ERRATUM (2026-06-09). CLXVII-1 (the 'clean zero-parameter 3D test' I3D*kF^2 = pi(xi*kF)^2 vs Ku+2012) is WITHDRAWN, on three independent grounds: (1) dimensional inconsistency (I3D = integral d3r has units length^3, so I3D*kF^2 is a length, not the dimensionless RHS; correct group is I3D*kF^3); (2) false premise -- it assumes g_updown(r->0)->0, but the exact Tan relation g2_updown=(I/16pi^2)(1/r^2 - 2/ar) DIVERGES as 1/r^2, so the integral is contact-contaminated; (3) Ku+2012 is a thermodynamic EoS measurement with no real-space g(r) to integrate. CLXVII-2 (the 2D dip-only, one-parameter ~15% qualitative support) stands. Files: original paper + erratum. ---- Paper CLXVI proposed the excluded-area sum rule R [1 −gpair(r)] d2r = πξ2 for the strongly-interacting Fermi gas, motivated by bulk-channel exclusion of Cooper pairs in the brane-bulk framework. Direct application to the 2D AFQMC data of Daix et al. (2026, PRL 136, 153402; arXiv:2504.01885) reveals a subtlety: in 2D, the pair correlation g↑↓(r →0) diverges logarithmically (as log2(kF r), following Werner & Castin 2012, their Eq. 8), rather than vanishing. The integrand 1 −g↑↓therefore mixes two physically distinct contributions: (i) intra-pair two-body physics controlled by the Tan contact C, and (ii) inter-pair exclusion — the actual prediction of the framework. We recast CLXVI-1 into two predictions: CLXVII-1 (clean, 3D): I3D · k2 F = π(ξ · kF )2 with ξ determined independently from the Tan contact, testable against Ku et al. (2012, MIT unitary gas) data; and CLXVII-2 (2D dip region only): Idip ·k2 F ≈π(ξexcl ·kF )2 restricted to g < 1. Applied to Daix et al. 2026 at crossover η ≡log(kF a2D) = 1.0–1.2, the triangular- dip integral evaluates to Idip · k2 F ≈2.76, matching π(ξkF )2 ≈2.77 for ξkF ≈0.94–1.0 — qualitative support within ∼15% without any free parameter. The 20–22% BCS violation (pair dip depth) and the location kF r ∼2 are both consistent with bulk-channel exclusion. The clean zero-parameter test requires 3D unitary gas data. 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.
ERRATUM (2026-06-09). CLXVII-1 (the 'clean zero-parameter 3D test' I3DkF^2 = pi(xikF)^2 vs Ku+2012) is WITHDRAWN, on three independent grounds: (1) dimensional inconsistency (I3D = integral d3r has units length^3, so I3DkF^2 is a length, not the dimensionless RHS; correct group is I3DkF^3); (2) false premise -- it assumes g_updown(r->0)->0, but the exact Tan relation g2_updown=(I/16pi^2)(1/r^2 - 2/ar) DIVERGES as 1/r^2, so the integral is contact-contaminated; (3) Ku+2012 is a thermodynamic EoS measurement with no real-space g(r) to integrate. CLXVII-2 (the 2D dip-only, one-parameter ~15% qualitative support) stands. Files: original paper + erratum. ---- Paper CLXVI proposed the excluded-area sum rule R [1 −gpair(r)] d2r = πξ2 for the strongly-interacting Fermi gas, motivated by bulk-channel exclusion of Cooper pairs in the brane-bulk framework. Direct application to the 2D AFQMC data of Daix et al. (2026, PRL 136, 153402; arXiv:2504.01885) reveals a subtlety: in 2D, the pair correlation g↑↓(r →0) diverges logarithmically (as log2(kF r), following Werner & Castin 2012, their Eq. 8), rather than vanishing. The integrand 1 −g↑↓therefore mixes two physically distinct contributions: (i) intra-pair two-body physics controlled by the Tan contact C, and (ii) inter-pair exclusion — the actual prediction of the framework. We recast CLXVI-1 into two predictions: CLXVII-1 (clean, 3D): I3D · k2 F = π(ξ · kF )2 with ξ determined independently from the Tan contact, testable against Ku et al. (2012, MIT unitary gas) data; and CLXVII-2 (2D dip region only): Idip ·k2 F ≈π(ξexcl ·kF )2 restricted to g < 1. Applied to Daix et al. 2026 at crossover η ≡log(kF a2D) = 1.0–1.2, the triangular- dip integral evaluates to Idip · k2 F ≈2.76, matching π(ξkF )2 ≈2.77 for ξkF ≈0.94–1.0 — qualitative support within ∼15% without any free parameter. The 20–22% BCS violation (pair dip depth) and the location kF r ∼2 are both consistent with bulk-channel exclusion. The clean zero-parameter test requires 3D unitary gas data. 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.
Daix, Dixmerias, He, Verstraten, de Jongh, Peaudecerf, Zhang and Yefsah (2026, Physical Review Letters, DOI: 10.1103/2t2k-3ftx) report the first direct imaging of Cooper pair inter-pair correlations in a 2D Fermi gas of ⁶Li atoms. Using atom-by-atom snapshot imaging and exact quantum Monte Carlo simulation, they find that the pair-pair correlation function g ² (r) drops below unity at short pair separations — Cooper pairs ⁻ ⁾ actively repel neighboring pairs, maintaining a minimum spacing. BCS theory, which treats the condensate as a mean field with no inter-pair correlations, predicts g ² = 1 at all separations and cannot account for this ⁻ ⁾ dip. The One-Octonion Brane-Bulk Framework (Papers XLIV and CLXIV, Jagadeesan 2025–2026) provides a natural explanation. Paper XLIV established that Cooper pairs are phase-locked T2 coherent zones and Type II vortices are topological brane threads whose repulsion forms the Abrikosov lattice. Paper CLXIV (April 2026) established that the Cooper pair is a coherent brane-to-bulk-to-brane transit through the interference-free AdS₅ bulk: two electrons that find a common brane thread travel through the bulk together, phase-coherent, and return to the brane as a standing wave. The inter-pair repulsion observed by Daix et al. is the direct consequence: two brane threads cannot share the same AdS₅ bulk region. The bulk channel has a topological hard core of radius ξ (the T2* coherence length = Cooper pair coherence length). When two pairs approach within r < ξ, their bulk channels attempt to overlap, generating destructive interference in the bulk — the pairs are expelled. The dip in g ² (r) is the brane-surface signature of this bulk ⁻ ⁾ exclusion. We derive a quantitative prediction: ∫ [1 − g ² _pair(r)] d²r = πξ² (the excluded brane area per ⁻ ⁾ pair), testable against the Daix et al. data. We further identify Daix et al.'s 'dancing couples keeping distance' metaphor as a precise physical description: each pair occupies its own bulk channel on the AdS₅ dance floor; channels are exclusive. 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.
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.
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.
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.
We show that many-body dynamical localization (MBDL) in the kicked Lieb-Liniger model [Yang et al., PRL 136, 123402 (2026)] is the exact many-body analog of balanced steady-state free precession (bSSFP) in magnetic resonance imaging, with the Gudermannian function gd(x) = arctan(sinh(x)) serving as the canonical mathematical bridge between the flat-space (brane) and hyperbolic-space (AdS₅ bulk) descriptions. Three identifications are established with full mathematical rigour and zero free parameters. (i) The on-site Lorentzian distribution of Vᴵ = tan(φᴵ) in the mapped lattice model is the exact analog of the off-resonance Lorentzian in bSSFP: both arise from the theorem that tan(Uniform[−π/2, π/2]) is Cauchy-distributed, and in bulk coordinates arcsinh(Vᴵ) has the Gudermannian as its cumulative distribution function. (ii) The algebraic hopping tail Wᴵᴵ' q λ in flat momentum space is exactly exponential in AdS hyperbolic ∼ ⁻ coordinates (q = sinh(ρ)) with rate λ, via q λ = sinh λ(ρ) ≈ 2λ exp(−λρ). (iii) The tail crossover λ = 4 ⁻ ⁻ → 3 as interaction strength increases corresponds exactly to the G₂ permutohedron eigenvalue transition k = 6 → k = 4, revealing hidden G₂ structure in the Lieb-Liniger model. The crossover scale γ 1 is reproduced geometrically at gd(ρ_cross) = π/4, giving q_cross = sinh(log(1+√2)) = 1 ∼ exactly without any free parameter. Additionally, the Gudermannian saturation gd(x) → π/2 as x → ∞ naturally encodes the MOND acceleration saturation at the sump T2* coherence radius. Three falsifiable predictions are stated. 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.