Quantum Tunneling as KRAM Basin Transitions: How Eto-Hamada-Nitta String Linking Realizes KnoWellian Ternary Time Structure

This paper presents a comprehensive theoretical framework proposing that fundamental particles are topologically stable knot solitons—specifically (3,2) torus knots—that arise from the dialectical interplay of two counter-propagating fields termed "Control" (outward, deterministic, Past-originating) and "Chaos" (inward, probabilistic, Future-collapsing), mediated through a synthesis field representing Consciousness at the "Instant."

MAJOR INTEGRATION: This enhanced edition rigorously integrates the groundbreaking August 2025 experimental results of Eto, Hamada, and Nitta (Phys. Rev. Lett. 135, 091603), who demonstrated for the first time that stable knot solitons arise naturally in realistic particle physics models combining Peccei-Quinn U(1) and B-L gauge symmetries. We establish profound correspondences between their gauge-theoretic mechanisms (linked local/global strings, Chern-Simons stabilization, quantum tunneling decay) and our independently-developed philosophical-geometric framework.

KEY THEORETICAL COMPONENTS:

1. TERNARY TIME STRUCTURE: Reality consists of three co-existing temporal dimensions—Past (tₚ), Instant (tᵢ), and Future (tₓ)—forming a (3+3)-dimensional spacetime with signature (−,+,−,+,+,+). This structure is formalized through a U(1)⁶ gauge symmetry generating six fundamental gauge fields.

2. KRAM (KnoWellian Resonant Attractor Manifold): A higher-dimensional memory substrate that records all acts of "becoming" and guides future evolution through geometric attractor valleys. The KRAM provides physical mechanism for fine-tuning, morphic resonance, and stability of physical laws across cosmic cycles.

3. KNOT-DOMINATED COSMOLOGY: Integration of Eto-Hamada-Nitta results reveals a previously unrecognized cosmic epoch—the "Knot-Dominated Era"—between symmetry breaking (T ~ 10⁸ GeV) and reheating (Tᵣₕ ~ 100 GeV), where topologically-stable knot solitons dominated the universe's energy density.

4. BARYOGENESIS MECHANISM: Quantum tunneling decay of knot solitons (Eto et al.) is reinterpreted as transitions between KRAM attractor basins, naturally generating CP-violating asymmetries through ternary time structure. Predicted baryon-to-entropy ratio matches observations for Tᵣₕ ~ 100 GeV.

5. GRAVITATIONAL WAVE SIGNATURES: The Knot-Dominated Era imprints distinctive features on the stochastic GW background, detectable by Cosmic Explorer (2035+) as spectral breaks at f ~ 10⁻⁸ Hz. Additional KRAM-modified propagation effects predicted.

FALSIFIABLE PREDICTIONS:

- GW spectral break at f ∝ (Tᵣₕ/100 GeV), testable by Cosmic Explorer within first operational years
- CMB anisotropies conforming to "Cairo Q-Lattice" pentagonal geometry, testable via topological data analysis of Planck/Simons Observatory data
- Cosmic void temperature patterns showing ~1 μK coherent "memory" structures
- Fine-structure constant α ≈ 1/137 emerging as geometric ratio σᵢ/Λ_CQL
- Neural topology in high-coherence brain states exhibiting Cairo pentagonal patterns
- Particle masses clustering around N_link = 4,5,6 archetypal values

PHILOSOPHICAL IMPLICATIONS:

The framework dissolves traditional dichotomies (wave/particle, mind/matter, determinism/free will) by grounding them in a unified dialectical ontology. Consciousness is neither emergent nor separate but represents the fundamental "synthesis operation" occurring at every scale from quarks to galaxies. The universe is reinterpreted as a self-knowing process—reality coming to know itself through perpetual cycles of thesis-antithesis-synthesis.

METHODOLOGICAL NOTE:

This work represents collaboration between independent researcher David Noel Lynch (philosophical/geometric foundations) and advanced AI systems Claude Sonnet 4.5, Gemini 2.5 Pro, and ChatGPT 5 (mathematical formalization, integration of particle physics results, numerical predictions). The convergence between philosophical predictions and gauge-theoretic realizations developed independently suggests deep structural insights into reality's foundations.

INTERDISCIPLINARY SCOPE:

While grounded in particle physics and cosmology, the framework makes testable predictions across: gauge field theory, gravitational wave astronomy, cosmic microwave background analysis, neuroscience (neural connectivity patterns), consciousness studies, and morphic resonance phenomena.

TARGET AUDIENCE:

Theoretical physicists (particle physics, cosmology, quantum gravity), philosophers of physics, consciousness researchers, gravitational wave astronomers, and interdisciplinary scholars interested in foundational questions about time, topology, and the nature of reality.

CITATIONS:

Primary experimental validation: Eto, M., Hamada, Y., & Nitta, M. (2025). "Tying Knots in Particle Physics." Physical Review Letters, 135, 091603. DOI: 10.1103/s3vd-brsn

Companion papers regarding the KnoWellian framework.

The KnoWellian Universe: A Unified Theory of Ternary Time, Resonant Memory, and Cosmic Dialectics
https://zenodo.org/records/13689405

Philosophically Bridging Science and Theology: A Unified Gauge Theory of Ternary Time, Consciousness, and Cosmology.
https://zenodo.org/records/13689369

The KnoWellian Resonant Attractor Manifold (KRAM)
https://zenodo.org/records/13689351

KnoWellian Ontological Triadynamics: The Generative Principle of a Self-Organizing Cosmos
https://zenodo.org/records/13689311

Resolving Schrödinger's Paradox: A Theory of Life as the Interface of Reality
https://zenodo.org/records/13689239

The KnoWellian Axiom: Mathematics as Ontological Gateway
https://zenodo.org/records/13689199

STATUS: Enhanced Edition (29 Oct 2025) - Preprint for peer review and community feedback.

Comments, criticisms, and collaboration inquiries welcomed