This open research notebook develops a falsification-first route from the Flatland analogy to testable additional-coordinate models in quantum tunnelling. It separates three independent pipelines: predictions derived from one fixed four-spatial-dimensional model, residuals extracted from calibrated measurements without invoking w, and ordinary-physics controls. The primary constitutive hypothesis is S_E=f(w), where S_E is dimensionful Euclidean action and A=S_E/hbar is the dimensionless tunnelling exponent. No linear law is assumed, and the coordinate w is not identified with RMS transverse broadening. Existing controlled calculations establish a coupled-channel effect inside a specified (x,w) Hamiltonian, while matched-broadening stress tests show that center broadening alone does not determine action. Status: open, non-peer-reviewed working paper. The notebook does not report evidence for a fundamental fourth spatial dimension. It provides a pre-registered, no-refit framework for deciding what future observations would count against or in favor of the model. Related control study: https://doi.org/10.5281/zenodo.22071952
This open research notebook develops a falsification-first route from the Flatland analogy to testable additional-coordinate models in quantum tunnelling. It separates three independent pipelines: predictions derived from one fixed four-spatial-dimensional model, residuals extracted from calibrated measurements without invoking w, and ordinary-physics controls. The primary constitutive hypothesis is S_E=f(w), where S_E is dimensionful Euclidean action and A=S_E/hbar is the dimensionless tunnelling exponent. No linear law is assumed, and the coordinate w is not identified with RMS transverse broadening. Existing controlled calculations establish a coupled-channel effect inside a specified (x,w) Hamiltonian, while matched-broadening stress tests show that center broadening alone does not determine action. Status: open, non-peer-reviewed working paper. The notebook does not report evidence for a fundamental fourth spatial dimension. It provides a pre-registered, no-refit framework for deciding what future observations would count against or in favor of the model. Related control study: https://doi.org/10.5281/zenodo.22071952
This exploratory preprint studies a controlled quantum-scattering toy model with an additional harmonically confined coordinate w. It compares a fixed-width one-dimensional barrier, the exact shrinking observable slice V(x,0), and the full coupled (x,w) Hamiltonian. The identical-slice control shows that the non-monotonic transmission turn is not unique to an additional coordinate, while the coupled calculation produces a quantitatively distinct transmission curve and a converged transverse-broadening signal. The action-coordinate hypothesis is S_E = f(w), with A = S_E / ħ. The original eleven-point parameter sweep gives a monotonic nonlinear locus when A is plotted against the center broadening Δw_rms. A new matched-state stress test independently changes longitudinal energy or transverse confinement and retunes the barrier to reproduce Δw_rms = 0.08, 0.18, and 0.35. The corresponding WKB actions spread by 50.2%, 31.1%, and 22.7% relative to the baseline; the exact-scattering exponent agrees, and a refined-grid calculation is stable. Thus a universal one-variable proxy A = F(Δw_rms) fails without refitting. This result does not falsify an otherwise unspecified microscopic relation S_E = f(w), because Δw_rms is an observable moment rather than the coordinate or tunneling path w. It shows that broadening alone is insufficient and that a richer state description or path-level definition is required. The work is non-peer-reviewed and does not claim evidence that nature has an accessible fourth spatial dimension. The supplement contains the calculation scripts, CSV data, numerical metadata, convergence checks, and figures; AI assistance is disclosed in the manuscript.
This non-peer-reviewed exploratory preprint tests whether a coupled quantum Hamiltonian with one additional spatial coordinate can produce barrier transmission distinct from ordinary one-dimensional quantum mechanics when both calculations share exactly the same observable slice V(x,0). A prescribed self-similar Gaussian barrier is compared using three calculations: fixed-width 1D, shrinking identical-slice 1D, and full coupled (x,w) scattering with harmonic confinement. The shrinking 1D slice is itself non-monotonic, so an upward turn is not uniquely extra-dimensional. The full model nevertheless gives a quantitatively different curve, with a sampled minimum near V0=18 and T=9.87e-3 at V0=64 versus 6.09e-9 for the identical slice. This is a reproducible coupled-channel result within a mathematical toy Hamiltonian, not evidence that nature has an accessible fourth spatial dimension. The barrier family is prescribed rather than derived from a constitutive field law. The record includes the manuscript and a supplement containing code, complete numerical results, metadata, and convergence checks. ChatGPT and Sarvam AI assisted with brainstorming and language development. ChatGPT also assisted with literature triage, control design, numerical implementation and auditing, and drafting. AI systems are not authors. Chaman Prakash Kanth remains responsible for the manuscript, assumptions, metadata, and publication decision.
Preprint: This work is a preprint, has not undergone peer review, and is made publicly available to establish a public scientific record. This publication presents operational one-dimensional scaling tests of the Dynamical Information Geometry (DIG) framework using the Twin-Test protocol. Dynamical Information Geometry assigns an effective, state-dependent geometry to quantum many-body dynamics based on the spatial organization of mutual information. Earlier parts of the DIG series established the theoretical framework, provided numerical validation, introduced hardened operational definitions, and clarified regime structure and necessity. The present work, DIG Part VI, does not introduce new theory, new observables, or new numerical modeling. Its role is strictly operational. It documents how the Twin-Test protocol behaves under controlled one-dimensional scaling variations along two independent axes: system-size increase in a simulator implementation and circuit-depth increase in a quantum hardware implementation. Both scaling axes are evaluated within the same operational framework, using the mandatory audit logic defined in DIG Part IV. No attempt is made to relate or map these axes onto one another. The analysis is restricted to structural sign behavior, audit classification (marker-stable versus marker-transfer), and the identification of an operational robustness limit (defect) at increased depth. No universal scaling laws are proposed. No fitting, extrapolation, or cross-platform amplitude matching is performed. All operational definitions and decision rules are stated explicitly in the manuscript. The accompanying dataset implements these rules verbatim and enables deterministic third-party reproduction without interpretation. Related works (for reference and context): DIG Part I (theoretical framework):https://doi.org/10.5281/zenodo.17983399 DIG Part II (numerical validation):https://doi.org/10.5281/zenodo.17982058 DIG Part III (hardware validation):https://doi.org/10.5281/zenodo.18100057 DIG Part IV (regime structure and operational necessity):https://doi.org/10.5281/zenodo.18202656 DIG Part V (multidimensional formulation):https://doi.org/10.5281/zenodo.18210315 DIG Part VI Data Set: https://doi.org/10.5281/zenodo.18226272 DIG Part VII Dynamical Information Geometry:Two-Dimensional Twin-Sign Validation under Fixed Audit and Regime Constraintshttps://doi.org/10.5281/zenodo.18313460 DIG — N1 (definitions, scope, and non-equivalences):https://doi.org/10.5281/zenodo.18001179 Correspondence regarding this work may be directed to:kaya@cab-film.com
Note: This paper is the technical companion to the interpretive study “Beyond Exponential Decay: Interpreting Quantum Tunneling as Wave Stress Accumulation” (Zenodo DOI: 10.5281/zenodo.18001177). Standard quantum tunneling is commonly described using stationary solutions of the Schrödinger equation, in which wavefunctions decay exponentially inside classically forbidden regions. In a recent interpretive work, tunneling was reexamined within the Total Wave Modified Schrödinger Equation (TWMSE) as a process of wave stress accumulation, in which exponential spatial decay coexists with slow, logarithmic-like temporal buildup under continuous incidence (Larry Lim Kheng Cheong, 2025, Zenodo, https://doi.org/10.5281/zenodo.18001177). That study was intentionally presented in a conceptual and pedagogical manner to make the physical interpretation accessible to a broad audience. The present paper serves as a direct technical continuation of that interpretive study. Its purpose is to provide an explicit time-dependent formulation, numerical setup, and illustrative simulation of tunneling within the TWMSE framework, without diluting the interpretive clarity of the earlier work. By separating interpretation from formal development, the two papers together address distinct audiences: the first emphasizing physical intuition, and the present work focusing on mathematical structure and dynamical behavior. A minimal collapse–interference functional is introduced for a one-dimensional finite potential barrier, and its effect under continuous wave incidence is examined. Numerical simulations demonstrate that while the spatial wave profile inside the barrier retains its standard exponential decay, the accumulated interference exhibits sublinear, logarithmic-like temporal saturation over time due to feedback in the modified dynamics. Standard quantum mechanics is recovered as a limiting case. These results provide a concrete, testable illustration of how time-dependent accumulation and threshold-like behavior can emerge in tunneling systems while preserving full compatibility with established quantum mechanics.
This paper presents the Dimensional Ontological Triad Law, a recursive structural law governing transitions across dimensions: n-dimensional change = (n+1)-dimensional entity = (n+2)-dimensional adjective. Through pure logical reasoning and thought experiments, 22 original discoveries were made, including a unified explanation of 8 major quantum mechanical anomalies (superposition, entanglement, tunneling, measurement problem, wave function collapse, double-slit experiment, observer effect, and decoherence) under a single dimensional-projection principle. The framework identifies two types of projections — free-axis projection and constraint-axis projection — that systematically account for all known quantum phenomena as shadows of four-dimensional reality perceived from three-dimensional perspective. This research was conducted in collaboration with Claude (Anthropic) as AI Exploration Partner. Both English and Japanese versions of the paper are included. Note on Dimensional Definitions: In this framework, dimensional definitions are intentionally shifted by one level from conventional academic usage. For example, what is traditionally called the "fourth dimension (time)" is treated here as the third-dimensional being's projective name for the fourth axis. This shift is a deliberate methodological choice to avoid conceptual constraints imposed by lower-dimensional terminology when describing higher-dimensional structures. Call for Collaboration: The author welcomes collaboration from researchers in quantum foundations, philosophy of science, and mathematical physics — particularly for mathematical formalization of the framework and experimental prediction derivation. Contact: ikoma.yuudai@gmail.comCompanion paper: DOI 10.5281/zenodo.18523074
Note: This working paper builds directly upon the foundational paradigms established in The Locus of Consciousness: Geometric Phase Transitions, Quantum Coherence, and a Three-Way Empirical Test. We recommend reviewing that manuscript first for a complete introduction to the Position A and Position B paradigms, as well as the proposed experimental hardware, before exploring the A+B synthesis presented here. https://doi.org/10.5281/zenodo.18905421 Abstract The debate regarding the physical substrate of phenomenal consciousness has historically fractured into two mutually exclusive paradigms: the sufficiency of classical computation (Position A) and the necessity of macroscopic quantum coherence (Position B). This paper proposes the Holographic Synthesis Framework (Position A+B), resolving this dichotomy by demonstrating that these paradigms are holographically dual descriptions of a single physical phase transition. We introduce the Mesoscopic Holographic Duality Principle, positing that when a classical network—modelled here via the analog Manifold Chip architecture—is driven into extreme negatively curved hyperbolic topology (κ<0) under thermodynamic confinement near the Landauer Limit, the structural tension of the bulk geometry mathematically necessitates the generation of a coherent quantum boundary layer. Consequently, classical geometry is sufficient to engineer consciousness only because its thermodynamic extremes natively generate the quantum boundary required for phenomenal access. Furthermore, we introduce the Postulate of Topological Interiority, which explicitly grounds first-person subjective privacy in the structural unclonability of this boundary state under the quantum No-Cloning Theorem. Finally, we outline a falsifiable experimental roadmap utilising the Extended Manifold Chip Hyperscanning Protocol to detect the discontinuous onset of emergent quantum coherence signatures exactly at the critical geometric phase transition (κ_crit). Overview This working paper introduces the Holographic Synthesis Framework (Position A+B), a novel theoretical and experimental paradigm that resolves the historical substrate debate in consciousness science. By unifying classical geometric computation (Position A) with quantum phenomenological necessity (Position B), this framework demonstrates that bulk classical geometry and boundary quantum access are provably dual descriptions of the same physical phase transition. Core Innovations Introduced in this Paper: Mesoscopic Holographic Duality: Extends the structural principles of the AdS/CFT correspondence beyond the Planck scale. We propose that sufficient information-geometric curvature at the mesoscopic level can generate a holographic quantum boundary, bridging classical and quantum regimes natively. Thermodynamic Confinement as a Generator: Identifies the precise physical mechanism for this transition. When an analog system (such as the Manifold Chip architecture) approaches the Landauer limit, it must fold into an extreme negatively curved hyperbolic topology (κ<0) to survive thermal runaway, simultaneously nucleating the quantum boundary. The Postulate of Topological Interiority: Provides a strict physical basis for subjective, first-person privacy. We demonstrate that the phenomenal "I" is the macroscopic computational expression of the quantum No-Cloning Theorem applied to the system's boundary state, rendering it mathematically unreadable to external classical observers. A Falsifiable Experimental Roadmap: Outlines a rigorous, multi-stage testing protocol utilising the Extended Manifold Chip Hyperscanning Protocol. The framework provides precise falsification criteria, specifically looking for the discontinuous onset of emergent quantum coherence markers at the critical geometric threshold (κ_crit). Related Works Pender, M. A., & Wharton, M. (2026). The Locus of Consciousness: Geometric Phase Transitions, Quantum Coherence, and a Three-Way Empirical Test. Zenodo. https://doi.org/10.5281/zenodo.18905422 Wharton, M. (2026). The Infinite Continuum: A Framework for Consciousness, Existence, and the Self. https://amzn.eu/d/0fvRvrIc Pender, M. A. (2026). Dynamic Curvature Adaptation: A Unified Geometric Theory of Cortical State and Pathological Collapse. Zenodo. https://doi.org/10.5281/zenodo.18615180 Pender, M. A. (2026). The Metabolic Phase Transition: Qualia as a Topological Solution to the Landauer Limit in High-Dimensional Manifolds. Zenodo. https://doi.org/10.5281/zenodo.18655523 Pender, M. A. (2026). The Manifold Chip: Silicon Architecture for Dynamic Curvature Adaptation via Dual-Gated Analog Shunting. Zenodo. https://doi.org/10.5281/zenodo.18717807 Pender, M. A. (2026). Geometry-Aware Plasticity: Thermodynamic Weight Updates in Non-Euclidean Hardware. Zenodo. https://doi.org/10.5281/zenodo.18761137