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

Bharathi Jagadeesan

Published Sep 1, 2026• 0 citations

Abstract

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.

DOI: 10.5281/zenodo.22232874

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

Paper CCLVIII: The Quantum Potential as Brane-Bulk Transit Feedback — Resolving the Lohmiller–Slotine / Vattay Debate via the One-Octonion Brane-Bulk Framework

Bharathi Jagadeesan

Lohmiller & Slotine (Proc. R. Soc. A 482:20250413, 2026) propose a classical contracting-flow construction on the eikonal phase S(x,t) which they argue recovers quantum-wave evolution. Vattay (Comment, arXiv:2605.02621) correctly observes that the construction reproduces only the Hamilton-Jacobi + continuity sector of the Madelung-Bohm decomposition: it cannot generate the quantum potential Q = −ℏ²∇²√ρ/(2m√ρ), without which the recovered evolution is the classical limit of the Schrödinger equation, not the equation itself. We resolve this debate within the One-Octonion Brane-Bulk (OOB) framework. In OOB, the classical sector is the brane-localised f_bulk → 0 limit. Q arises as the back-reaction of brane-bulk transit components of the wavefunction on the brane density profile, with characteristic length the particle Compton scale ℓ_C = ℏ/(mc) and characteristic weight the transit probability f_bulk(E) = 1 − sinc²(E/2m_π). An order-of-magnitude estimate recovers the Madelung-Bohm form |Q| ≈ (ℏ²/2m)·|∇²√ρ|/√ρ structurally. The Gudermannian Class-III bridge (CCLII) supplies the smooth classical ↔ quantum interpolation via the same f_III = 1 − 4/π² blend used in the neutrino-sector chain. The Lohmiller-Slotine theorem is exact at f_bulk = 0; Vattay's missing piece is exactly the contribution identified here. Five predictions span atomic (null OOB at E ≪ m_π) to GeV (0.98 coherence loss in transparent media, tying to CCLVII). Honest scope: structural argument, not rigorous Schrödinger re-derivation; the O(1) coefficient is not pinned without further assumptions. Companion to CCLVII (same f_bulk(E) wavelength-asymmetry channel). 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

One-Octonion Brane-Bulk Framework - Paper CCCLIX: Reading Madelung-Bohm Hydrodynamics as the Brane-Side Dictionary of Bulk Transit

Bharathi Jagadeesan

Consolidation-bridge paper - standard equations untouched, no new prediction registered. Madelung's hydrodynamic split of the Schrodinger equation (psi = sqrt(rho) exp(iS/hbar) giving continuity plus a quantum Hamilton-Jacobi equation with the single extra term Q = -(hbar^2/2m) laplacian(sqrt rho)/sqrt rho) is kept exactly, and the One-Octonion Brane-Bulk (OOB) framework's existing account of Q - Paper CCLVIII's brane-bulk transit feedback, inherited strictly at its own claim level (a structural, order-of-magnitude recovery resolving the Lohmiller-Slotine / Vattay debate; Compton length, transit-fraction weight) - is organised against those identities as a disciplined dictionary. Three contributions: (1) the dimensional grammar of any bridge, Q_OOB ~ E_scale x f_bulk x C[rho], with a matched-point lemma showing that Compton-normalising the curvature functional forces E_scale x f_bulk = mc^2/2, so the transit weight cancels out of the exact term and no suppression of the exact Q of a given state by a small f_bulk is implied - the framework's f_bulk -> 0 statements concern sector occupancy and the action-violation scale, not the value of the Madelung identity; (2) explicit bookkeeping separating the canonical Class I calibration constant f_bulk = 1 - sinc^2(alpha_0) = 3.6919% (charged-pion decay calibration, alpha_0 = E_nu/2m_pi = 0.10673, E_nu = 29.792 MeV) from the energy-dependent transit spectrum on the neutral-pion brane-resonance scale (Paper CCLXX), including the gate-checked seam guard that evaluating the pi0-scale spectrum at E_nu gives 3.94%, a different object; (3) the two companion calibrations - the Aharonov-Bohm holonomy (Paper CCCLVIII) as the global entry of the framework's phase ledger beside Q's local curvature-energy entry (a framework reading, not a mathematical identity), and the pi0 -> e+e- coherent return factor 1 + 4/pi^2 (Paper CCXCI, documentary only) as the standing lesson that dimensionless weights become observable only through the observables they multiply. The f_bulk(E) argument is scoped to on-shell process energies; superpositions, driven states, and shifted energy origins are explicitly outside the corpus definition and not extended here. Bharathi Dasan Jagadeesan, M.D., University of Minnesota CMRR. ORCID 0000-0002-1143-941X. CC-BY-4.0.

Sep 2, 20260 citations

Paper XLI: Quantum Tunneling as Transient Bulk Excursion of the Focal Zone

Bharathi Jagadeesan

Quantum tunneling is the transient excursion of a particle's focal zone into the 5D bulk, bypassing a barrier that exists on the brane but has no bulk counterpart. (1) Imaginary momentum p = iℏκ is literally bulk-directed momentum: the imaginary unit i is the 90◦rotation from brane to bulk on S7 (Paper IV). (2) The tunneling probability e−2κd is the probability of completing a bulk excursion of length κd. (3) The Hartman eect is resolved: the traversal time is set by brane-bulk coupling and decoupling timescales, both barrier-thickness independent. (4) Resonant tunneling is a bulk standing wave condition. (5) The Gamow factor G = R κ(r) dr for α decay is the total bulk path length to bypass the Coulomb barrier. The Geiger-Nuttall law (115 years of α decay data) is the bulk-path-length formula for the Coulomb potential. 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

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

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.

May 19, 20260 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