Paper L: Diusion, the Random Walk, the Bose-Einstein Condensate, and the Feynman Path Integral as Expressions of the G2 Fano Valve on S 7 Paper L

Bharathi Jagadeesan

Published May 19, 2026• 0 citations

Abstract

Part of the One-Octonion Brane-Bulk Framework paper series. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.

DOI: 10.5281/zenodo.20299874

Related papers

One-Octonion Brane-Bulk Framework - Paper CCCLVIII: Reading the Aharonov-Bohm Phase as e7 Holonomy

Bharathi Jagadeesan

Consistency-bridge paper - standard equations untouched, no new prediction registered, and no claim that the Aharonov-Bohm experiment observes brane-bulk transit. The magnetic Aharonov-Bohm phase Delta_phi = q Phi_B / hbar - the holonomy of the U(1) gauge connection around a non-simply-connected region (Aharonov & Bohm 1959; observed by Chambers 1960 and, with fully shielded toroidal flux, Tonomura et al. 1986) - is given its One-Octonion Brane-Bulk (OOB) dictionary. The electromagnetic fields E and B remain the brane-measured force fields; the vector potential A is read as the brane-visible phase connection sampled by a charged standing wave on the Fano-incidence lattice, with the e7 separator as the framework's brane-bulk phase gate. The fringe shift is the relative e7 holonomy of two path components of one wavefunction sampling the same globally nontrivial connection with opposite orientation: the framework's antegrade/retrograde transit language is made precise as the two half-loop line integrals +/- Phi_B/2, with no local force on the exposed field-free path and no beam-sourced potential. The reading connects to the phase-only transit theorem of Paper CCCLVII and the Gudermannian phase ledger, and it names an internal benchmark for any future formalization of the Fano/e7 sampling dictionary: it must reduce exactly to the Abelian U(1) holonomy exp[(iq/hbar) closed-loop-integral A dx] in the electromagnetic sector, must not predict a local force where the standard setup has none, and must not make the beam the source of the background potential - explicit failure conditions are stated. Bharathi Dasan Jagadeesan, M.D., University of Minnesota CMRR. ORCID 0000-0002-1143-941X. CC-BY-4.0.

Sep 1, 20260 citations

One-Octonion Brane-Bulk Framework - Paper CCCLVII: Phase-Only Transit Makes Feynman's Two Path-Integral Postulates a Shallow-Sector Theorem

Bharathi Jagadeesan

The One-Octonion Brane-Bulk (OOB) framework reads Feynman's 'all paths' as virtual bulk-excursion channels whose coherent return determines the observed brane probability. This paper gives that reading a mathematical and experimental form. (1) Theorem: on Paper CCLVIII's shallow-sector premise that phase-only transit feedback closes to standard Schrodinger dynamics, Feynman's two path-integral postulates (equal-magnitude path amplitudes with phase S/hbar; probabilities from the coherent sum) follow as theorems for free equal-time segments. (2) First table-level bound: Wen et al. (Science Advances 12, eaeh1011, 2026, DOI 10.1126/sciadv.aeh1011) test both postulates directly by single-photon propagator tomography over 17^5 = 1,419,857 paths; fitting their public Dryad Fig4B table (DOI 10.5061/dryad.x0k6djj14) with the action-cost model |phi|^2 = C(1 - kappa S/hbar) gives kappa_hat = 8.27e-3 with row-bootstrap 95 percent interval [5.59, 10.85]e-3, so |kappa|_95 <= 1.09e-2, a table-level bound and replication target; the tables are processed figure means without path-level covariance, and the trend lies inside the experiment's stated 17.4 percent postulate-II error. (3) Registered tests: P-CCCLVII-1 registers the kill condition kappa = 0 in the shallow free sector (a confirmed path-level amplitude trend falsifies phase-only transit there); P-CCCLVII-2 registers the barrier-sector discriminator, propagator tomography with a controlled tunnelling barrier of WKB depth rho_B, where the flux-normalized Gudermannian/JUNO return vertex gives a linear self-energy onset tanh(rho_B) against the quadratic tanh^2(rho_B) onset of the analytic-vertex alternative. Files: PDF, the amplitude-cost verification script with its output and fitted bound, and the figure script and figure. Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID 0000-0002-1143-941X. CC-BY-4.0.

Sep 1, 20260 citations

Paper CCI: The Quantum Wave Function as a Brane Displacement Field: Deriving the Schrödinger Equation Without Quantization Postulates embedded in a five-dimensional anti-de Sitter space, the quantum wave function arises as the brane

Bharathi Jagadeesan

May 19, 20260 citations

Paper CLXXII: Time Rondeau Crystal as Mesoscopic Brane-Bulk Transit Disorder April 20, 2026 · Zenodo: 10.5281/zenodo.19120873

Bharathi Jagadeesan

Moon, Schindler et al. (Nat. Phys. 21, 1813-1819, 2025) demonstrate a time rondeau crystal in 13C nuclear spins: long-range stroboscopic DTC order coexisting with short-range micromotion disorder. We identify this as the mesoscopic realisation of brane-bulk transit disorder. The transit-to-period ratio t/tau_pi = 4.685 (PDG) is irrational, involving sqrt(3). f_bulk = 3.691% is transcendental. The n-RMD multipole spectrum maps to G2 permutohedron eigenvalues. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.

May 19, 20260 citations

Chapter 15. The Beta Function for the Bose Conden

G. Benfatto, Giovanni Gallavotti

Princeton University Press eBooksDec 31, 19950 citations

Paper CLXI: One-Octonion Bell Correlations in Motional States of Massive Particles as a Confirmation of the 5D Brane Thread Entanglement Mechanism

Bharathi Jagadeesan

Athreya et al. (2026, Nature Communications 17:2357) report the first experimental observation of Bell correlations in motional (momentum) states of massive particles, using momentum-entangled pairs of ultracold ⁴He* atoms from Bose-Einstein condensate collisions. They observe a Bell correlation amplitude A = 0.86(3) and violation of a steering inequality at 3.9σ (C = 1.752 ± 0.085 > √2). We show that this result is a direct confirmation of Prediction P_XV-1 of the One-Octonion Brane-Bulk Framework (Paper XV, Jagadeesan 2025): nonlocal Bell correlations for massive particles in motional states arise from a topological fixed line in 5D phase space — a geometric thread in the AdS₅ bulk shared by both entangled atoms. The framework's entanglement model has two components: (1) a topological brane memory thread, a 1D closed curve in brane × bulk coordinates visible only in cross-particle joint measurements, and (2) bulk communication through a common focal zone in AdS₅. The octonionic non-associativity (e_i · e_j) · e_k ≠ e_i · (e_j · e_k) is the algebraic reason entangled states cannot be factorized, and G₂ = Aut( ) organizes the 𝕀 complete space of non-factorizable correlations. We verify the key experimental numbers from first principles, identify what is derived vs. inherited from quantum optics, state four corrected predictions for the next generation of experiments, and update the confirmed prediction count. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.

May 19, 20260 citations