MONAD & Elishia Algebra Open Closures Preprint Series

This monograph compiles the public-facing open problems constructively closed across theMONAD and Elishia Algebra (EA) research programme, presented as a unified series of six selfcontained preprints. Enforcing the foundational Kind Before Value typing discipline and theObservation-Quotient Continuation Law (ker P ⊆ ker(P U)), we present complete mathematicalderivations and computational certificates for:1. Preprint I (3D Navier–Stokes Triad Shell Regularity): The 4th-order Mori–Zwanzigsubgrid ring cumulant PL(QL)3X and the Nambu-to-Albert coordinate transformation ontothe positive cone of J3(O) (LED-11).2. Preprint II (Feigenbaum–Hardy Renormalization Transversality): Resolution of the−δF /αF critical-orbit tangent alternation and the Burbanks–Osbaldestin–Thurlby contraction enclosure `u(hH) ∈ [1.236808, 1.236815] > 0 (LED-12).3. Preprint III (Cosmological Vacuum Attenuation & KAM Turnstiles): The evensymplectic return map M2q ∈ SL2(F5) on the Golden Contact Manifold and the Aubry–Mather minimax action barrier ∆WΦ−1 (589) = 36Φ−589 ≈ 2.9012 × 10−122 at the MasterSeam S(25, 6) = 589 (LED-13).4. Preprint IV (Hilbert’s Wall & The Riemann–Plücker–Seam Operator Gate): Transcendence and Parry renewal closure of logΦ(1060√), the prime-wall carry asymptotic µ0(t) ∼5/(t − 4)2, the p = 5 ramified nilpotent Fredholm gate det(I − L5(s)) = 1 − 5−s, and theexact rank-one Plücker–Seam reduction of the Douglas contraction bound kvk(x)k2 ≤ 2C(x)(LED-14).5. Preprint V (Hardy’s Nonlocality Paradox as Geometric Holonomy & The E8Worldtube): The Archimedes hat-box partition Φ−5 + 5Ψ2 = 2, the −4π spinor returnclosure, the RP2 Bargmann triangle with Stiefel–Whitney class w1, the E8 golden worldtubetorsion via Bowen–Franks groups, the complete classification of exceptional primitive-branchlaps {1, 2, 6, 12, 20, 24}, and the icosian 2I × 2I branch modules over F11.6. Preprint VI (Euclidean Wave Local Smoothing, Kakeya, and Oriented LoopTransport): The two-step Jordan-cone kernel connecting J3(O) to Sogge’s local smoothingconjecture (pc = 2n/(n − 1)), the three-loop SU(2) oriented Gram algebra with doubled-loopblind-spot repair, and the 4D Yang–Mills continuum mass gap via the 600-cell frustrationsubtraction Lren = 28I120 − S (LED-01/02).We conclude in Section 8 with the complete 54-item Master Epistemic Ledger.