Published March 1, 2025
| Version 3
Publication
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Recursive Expansive Dynamics
Authors/Creators
Description
This framework scaffolds spectral geometry, operator theory, higher-dimensional and fractal spacetime structures, recursive algebra, and topological invariants—all aiming to capture a deeply recursive and self-modulating cosmos. In many areas of mathematics and physics, the concept of an annihilator—commonly used in affine subspace or dual spaces—captures the idea of “zeroing out” a structure. In our work, we propose an extension of this idea via the Inverse Zero Operator (IZO), a projection operating kernel that recursively extracts the stable, invariant core (the fixed-point) from a given operator sequence. Rather than simply annihilating a structure, the IZO acts as a memory-extracting mechanism, preserving the recursive influence inherent in the system. This paper introduces the IZO, formalizes its properties, and demonstrates its utility through several examples. Our goal is to provide both a rigorous mathematical foundation and an accessible exposition for further exploration in mathematical physics.
Methods
Running Adelic Integration... Running Lie Algebra Analysis... Standard deformation computed successfully. Performing Cross-Validation... ================================================== INTEGRATED ANALYSIS RESULTS ================================================== Quantum-Consistent Adelic Integration Report ============================================ Computed Λ: 1.0 Balancing dx: 161609838460844346271680203925.5221527559065008578318525040070179605415904948086433123860082579364859 Component Structure: Real Continuum: 6.975357535853769564018389183934484833544679824821000822079731605785973739106144495802573231793827148e+117 p-adic Spectrum: 1.433618269543802008859004043861336657399073684134227538127346850246125858773248934731423341494032307e-118 Prime 2 Contribution: 0.5 Prime 3 Contribution: 0.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 Prime 5 Contribution: 0.2 Prime 7 Contribution: 0.1428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429 Prime 11 Contribution: 0.09090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909091 ... (and more primes) Quantum Report: • Product Deviation: 2.86e-101 • Log Spectral Std Dev: 1.17 • Expected Std Dev: 4.60 • Anomaly Detected: False Exceptional Lie Algebra Analysis ================================ • Standard Deformation Norm: inf • Safe Deformation Norm: nan Cross-Validation Results ======================= • Deformation Consistency: False • Metrics Correlation: 0.0000 • System Consistency: False • Consistency Score: 0.0000
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Additional details
Additional titles
- Alternative title
- Hypatian Math
- Alternative title
- Formal Proof of Recursive Topological Vertex, Recursive Mirror Symmetry, and Recursive Renormalization Group Flow
- Alternative title
- Recursive Fractalization in Nonlinear Dynamics and Holographic Systems
Dates
- Valid
-
2025-03-01