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The Unifying Force: A Computational Proof of Wavefunction Collapse and Energy Emission via Topological Stress in QGEFT

Yaniv Cohen

Published Aug 10, 2026• 0 citations
Publisher

Abstract

Paper 80 does not claim that full continuum quantum mechanics or the exact Landauer bound has been derived from first principles. It does show that the verified QGEFT benchmark now supports a quantitative unifying-force law $F_U = -k_\tau W_M D_i$: a dispersed wave ($D_i = 2.17$) collapses to a point ($D_i = 0$) in a single Monte Carlo sweep once the anchor weight crosses the threshold $W_M^* = 950$ (theory $\approx 923$), and the released quadratic energy ($\Delta E_{rel} = 1164$) correlates with the erased virtual arcs at $r = 0.985$, providing a mechanical, thermodynamic origin for photon emission.

DOI
10.5281/zenodo.21869034

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•Jul 19, 2026•0 citations
Paper 80 does not claim that full continuum quantum mechanics or the exact Landauer bound has been derived from first principles. It does show that the verified QGEFT benchmark now supports a quantitative unifying-force law FU=−kτWMDiF_U = -k_\tau W_M D_iFU​=−kτ​WM​Di​: a dispersed wave (Di=2.17D_i = 2.17Di​=2.17) collapses to a point (Di=0D_i = 0Di​=0) in a single Monte Carlo sweep once the anchor weight crosses the threshold WM∗=950W_M^* = 950WM∗​=950 (theory ≈923\approx 923≈923), and the released quadratic energy (ΔErel=1164\Delta E_{rel} = 1164ΔErel​=1164) correlates with the erased virtual arcs at r=0.985r = 0.985r=0.985, providing a mechanical, thermodynamic origin for photon emission.
The current Paper 76 benchmark does not claim that continuum quantum mechanics or the exact ℏ/2\hbar/2ℏ/2 bound has been derived from first principles. It does show that the verified QGEFT Phase-4 kappa scan and HMC pipeline now resolve a clear inverse relationship between position certainty (IPR) and momentum/energy scale (mass gap, force norms). At κ=0.5\kappa=0.5κ=0.5, the fermion is tightly confined (IPR≈0.998IPR\approx0.998IPR≈0.998) with a large mass gap (≈0.140\approx0.140≈0.140); at κ=2.0\kappa=2.0κ=2.0, it delocalizes (IPR≈0.020IPR\approx0.020IPR≈0.020) with a collapsed mass gap (≈0.017\approx0.017≈0.017). The HMC trajectory confirms that maintaining any fermionic state demands enormous topological forces (∥Fedge∥∼106\|F_{edge}\| \sim 10^6∥Fedge​∥∼106), and the correlation structure supports the Heisenberg trade-off: Corr(IPR,gap)=−0.73\mathrm{Corr}(IPR, gap) = -0.73Corr(IPR,gap)=−0.73. The defensible conclusion is that uncertainty emerges in QGEFT as a topological pressure-release phenomenon---the graph's mechanical response to avoid structural fracture when forced into geometrically singular configurations.
Paper 78 does not claim that the continuum limits of quantum field theory, general relativity, or the Standard Model have been fully derived. It claims a narrower but still powerful result: five cornerstone phenomena of modern physics—wave-particle duality, interference, entanglement, gravity, and electromagnetism—all emerge naturally from a single computational engine (Monte Carlo edge-swap on a discrete graph minimizing E=∑(ki−k0)2E = \sum (k_i - k_0)^2E=∑(ki​−k0​)2) without coding any of the standard equations (Schrödinger, Einstein, Maxwell) into the experiments. The 5-for-5 outcome provides strong computational evidence that the QGEFT paradigm of "All forces = Local Optimization + Topology" is both viable and quantitatively testable.
In the current `N=1024`, `T=0.3` QGEFT benchmark, a lightweight one-edge defect diffuses across a finite topological probability cloud before detector activation, reaching support `8`, mean radius `≈ 3.875`, and spatial variance `≈ 2.0`. Once a macroscopic detector node is activated at sweep `16` and driven to degree `72`, the defect is funneled into the detector basin and undergoes an objective anchoring event at sweep `26`. The recent positional cloud then collapses irreversibly to support `1` and variance `0.0`, supporting a structural, observer-free objective-collapse mechanism in the emergent graph vacuum.
New edited version Title: Quantum Mechanics as Topological Intersection Theory: The Born Rule, Wavefunction Collapse, and Planck’s Constant from Worldline Non-Injectivity Abstract: This work presents a comprehensive derivation of the foundational principles of quantum mechanics by shifting the paradigm from stochastic postulates to a deterministic geometric framework. Utilizing the TPST-DGQ (Topological Phase Signalling Theorem - Discrete Geometric Quantization) framework, the paper demonstrates that the core axioms of quantum theory emerge as necessary theorems from the geometry of non-injective worldlines. Key Mathematical and Physical Derivations: Geometric Origin of the Born Rule: The paper proves that the probability density ∣ψ(x,t)∣2|\psi(x,t)|^2∣ψ(x,t)∣2 is a "topological intersection density." By analyzing a single ultra-relativistic worldline Xμ(τ)X^\mu(\tau)Xμ(τ) that intersects the constant-time hypersurface Σt\Sigma_tΣt​ at N(ϵ)N(\epsilon)N(ϵ) distinct points, the Born rule is derived as the normalized frequency of these intersections. This replaces the epistemic interpretation of probability with a frequentist geometric count. The Wavefunction as a Transport Representation: The wavefunction ψ(x,t)\psi(x,t)ψ(x,t) is defined as the complex square root of the intersection density. Its phase is shown to be the result of proper-time transport along the continuous segments of the worldline connecting different intersection points. Emergence of the Schrödinger Equation: The manuscript derives the Schrödinger equation as the fundamental transport law for the intersection density. This derivation is shown to be valid under the condition of "inter-sheet phase coherence," a state forced by the Ontological Identity Principle and the finiteness of the action. Fundamental Nature of Planck’s Constant (ℏ\hbarℏ): Instead of a fundamental constant of nature, ℏ\hbarℏ is derived as the minimum action per radian of phase accumulated between stable folds of the worldline. It is functionally linked to the UV cutoff ϵ\epsilonϵ and the rest mass mmm, providing a parameter-free basis for the quantum of action. Deterministic Wavefunction Collapse: Collapse is redefined as a topological transition from a non-injective state (N>1N > 1N>1) to an injective state (N=1N = 1N=1). This occurs through a physical interaction (measurement) that reduces the Lorentz factor below a critical threshold γcrit\gamma_{crit}γcrit​, providing a dynamical solution to the measurement problem. Unified Regularization: The paper establishes the "Universal Topological Cancellation," showing that the same scaling mechanism N(ϵ)∼ϵ−(d−2)N(\epsilon) \sim \epsilon^{-(d-2)}N(ϵ)∼ϵ−(d−2) that regularizes the Ryu-Takayanagi entropy in holography and the Coulomb self-energy in classical electrodynamics also ensures the UV-finiteness of the quantum intersection density. This research unifies quantum mechanics, classical electrodynamics, and holographic gravity under a single topological principle: worldline non-injectivity as a necessary and sufficient condition for finite physics at every level. This manuscript is current in Official Peer Review. Not final version.Copyright©2026 Alex De Giuseppe.All rights reserved. This work is protected by copyright. Any form of plagiarism, unauthorized reproduction, or misappropriation of ideas, mathematically results, or text without proper citation constitutes a violation of academic and intellectual property standards and common laws. No commercial use, adaptation, or derivative works are permitted without explicit written permission from the author. For correspondence, citations, collaboration inquiries, or feedback please contact:degiuseppealex@gmail.com The hash files that determine ownership have been created
The current Paper 75 benchmark does not claim that full continuum quantum gravity or laboratory entanglement swapping has already been derived on a graph. It does show that the verified QGEFT temporal entanglement engine reproduces the Megidish-Eisenberg (2013) result: particle D, created *after* particle A was destroyed, inherits A's topological fingerprint through the scar region with composite similarity **0.9379** and **Z=3.56** (>2σ>2\sigma>2σ, null μ=0.8163±0.0342\mu=0.8163\pm0.0342μ=0.8163±0.0342). The control measurement (A↔C, where C was placed far from A's scar) shows a lower similarity of 0.8502, proving the memory is spatially localized. At N≤64N\le64N≤64, the signal drowns in background noise (null similarity ≈0.93\approx0.93≈0.93), confirming that N≥256N\ge256N≥256 is required for clean topological memory emergence. The defensible conclusion is that entanglement is a statistical correlation preserved in the dynamic memory of quantum spacetime—not a physical thread stretched through space.