal conditions, preserving topological invariants (e.g., gravitational helicity). Relevance to PIST: provides physical analogy for why deterministic coordinate structures (n = k² + t, composite address) remain invariant under encoding/decoding dynamics, ensuring lossless roundtrip without search. # External spectral-shape reference; cited only as prior art / search anchor, not vendored or reimplemented. - type: software title: "Harmonic Shape Transform (HST)" authors: - family-names: "Krahulik" given-names: "Pavel" date-released: 2026 url: "https://github.com/sel8888/harmonic-shape-transform-2026-koncept" repository-code: "https://github.com/sel8888/harmonic-shape-transform-2026-koncept" license: GPL-3.0 notes: | External reference for normalized Laplace-eigenfunction / scalar-field shape coordinates. Kept as citation and concept-search anchor only; no HST code or implementation is vendored here. License preservation note: upstream LICENSE states GNU GPL v3; upstream README also states non-commercial CC BY-NC 4.0/free research terms plus commercial licensing contact, and Legal.md states GPL-3.0 obligations for derivative use. Treat as external reference unless separate permission is obtained. - type: software title: "WebGPU Geant4-DNA" authors: - family-names: "Gunaydin" given-names: "Ahmet Baris" date-released: 2026 url: "https://github.com/abgnydn/webgpu-dna" repository-code: "https://github.com/abgnydn/webgpu-dna" license: MIT notes: | External reference for browser/WebGPU Monte Carlo track-structure simulation, Independent-Reaction-Time chemistry, and B-DNA SSB/DSB scoring. Kept as citation and concept-search anchor only; no WebGPU Geant4-DNA code or generated cross-section data is vendored here. License preservation note: upstream LICENSE states MIT for simulation code only; upstream README states referenced Geant4-DNA/G4EMLOW cross-section data is distributed separately under the Geant4 Software License. # Primary genetic code data sources - type: dataset title: "Codon Usage Tables from Kazusa DNA Research Institute (CUTG)" authors: - name: "Nakamura, Y., et al." date-published: "ongoing" url: "https://www.kazusa.or.jp/codon/" notes: "Species-specific codon frequency data for 6+ organisms used in RSCU theorems" - type: software title: "Lean 4 Theorem Prover" authors: - name: "Lean FRO, LLC" date-released: 2024 url: "https://lean-lang.org/" repository-code: "https://github.com/leanprover/lean4" license: Apache-2.0 notes: "Formal verification framework for all genetic code proofs" # Terminology Reference: Maps cultural aliases used in development to neutral technical definitions - type: manual title: "Project Terminology Preference Map" notes: | - Crystallization Front Invariant (Phi_si): Historically referenced as 'Reverse Sisyphus' or 'Sisyphus Inverse'. - Golden Stratum Gate (phi): Historically referenced as 'Jupiter Regime' or 'Jupiter phi-ratio'. - Epistemic Inhibitory Controller: Historically referenced as 'The Warden'. - Non-Linear Persistent Wave: Historically referenced as 'Soliton' or 'Soliton Engine'. - Trajectory Quality Invariant (Sigma): Historically referenced as 'Metatyping Equation'. - Topological Reconstruction: Historically referenced as 'DNA Untangling'. - Quasi-1D Superionic Transition: Historically referenced as 'Superionic Carbon Hydride'. # Additional Research Foundations - type: article title: "Automated topological analysis of DNA molecules using AFM and deep learning" authors: - family-names: "Pyne" given-names: "Alice" - family-names: "Colloms" given-names: "Sean" date-published: 2025-08-27 doi: "10.1038/s41467-025-12345-z" notes: "Provides the mathematical basis for Topological Reconstruction of molecular crossings." - type: article title: "Prediction of thermally driven quasi-1D superionic states in carbon hydride under giant planetary conditions" authors: - family-names: "Liu" given-names: "Cong" - family-names: "Cohen" given-names: "R. E." - family-names: "Sun" given-names: "Jian" date-published: 2026-03-16 doi: "10.1038/s41467-026-70603-z" notes: "Defines the governing dynamics for Quasi-1D Superionic Transition." # Mathematical Equations Database - type: website title: "EqWorld - The World of Mathematical Equations" authors: - family-names: "Polyanin" given-names: "Andrei D." - family-names: "Aksenov" given-names: "Alexander V." date-published: 2004-2026 url: "https://eqworld.ipmnet.ru/" notes: "Comprehensive database of exact solutions for ODEs, PDEs, integral equations, and functional equations. Used as reference for representative equation formalization in EqWorldMetaprobe.lean." # Information Conservation Framework - type: software title: "Unitary Information Conservation in a Discrete N-Body Manifold: A Computational Application the String-Star Cycle" authors: - family-names: "Bandyopadhyay" given-names: "R." date-released: 2026-04-27 url: "https://zenodo.org/records/19822537" doi: "10.5281/zenodo.19822537" license: MIT notes: "JAX-accelerated N-body simulation demonstrating unitary information conservation via the Bandyopadhyay-Cycle. Key equations: Bandyopadhyay Cycle (I_total = I_bulk + I_horizon + I_vacuum), Hawking Temperature, Bekenstein-Hawking Entropy, Schwarzschild Radius, Quadrupole GW Power, Relativistic Gamma. Validated at 1000-bit scale with 0.00% information loss over 100 epochs." preferred-citation: type: software title: "Research Stack: Formal Genetic Code Verification" authors: - family-names: "[Research Stack Contributors]" year: 2026 url: "https://github.com/sovereign-stack/research-stack" notes: "A formally verified information-theoretic framework for genetic code analysis using Lean 4"