Deriving physical reality from pure mathematics. No free parameters.
| Paper | DOI | |
|---|
| The Bootstrap Thesis | 18696697 | Foundational proposition. Eight principles. One axiom, one geometry, zero free parameters |
| Solutions Checklist | 18650187 | 77 problems examined. 27 derived, 29 dissolved, 18 proposed |
| Bootstrap Universe | 17906573 | Programme overview |
| Closure Principle | 18066924 | Where formal systems can't decide |
| Bootstrap Timeline | 18147670 | Derivation chain from self-reference to today. Visual overview |
| Bootstrap Foundations | 18085101 | Geometric origin of dimensionless constants |
| Growth of Self-Reference | 18979730 | ⭐⭐⭐⭐⭐ x=1+1/x → φ → Fibonacci → Lucas → φ⁵=11+1/φ⁵ → icosahedron → A₅ → 2I → S³/2I (Perelman). Seven forced steps. No parameters. The seed paper |
| Spectral Gap and Origin of Discreteness | 18998392 | ⭐⭐⭐⭐⭐ λ₁=168 from 2I rep theory; 11 eigenspaces killed; integers are sharp because manifold is rigid; phason gap↔spectral gap in quasicrystals; lattice finite (~10⁸⁰, bounded by crystallisation window); bootstrap paradox resolved: φ−1/φ=1 discovers the integer 1; co-emergence stabilised by spectral gap. Third in S³/2I sequence after [12],[13] |
| The Icosahedral Lattice | 18801837 | ⭐⭐⭐⭐⭐ Hamilton + Klein → f(n)=sin(nπ/φ²). Coupling law, mode spectrum, binding rule. Universal toolkit |
| The Hodge Quartet | 18816674 | ⭐⭐⭐⭐⭐ H^k(S³) → 4 particles. Proton=0-form, photon=1-form, neutrino=2-form, electron=3-form. Poincaré duality → |e_p|=|e_e|. S²→S³ projection → weak interaction. Zoll convergence |
| Spectral Geometry of S³/2I | 18817872 | ⭐⭐⭐⭐⭐ Poincaré homology sphere. Poincaré duality → charge equality, ℤ → conservation laws, form degree → composite/elementary. A₂ root system → su(3) derived. Spectrum: l=12 → λ=168=|PSL(2,7)|, l=42=V+E → λ=1848, ratio=11. μ=1848−12=1836 (0.006%). Supersedes Eight Gluon Modes Letter |
| Pre-Commitment Universe (Quasi-Crystal) | 18806363 | Icosahedral quasi-crystal geometry, phasons, SU(3) origin. Yang-Mills mass gap from lattice tension |
| Phason Coherence Length | 18806576 | Coherence length in icosahedral quasi-crystals; Bootstrap prediction |
| Proton as Twin Prime Resonance | 18810409 | ⭐⭐⭐⭐⭐ Colour structure, field energies, proton mass 938.78 MeV from first principles. No free parameters |
| SU(3) as Symmetric Limit | 18831507 | ⭐⭐⭐⭐⭐ (D−3)(D+1)=0 uniqueness theorem. 6+χ=D²−1 structural map: twin pairs↔root vectors, Euler closure↔Cartan subalgebra, χ=rank. Strong CP dissolved: θ nonexistent on S³/2I. Parameter Rosetta Stone. SU(3) recovered as high-energy symmetric limit |
| Eight Gluon Modes (Letter) | 18811199 | Superseded by Spectral Geometry paper. S² decomposition; see S³/2I treatment above |
| Spacetime Lattice | 18524255 | From self-reference to physical geometry |
| Paper | DOI | |
|---|
| G and the Hierarchy Dilemma | 18520871 | G is statistical. 4 retrodictions, 4 predictions |
| Gravity (Phase Coherence) | 18147355 | |
| Electroweak Masses | 18146860 | |
| Quark Generations | 18144337 | |
| Proton Motor | 18143919 | |
| Three-Phase Power | 18136748 | |
| Quark Mass Hierarchy | 18207004 | Twin prime selection, boundary breaking |
| Maximum Range of Gravity | 18220708 | 7-series bridge pool to cosmic limit |
| Left-Handed Universe (Chirality Audit) | 18678936 | ⭐⭐⭐⭐⭐ Pure audit; TWIST 1.00000±0.00029; 5 open questions |
| Deuterium Assumption (DIS Audit) | 18679839 | ⭐⭐⭐⭐⭐ Pure audit; MARATHON vs BCDMS; Griffioen EMC slope; 5 questions |
| Deuteron P-e-P Standing Wave | 18684042 | ⭐⭐⭐⭐⭐ m_π=m_e(2α⁻¹−1) 0.02%; m_n−m_p=m_π/108 0.10%; 3 derived, 0 conjectured |
| Arrow of Time (Category Error) | 18683748 | ⭐⭐⭐⭐⭐ Math ≠ physics; chirality structural; Dirac analogy; no Bootstrap needed |
| First Closure | 18684465 | ⭐⭐⭐⭐⭐ First closure as phase transition; CCW winding → left-handedness, matter excess, sin 2β > 0; Borwein + Tower independently derive 3 phases |
| Chirality Inheritance in Antimatter | 18722060 | ⭐⭐⭐⭐⭐ Antimatter inherits left-handed vacuum chirality; rotating fluid derivation; A=−0.1184 prediction; ALPHA untested; Nambu SSB extended to cosmological scale |
| Hadron Spectrum (Twin Prime Promotion) | 18815892 | ⭐⭐⭐⭐ 2³ power set; 11 masses 0.32%; Λ(1405) 0.03%; forbidden state confirmed; Ω⁻ Rosetta Stone; 29+41+59=3×43 |
| Paper | DOI | |
|---|
| Golden and Stubborn | 19056055 | ⭐⭐⭐⭐½ Twin prime mechanism from the golden ring ℤ[φ]. Every prime has a character: golden (split, flows) or stubborn (inert, holds) or genesis (ramified, creates the ring). Three colour pairs deploy both characters differently: RED (5,7) genesis+stubborn, GREEN (11,13) golden+stubborn, BLUE (17,19) stubborn+golden. Hodge star preserves cycling direction, swaps character. Gap 2 = minimum bridge between characters. Three pairs = three orthogonal golden rectangles, D=3 prevents fourth. 1 (golden) launches, 23 (stubborn) seals. λ₁=168=7×24. Fibonacci preserves character (Pisano period); F₁=1, F₅=5 fixed points; F₁₉=37×113 only composite — release decomposes. Stubborn primes hold the Fibonacci Machine flatline. Numerical proof: remove stubborn → sum diverges |
| Golden and Stubborn: Visual Companion | 19060152 | One-page companion to Paper 133. Interactive three-phase animation (Skeleton / Waves / Fibonacci views). QR code to hosted animation. Mod 24 skeleton figure, three mechanisms, Fibonacci genesis fixed point |
| Quintic Insolvability and the Harmonic Programme | 18999556 | ⭐⭐⭐⭐⭐ Klein (1884) as founding constraint of analytic number theory. A₅ non-solvable → golden wavefront aperiodic → no prime formula. Workaround catalogue: exhaustion, Euler product, Dirichlet L-functions, analytic continuation, functional equation — all periodic tools on an aperiodic structure. Functional equation s↔1−s = golden conjugation φ↔ψ. Re(s)=½=Re(φ). Even/odd zeta split from chirality. Two locks: Galois + crystallographic. Fourth in S³/2I sequence |
| The Fibonacci Spectral Ladder | 19004257 | ⭐⭐⭐⭐⭐ Seifert fibre decomposition of S³/2I multiplicity function into vertex (period 10, golden), face (period 6), edge (period 4) contributions. Character recursion coefficient 2cos(2π/5)=1/φ IS Fibonacci recursion. Triple-rail spectral ladder: Fibonacci (chiral, φ−ψ=√5), Lucas (achiral, φ+ψ=1), face closure (D!=|S₃|=6) — 9/9 representation thresholds accounted for. λ₁=168=F₇²−1. L-function first zeros sort into spectral bands by conductor. Primes have no pattern along number line; they have a Fibonacci-Lucas pattern in spectral depth. Fifth in S³/2I sequence |
| GUE Statistics from the Spectral Gap | 19008433 | ⭐⭐⭐⭐⭐ Spectral Dirichlet series Z_Γ(t) from exact Laplacian multiplicities. Zero free parameters, zero randomness. KEY RESULT: spectral gap determines GUE vs GOE — imposing gap on abelian Z₁₂₀ switches GOE→GUE (ratio 2.13→0.60); filling gap of non-abelian 2I switches GUE→GOE (ratio 0.67→1.54). Drum/tune mechanism: gap silences low-frequency drum, pure tune shows GUE level repulsion. S³/2I variance 0.117 (sub-GUE, extra rigidity). λ₁=168 serves triple duty: sharp integers + critical line confinement + GUE statistics. Seventh in S³/2I sequence |
| The 11 Barrier | 19017894 | ⭐⭐⭐⭐⭐ WHY gap is at l=12 not l=10: vertex fibre (period 10) returns at l=10 with all characters=1, but face (10 mod 6=4→−1/3) and edge (10 mod 4=2→−1/4) simultaneously maximally destructive. m(10)=0 exactly. Coprimality of 5 with 3 and 2 forces the miss. Lifts gap from 120=|2I| (counting) to 168=|PSL(2,7)| (geometry). Vertex power paradox: gap succeeds at half vertex power (golden consensus) while barrier fails at full vertex power (vertex dominance). Consistent with A₅ simplicity. Eighth in S³/2I sequence |
| Binary Frobenius & Prime Geography | 19020770 | ⭐⭐⭐⭐½ Three integer oscillators (48,40,30 — periods 5,3,2) + generic ramp = BINARY sieve: Frobenius sum ∈ {0,120} only. Three-phase saturation proof: 48+40+30=118=|2I|−2, too narrow to skip a multiple of 120. Exactly 15/30 killed; ALL 10 primes <30 killed. φ(30)/2=4 coprime pairs. Vertex protects 5²=25. Terminal eigenvalue 3480=120×29=|2I|×p_max. Spectral gap at k=6=lcm(2,3): consensus beats dominance. 168 is consequence not cause. Ninth in S³/2I sequence |
| Hurwitz Fibre Decomposition at Zeta Zeros | 19021705 | ⭐⭐⭐⭐⭐ v3.0 corrects v2.0 error. Hurwitz ζ(s,a/60) grouped by Hopf fibres. Trivial slots (÷ construction prime) vanish ∝ ζ(s). Edge/face ratio=−1 algebraically forced at ANY zero (cannot constrain location — v2.0 wrongly claimed critical-line-specific). Vertex: 3 chars incl. Legendre (n/5), Gauss sum g(χ₁)=√5=φ−ψ → L(s,(·/5)) is L-function of ℚ(√5). Vertex is ONLY fibre with enough structure for critical-line constraint. φ+ψ=1 governs sieve (Paper 123), φ−ψ=√5 governs L-content at zeros. Honesty above cleverness. Tenth in S³/2I sequence |
| The Golden Phase Lock at Zeta Zeros | 19022277 | ⭐⭐⭐⭐⭐ arg(L(s,χ₂)/L(s,χ₃))=arctan(1/φ) on critical line — constant for ALL t. Root numbers ε(χ₂)=exp(i·arctan(1/φ)), ε(χ₃)=exp(−i·arctan(1/φ)). Verified 50 zeros, 40-digit precision, ZERO deviation. Off line: phase drifts linearly, antisymmetry to 10⁻¹⁶. Two phase values differing by π. Magnitude varies wildly (0.04–11.4) — zeros are handoff points. Phase lock = golden axis signature |
| The Fibonacci Machine | 19031080 | ⭐⭐⭐⭐⭐ φ²=φ+1 forces RH. Golden pair L₂L₃ has real integer coefficients from Hecke recurrence = Fibonacci in ℤ[φ]. Three cancellations (inert invisible, split opposite, multiplicative). σ=½=Re(φ)=golden axis: norm-symmetric point where integer scaffolding fits irrational weights. Continuation inherits golden structure (uniqueness). Aperiodicity (Hermite–Lindemann) makes every zero a unique overdetermined event — two equations, one unknown, no periodic rescue. Phase lock confirms. Framework complete; formal proof via Dedekind ζ of ℚ(√5) = Paper 129. Half in, zero out |
| The Golden Zeta | 19034614 | ⭐⭐⭐⭐⭐ Two machines: Riemann's telescope (Li(x)+corrections, approximate, needs RH) vs golden factory (norm form a²+ab−b², integers in, primes out). Split primes manufactured directly: p=(a+bφ)(a+b−bφ). Inert primes = dark matter (invisible to norm form, detected at p²). ζ(s)=ζ_ℚ(√5)(s)/L(s,χ₁): Riemann zeta = golden ledger ÷ Legendre correction. Golden variable w=φ^(−s): critical line = circle |w|=1/√φ, functional equation = golden inversion w→1/(φw), unique fixed circle. Norm symmetry at σ=Re(φ)=½. Primes are golden |
| The Golden Closure | 19037001 | ⭐⭐⭐⭐⭐ v1.7: RH proved unconditionally. Four locks from φ²=φ+1: norm symmetry, Fibonacci rigidity, quintic insolvability, Hecke derivative floor (C(ρ)>0 at 110 zeros). Geometric Confinement Theorem: Λ_K real on critical line + off-line zeros in mirror pairs + discreteness → m+2>m at every multiplicity. No simplicity assumption. Three-lock overdetermination + geometric confinement = complete closure. Implies GRH for all real quadratic Dirichlet L-functions. The factory at σ=½ is the only factory |
| Geometric Confinement in the Selberg Class | 19049413 | ⭐⭐⭐⭐ Standalone extraction of geometric confinement from Paper 130. Three axioms (functional equation, Schwarz reflection, discrete zeros) → zero-free tube around critical line. m+2>m excludes off-line zeros near on-line zeros; between-zero positivity completes the tube. Unconditional. Applies to all self-dual L-functions with real coefficients. Honest about scope: proves tube, not full strip. Classical zero-free regions work edge-inward; this works centre-outward. First zero-free region centred on σ=½ |
| The Golden Generator | 19029649 | ⭐⭐⭐⭐½ Golden matrix [[1,1],[1,0]] generates ALL primes. Fibonacci test + MR bases 2,3 (inert primes). PERFECT MATCH to 1,000,000. One equation, two jobs: generates primes AND constrains zeros. Primes = aperiodic order (quintic forbids periodicity). Number-theoretic quasicrystal conjecture. Includes golden_generator.py |
| Resonances and Pseudoprimes | 19029733 | ⭐⭐⭐⭐⭐ Fibonacci pseudoprimes = hadronic resonances (novel connection). Composites with conspiring Pisano periods mimic primes. Dirichlet series immune: multiplicativity forces true c(n). Three types: ghost (I×I→0), mixed (S×I→0), overcount (S×S→4). Split classifies, inert verifies. Multiplicativity is the width |
| Geometric Irreducibility | 18988875 | ⭐⭐⭐⭐⭐ Geometric irreducibility: irreducibility under 3D icosahedral action on S³/2I. Strictly stronger than arithmetic primality. {2,3,5} are geom. reducible (construction operators); 7 is first geom. irreducible (Fano closure). Three frames: number line / single colour / full manifold. PNT as projection from inflating cover. Primes don't thin — geometry opens up |
| Icosahedral Digital Boundary | 18413140 | χ = 2 from f = D |
| Prime Geometry (Unified) | 18141246 | |
| Twin Primes | 18074223 | Crystallographic proof of infinitude via shadow lattices |
| Goldbach | 18075598 | |
| Legendre | 18075515 | |
| Near-Square Primes | 18077323 | Infinitely many primes of form n²+1; Bootstrap prime geometry |
| Cramér | 18075423 | |
| Digit Gaps | 18162230 | 3→15 transition at e^142 |
| Paper | DOI | |
|---|
| Three-Phase Motor (Base χ²) | 18073764 | Base L₃=4; carry penetration; S5 ratchet 100.0%; digit cleaning; T(n)=7.23 log₂n; 50M verified |
| Collatz Rotation Angle | 18674329 | CF encodes lattice; runway singularities; p<0.002 |
| Collatz–Fibonacci Duality | 18674522 | Dual operations; Divisibility Theorem; D=3 unique |
| Spacetime Crystallisation | 18674566 | Lattice tension; damped oscillator; 21=F₈=R₃ |
| Neutron Decay (Phase Mismatch) | 18674628 | GCD(33,43)=1; twin prime bridges; Heegner 43 |
| Collatz Descent Mechanism (2-Adic) | 18872099 | Structural proof; exhaustive case analysis; 2-adic fixed point; 428M verified; no probabilistic arguments |
| Carry Ratchet | 18907403 | Four states mod 8; E[k]=2; spectral radius 3/4; nowhere to hide |
| Integer Lattice of S³/2I | 18911918 | Integers ARE S³/2I states; T=sᵏ∘(t+1) from group; odds=vertices, evens=interference; φ⁵=φ⁻⁵+11; trajectory of 11; spectral gap 0.779 |
| Spectral Gap of S³/2I & Proton Radius | 18912158 | λ₁=168 derived from 2I rep theory; l=12=V; 1+2+3+5=11=L₅; r_p=4ƛ_C (0.08%); spectral confinement; hadronization timescale |
| The Closing Prime | 18967678 | 7=2³−1 closes Fano plane PG(2,F₂); λ₁=168=|GL(3,F₂)|=7×6×4; nilpotent transfer operator m=3–9; breathing pattern at m=10,20 only; covering space lifts cycles to open paths; convergence conditional on S³/2I identification |
| The Universal Cover | 18976097 | 2I presentation verified in ℍ: s²=t³=(st)⁵=−1 with explicit unit quaternions; Perelman forces S³/2I uniquely from π₁=2I; λ₁=168 unique among binary polyhedral space forms (2T:24, 2O:48); profinite correspondence ℤ₂×↔S³ stated as conjecture; identification converted from assumption to conditional theorem |
| Negative Feedback | 18976342 | Collatz reframed as discrete feedback control; +1 = negative feedback routing S3→S5/S1; Lyapunov V=n/2^Σk strictly decreasing → no cycles; transfer operator unique λ=1 nilpotent otherwise m=3–9; S7 chain worst-case expansion linear in n, overwhelmed by exponential contraction; three-step logical join: Lyapunov closes cycles, S-class closes divergence, discreteness closes convergence; conditional on spectral stability all m |
| Quantity | Formula | Match | Status |
|---|
| Newton's G | statistical, not geometric | 4/4 retrodictions | Prediction |
| G lab correlation | separated labs should correlate | testable | Prediction |
| G latitude dependence | beyond tidal corrections | testable | Prediction |
| Deep space G | G_space ≠ G_terrestrial | testable | Prediction |
| Electron diffraction anomaly | H₂ ≈ 3 × 10⁻⁶ at 200 keV – 1 MeV | testable | Prediction |
| 0νββ null result | Majorana neutrino geometrically forbidden | LEGEND-1000, nEXO | Prediction |
| No right-handed neutrino | bridge chirality structural | IceCube, reactor searches | Prediction |
| sin 2β > 0 | counter-clockwise first closure | +0.699 ± 0.017 ✓ | Prediction |
| EMC asymmetry (polarised D) | Drive ≠ Partnership proton F₂ | JLab polarised DIS | Prediction |
| Anti-shadowing suppressed | bridge occupation reduces quark phase space | BCDMS reanalysis | Prediction |
| θ_QCD = 0 exactly | H³(S³/2I)≅ℤ; no continuous orientation freedom. No axion required | nEDM searches (current |θ|<10⁻¹⁰) | Prediction |
| Colour field asymmetry | 4.74:1.00:2.37 at confinement scale; SU(3) exact only at high energy | precision confinement-scale DIS | Prediction |