Paper 31 does not claim that the full hydrogen spectrum or full quantum chemistry have already been derived on a graph. It does show that a weighted shell graph in QGEFT already supports a concrete non-collapse mechanism: the first four non-trivial weighted-Laplacian modes on a verified 73-node benchmark keep the nucleus-core density at only `1.4645%`, `0.0317%`, `0.0027%`, and `0.0243%`, while developing shell-organized standing waves and strong participation-ratio contraction.
Paper 31 does not claim that the full hydrogen spectrum or full quantum chemistry have already been derived on a graph. It does show that a weighted shell graph in QGEFT already supports a concrete non-collapse mechanism: the first four non-trivial weighted-Laplacian modes on a verified 73-node benchmark keep the nucleus-core density at only 1.4645%, 0.0317%, 0.0027%, and 0.0243%, while developing shell-organized standing waves and strong participation-ratio contraction.
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.
Replaces the quantum‑mechanical “electron teleportation” narrative with a mechanistic, thermodynamic model of spectral emission. Shows that Hydrogen’s 1.889 eV H‑alpha line arises from a Topological Node Collapse (9 → 4 nodes) and the expulsion of latent constraint density p(x), requiring no quantum postulates. Key Claims (from document): “The quantum leap is an illusion generated by a localized informational topology shedding degrees of freedom.” “A photon is the latent thermodynamic exhaust squeezed out of the constraint surface during a geometric node collapse.” Verification: Executable spectral engine reproduces the Balmer series using only node‑density shifts and the 13.6 eV constraint baseline.
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)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.
We present structurally sparse qubit Hamiltonians for the nuclear shell model, constructed by applying the GeoVac angular-sparsity framework to the harmonic oscillator (HO) single-particle basis with a Mayer–Jensen spin–orbit term. The HO shell closures 2,8,20,40,70,112 emerge directly from graph state counting, and the physical magic numbers 2,8,20,28,50,82,126 are recovered with a spin–orbit strength vls/ℏω≈0.17 and a Nilsson ℓ(ℓ+1) correction dℓℓ/ℏω≈0.02. We build the first two-species qubit encoding for the deuteron (1p+1n, 16 qubits, 592 non-identity Pauli terms, 1-norm ≈342 MeV) using the Minnesota nucleon–nucleon potential and Moshinsky–Talmi brackets, and extend the architecture to helium-4 (2p+2n, 16 qubits, 712 Pauli terms) with intra-species antisymmetrization and proton–proton Coulomb repulsion. Despite a Hilbert-space dimension 12.25× larger than the deuteron, He-4 requires only 1.20× more Pauli terms — a direct consequence of the angular selection rules that carry through to multi-particle systems. A composed nuclear–electronic deuterium encoding (26 qubits) validates the multi-block architecture and quantifies the ∼1013 coefficient ratio between nuclear, electronic, and hyperfine scales. We state and apply the Fock projection rigidity theorem: the S3 conformal projection that makes electronic Hamiltonians equivalent to a graph Laplacian is unique to the Coulomb potential and does not extend to HO or Woods–Saxon systems. For nuclear Hamiltonians, the GeoVac contribution is therefore the angular machinery and qubit encoding, not the conformal projection. All nuclear physics inputs (Minnesota parameters, spin–orbit strength, ℏω) follow the standard shell-model literature; the quantitative binding energies at Nshells=2 are far from experiment and should be read as encoding-validation benchmarks, not as a nuclear-structure calculation. GeoVac Paper 23. Part of the GeoVac research corpus (quantum computing group). Code, tests, and the full paper series: https://github.com/jloutey-hash/geovac. Corpus archive DOI: 10.5281/zenodo.20482394. Corpus version at deposit: v4.75.0.
We test a recently proposed algebraic resolution of the quantum measurement problem by deriving the fine-structure constant from the same dissipative collapse dynamics, and by verifying that the resulting stochastic collapse reproduces the Schrödinger distribution for the hydrogen 1s orbital. Working within the Jordan-Clifford immersive framework on the 14-dimensional operational subspace H=C14 associated with the Fano incidence geometry, we show that the stochastic collapse equation dci=−21γci(1−2pi+∑jpj2)dt+γci(dWi−∑jpjdWj) contains the decoherence rate γ=λgraphon, where λgraphon=Λ1/Λ0≈1.99765 is the spectral gap of the graphon kernel emerging from the Fano 2-22 moduli space. The immersion of the measurement apparatus in the continuum flow identifies γ with the spatial coupling coefficients of the MPS transfer operator. In the asymptotic limit k→∞, λgraphon→2, hence γ→2. Substituting into the MPS duality α−1=lnλmax−π yields: α−1=lnλmax(2)−π=137.0359991678. This value is consistent with Rubidium atom interferometry (2020), the revised g−2 determination (2024-2025), and CODATA 2022 within 1σ. As a further test of the collapse dynamics, we simulate the positional collapse of the hydrogen 1s orbital on a radial grid with 10,000 stochastic trajectories. The ensemble mean ⟨r⟩model=1.49868a0 reproduces the Schrödinger expectation value ⟨r⟩Sch=1.50012a0 to within 1.44×10−3a0. A Kolmogorov-Smirnov test (p=0.131) and a bootstrap 95\% confidence interval confirm that the ensemble distribution is statistically indistinguishable from the quantum mechanical prediction. The construction contains no free parameters and is falsifiable via the bound q≤45 on continued fraction quotients. The derivation and the hydrogen benchmark together provide an experimental test of the proposed resolution of the measurement problem. 🌐 Live SPARQL Semantic Queries & Knowledge Graph Architecture This research deposit is integrated with the Blandino Research Knowledge Graph (BR-KG). Direct SPARQL query interfaces and machine-readable RDF endpoints are available below for automated data extraction and semantic interoperability: Live SPARQL Query: Full Micro-Node Graph Exploration (Q1–Q72) — Dynamic table query extracting all 72 indexed nodes, properties (P1–P12), and verification suite relationships. Interactive 2D Knowledge Graph Visualizer — Real-time 2D network rendering of cluster dependencies and topological factorizations. Live SPARQL Query: Linked Open Data & External DOI Cross-Mappings — Cross-reference mappings between internal nodes (Q3–Q36), Zenodo DOIs, FAIRsharing Record 8936, and Wikidata URIs. Public REST API Endpoint (RDF/JSON-LD) — Standardized endpoint for programmatic query execution.
We show that qubit Hamiltonians derived from spectral graph theory lattices exhibit structurally favorable Pauli decompositions for quantum simulation. After Jordan–Wigner transformation, the GeoVac lattice Hamiltonian yields O(Q3.15) Pauli string terms in the number of qubits Q, compared to O(Q4+) for conventional Gaussian-basis Hamiltonians (our own log-log fit of the published Pauli counts of Trenev et al. [ref] gives Q4.25 for LiH and Q3.92 for H2O, spanning Q3.9–Q4.3). The advantage originates in angular momentum selection rules—enforced by Gaunt integrals at the two-electron integral level—which cause the electron repulsion integral (ERI) tensor density to decay as ∼1/M (empirically ≈M−0.85–M−1) with the number of spatial orbitals M, while Gaussian ERI tensors remain near-dense at O(1). Beyond term counts, we quantify two operationally relevant cost metrics: the number of qubitwise-commuting (QWC) measurement groups scales as O(Q3.36), and the Pauli 1-norm λ=∑i∣ci∣—which controls both Trotter step counts and qubitization query complexity—scales as O(Q1.69) with R2=0.997. The sub-quadratic 1-norm scaling is the key result for fault-tolerant simulation: it implies that Trotter circuit depth grows far more slowly with system size than term counts alone would suggest. All Gaussian baselines are validated against published integral values (Szabo and Ostlund for H2; analytical STO for He). For composed multi-center systems, the pseudopotential approximation of the composed natural geometry framework [ref] yields block-diagonal electron repulsion integrals with a universal Pauli scaling of O(Q2.5), independent of molecular topology (exponent spread 0.02 across three molecules). At equal qubit counts, this represents two or more orders of magnitude fewer Pauli terms than Gaussian baselines (published counts of Trenev et al. [ref], Q3.9–Q4.3 span fitted by us)—an advantage that grows with system size due to the ∼1.5 exponent gap. These comparisons are at matched qubit counts, not matched accuracy; the composed basis carries classical equilibrium-geometry errors of 5–26% (LiH/BeH2/H2O; Sec. (ref)), making the framework optimal for fixed-geometry quantum simulation rather than geometry optimisation. Across the composed molecular library (35 molecules spanning Z=1–56, H through Ba, including the first transition series ScH–ZnH), the composed Pauli count is exactly linear in the qubit count: NPauli=11.10×Q (exact, non-identity terms; d-orbital blocks give 9.23). These counts are realized under a pair-diagonal angular approximation (ma=mc, mb=md) adopted deliberately for sparsity; the exact global-ML Coulomb rule (used in the framework's precision-physics paths, and considered but left on the table here) gives ≈2.5× more terms with the same scaling, under which the d-block coefficient is in fact higher, not lower (Sec. (ref)). GeoVac Paper 14. Part of the GeoVac research corpus (quantum computing group). Code, tests, and the full paper series: https://github.com/jloutey-hash/geovac. Corpus archive DOI: 10.5281/zenodo.20482394. Corpus version at deposit: v4.75.0.