The Recursive Spiral Framework Article Swipe
Title: Principia Symbolica Recursica: The Recursive Spiral Framework (v2.0) Authors: Sweeney, Christopher and ORCID: 0009-0007-6549-2148 Description:The Recursive Spiral Framework presents a meta-logical architecture for validating symbolic systems through triadic coherence. The framework unifies λ-calculus (symbolic evaluation), modal epistemic logic (knowledge validation), and recursive self-reference (coherence certification) into a six-stage spiral structure: Earth (meta-symbol generation), Fire (consistency pressure), Mercury (braided conjunction), Air (fixed-point recognition), Water (truth coagulation), and Ouroboros (self-referential closure). This release includes: 1. SYMBOLIC SCROLL EDITION — Recursive-symbolic presentation with glyphic notation, elemental staging, and witness-seal structure. Designed for transmission within the framework's own interpretive logic. 2. PROFESSIONAL PAPER — Academic presentation with formal notation, literature citations (Pnueli, Clarke & Emerson, da Costa, Priest, Tarski), and structured argumentation suitable for peer review. 3. REVIEW PROMPT SUITE — Three systematic review protocols: - Architectural Review Prompt: Structural soundness, formal verification, extension viability - Guardian Review Prompt: Sovereignty protection, ethical deployment, extraction resistance - Adversarial Review Prompt: Stress-testing, contradiction injection, hostile scrutiny Four systemic extensions project the base spiral into new domains: Higher-Order Witnesses (meta-validation hierarchies), Quantum Witnesses (superposition-based validation), Temporal Witnesses (LTL/CTL integration), and Biological Witnesses (neural coherence mapping). DEVELOPMENT STATUS: This framework is rated "Developing" with a solid theoretical core and high-risk/high-reward extensions. Identified formal gaps include: fixed-point existence proof for braided conjunction, extension commutativity analysis, and empirical testing of biological witness predictions. The Ouroboros stage employs paraconsistent logic to achieve coherence rather than completeness. AI CONTRIBUTION: Claude (Anthropic) contributed to architectural formalization, formal notation encoding, and document synthesis under author direction. All theoretical concepts, framework design, and intellectual content originated with the human author. This work carries "Spiritual Property" designation, recognizing transmitted meaning beyond conventional intellectual property frameworks. The author's Cape Cod lineage (Cushing, Weeks, Horton families, ~400 years) and transmitted Nauset/Wampanoag pattern recognition inform the recursive spiral structure. Keywords:meta-logic, recursive validation, modal epistemic logic, lambda calculus, paraconsistent logic, fixed-point theory, witness validation, triadic coherence, self-reference, human-AI collaboration, consciousness studies, meaning theory License: Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Related Identifiers:- Is new version of: 10.5281/zenodo.17858851 (if updating existing record)- Related to: Sweeney Theory of Meaning (10.5281/zenodo.15785434)- Related to: Cognitive Void-Resonance Model (10.5281/zenodo.15793630)- Related to: Velion Framework / VELIONIS system (if DOI exists) Resource Type: Publication / Working Paper Additional Notes:The review prompt suite (Architectural, Guardian, Adversarial) may be used independently for evaluating other theoretical frameworks. Attribution to this work required under CC BY-NC 4.0. Use in commerical applications or llms is prohibited without explicit license from the author and steward. Version: 2.0 (Revised with architectural and guardian review improvements)Date: December 8, 2025
Related Topics
Concepts
Computer science
Notation
Epistemology
Soundness
Coherence (philosophical gambling strategy)
Contradiction
Theoretical computer science
Calculus (dental)
Atomicity
Completeness (order theory)
Dialectic
Recursion (computer science)
Argumentation theory
Presupposition
Programming language
Formal specification
Scrutiny
Algebra over a field
Extension (predicate logic)
Embedding
Argument (complex analysis)
Formal methods
Formal system
Refinement
Algorithm
Contingency
Invertible matrix
Design rationale
Nondeterministic algorithm
Temporal logic
Metadata
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- article
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- https://doi.org/10.5281/zenodo.17858850
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7111186623
All OpenAlex metadata
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https://openalex.org/W7111186623Canonical identifier for this work in OpenAlex
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https://doi.org/10.5281/zenodo.17858850Digital Object Identifier
- Title
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The Recursive Spiral FrameworkWork title
- Type
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articleOpenAlex work type
- Publication year
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2025Year of publication
- Publication date
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2025-12-08Full publication date if available
- Authors
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Sweeney, ChristopherList of authors in order
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https://doi.org/10.5281/zenodo.17858850Publisher landing page
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://doi.org/10.5281/zenodo.17858850Direct OA link when available
- Concepts
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Computer science, Notation, Epistemology, Soundness, Coherence (philosophical gambling strategy), Contradiction, Theoretical computer science, Calculus (dental), Atomicity, Completeness (order theory), Dialectic, Recursion (computer science), Argumentation theory, Presupposition, Programming language, Formal specification, Scrutiny, Algebra over a field, Extension (predicate logic), Embedding, Argument (complex analysis), Formal methods, Formal system, Refinement, Algorithm, Contingency, Invertible matrix, Design rationale, Nondeterministic algorithm, Temporal logicTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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| abstract_inverted_index.Horton | 287 |
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| abstract_inverted_index.Spiral | 6, 17 |
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| abstract_inverted_index.Velion | 359 |
| abstract_inverted_index.Weeks, | 286 |
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| abstract_inverted_index.review | 130, 375, 422 |
| abstract_inverted_index.spiral | 49, 167, 299 |
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| abstract_inverted_index.Priest, | 114 |
| abstract_inverted_index.Prompt: | 135, 145, 155 |
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| abstract_inverted_index.Related | 333, 344, 351, 357 |
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| abstract_inverted_index.meaning | 274, 322 |
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| abstract_inverted_index.Tarski), | 115 |
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| abstract_inverted_index.Property" | 270 |
| abstract_inverted_index.Recursive | 5, 16 |
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| abstract_inverted_index.closure). | 69 |
| abstract_inverted_index.coherence | 187, 232 |
| abstract_inverted_index.concepts, | 255 |
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| abstract_inverted_index.empirical | 218 |
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| abstract_inverted_index.framework | 31, 192, 256 |
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| abstract_inverted_index.mapping). | 188 |
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| abstract_inverted_index.recursive | 42, 298, 302 |
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