One-Octonion Brane-Bulk Framework - Paper CCCXXXVIII: The e7-Bypass Circuit Theorem — Closed Double-Bridge Circuits on the Fano Plane, the Junction-Toll Selection Rule via the CCXLIII Geometric Decay Map, and the Kinematic Transit Classification of Fully-Heavy Tetraquarks
Year: 2026
Type: article
Abstract: One-Octonion Brane-Bulk Framework, Paper CCCXXXVIII (short note). Paper LVIII builds a meson as a single cross-sector Fano bridge tolling through the e7 equatorial junction; its Prediction 103 reads the exotic states as double bridges. This note proves what separates closed circuits from every open-path process: (1) Circuit theorem [THEOREM]. Completing LVIII's three cross-sector lines forces the Fano plane uniquely; e7 lies on exactly three junction lines (one spatial + one colour node each); exactly four lines avoid e7 — the three bridges plus a forced pure-colour line {e4,e5,e6} — closing into exactly four zero-junction-crossing triangles: three tetraquark circuits and the baryon-side spatial triangle. The bypass belongs to closed circuits only. (2) Junction-toll selection rule. CCXLIII's geometric decay map (amplitude e−s per crossing, s = arccosh(3)/3, zero free parameters) prices the channels: pair snap = 0 crossings; open-flavour = 2 (toll e−4s ≈ 10%); one heavy-pair annihilation = 6 (toll ≈ 10−3); all-light ≈ 10−6 [IDENTIFICATION-grade counts; additive-toll assumption named]. The annihilation-minus-string-break difference Δ = 5 is calibrated family-universally (4.84 charm, 5.05 bottom) — the same integer from both families, as a geometric toll predicts; the toll ladder 6→1→0 reproduces the J/ψ ≪ ψ(3770) < X(6900) width ordering, a geometric counterpart of OZI suppression [INTERPRETATION]. (3) Kinematic classification. CLXXXV's kinematic formula (validated on its own benchmarks: pion–muon hop x = α0, f = fbulk) gives X(6900) f ∈ [0.8%, 12.4%] — weak bulk coupling; Class III (59.47%) is unreachable for real masses (Wolfram-symbolic). (4) Structure results: same-sense handle threading (one-way valve) with the homology obstruction making annihilation bulk-mediated within the framework's process inventory; the four constituents superimposing into two waves; the wave-correspondence selection principle [PRINCIPLE — introduced; kill test: bc-bbar-cbar states favour bottomonium+charmonium over Bc-pair]; the valve-resonance mechanism [MECHANISM] favouring the per-bridge reading (f = 12.4%) and suggesting a sequential dwell-time formation pathway (long-dwelling resonant pairs quartet-ize — consistent with the heavy-pair pattern of the narrow exotic candidates). Honest scope: the theorem and toll arithmetic are machine-verified; the crossing counts, principle, and mechanism are identification/principle-grade with owed formalizations named (transitional-wave sign structure; the dwell condition; deriving Δ = 5 from the quartic path). No new numerical predictions registered; framework total remains two free parameters (mt, δM/M). Verification: Python 9/9 + 12/12 + 23/23; Wolfram 10/10 + 12/12 (exact: e2s = (3+2√2)2/3, tanh(3s/2) = 1/√2); fresh-context fugu find + confirm rounds on every section. 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.
Author: Jagadeesan, Bharathi Dasan
Institution: University of Minnesota
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7169835751