This is the research archive of Giovanni Levratti, an independent researcher based in Modena, Italy. The work presented here grew from a single algebraic observation and developed into a unified framework connecting non-associative geometry, induced gravity, and quantum information.
The series investigates the Informational Identity Boundary (IIB) — a structural discontinuity that emerges at the fourth step of the Cayley–Dickson doubling tower, where real numbers, complex numbers, quaternions, and octonions are extended to the sedenions. At this level, zero-divisors first appear: pairs of nonzero elements whose product is zero. Far from being a pathology, these zero-divisors carry extraordinary geometric structure. Their graph has exactly 84 vertices, governed by an automorphism group of order 2688, and the Fano plane — a seven-point projective geometry — organises the zero-divisor structure in three structurally distinct roles across the algebra.
The central physical conjecture of the series is that gravity is the Cayley–Dickson norm — the unique multiplicative structure that survives every doubling step. Where zero-divisors first appear, the norm loses its composition property, and the algebraic structure splits into gravity and matter. Via the Sakharov–Adler induced gravity mechanism applied to the sedenion scalar field, the series derives Newton’s gravitational constant and the Black Circle thermodynamics from algebra alone, without geometric input. The four physical sectors — gravitational, gauge, fermionic, and Majorana — correspond canonically to the four simple modules of F₂[GL(3,F₂)].
The series comprises 42 papers, all openly accessible on Zenodo with individual DOIs. Paper 1 is under peer review at Communications in Algebra and Paper 2 at the Journal of Mathematical Physics. All work is indexed through ORCID 0009-0000-9804-3452.
Research Papers Archive (42 papers)
- Paper 42 — The Gauge Sector of the Black Circle: Structural Reduction and Zeta Framework v2
- Paper 41 — Fano: The First Stone v3
- Paper 40 — Fano Trifrontality and the Spectrum of the Majorana–Dirac Operator v1
- Paper 39 — The Majorana–Dirac Operator and the Fano–Cayley–Dickson Doubling v2
- Paper 38 — Modular Universality: The Schubert Tower and the Matter–Gravity Split v2
- Paper 37 — Spinorial Boundary Conditions in the Black Circle v2
- Paper 36 — Three Algebraic Closures in the Cayley–Dickson Zero-Divisor Series v2
- Paper 35 — The Missing 28: Fano Non-Incidence and the Octonion Cocycle v1
- Paper 34 — A Single Fano Plane: Zero-Divisors, Gauge Structure, and the Massless Sector v1
- Paper 33 — Before the Zero-Divisors: Residues, Automorphisms and Gauge Coupling Constants in Cayley–Dickson Algebras v1
- Paper 32 — The Fano Bifrontality: Gravity and Matter at the Cayley–Dickson Boundary v2
- Paper 31 — The Euler–Gauss Obstruction for Black Circle Quasi-Normal Mode Coefficients v1
- Paper 30 — High-Precision Quasi-Normal Mode Spectrum of the Black Circle Interior v1
- Paper 29 — The Missing Four: Fano Non-Incidence in the Sedenion Zero-Divisor Algebra v2
- Paper 28 — Black Circle Thermodynamics, Norm-Gap Identity and IIB-IV Gravitational Structure v1
- Paper 27 — Two-Loop Induced Gravity and Branch Selection for the Black Circle Self-Consistency Equation v1
- Paper 26 — Induced Gravity from the Sedenion Scalar Field Theory S₄: Newton Constant as the Cayley–Dickson Norm v1
- Paper 25 — Fano Block Structure: The Complete Fermionic Chain and One-Loop Yukawa Corrections in S₄ v1
- Paper 24 — The Fano Dictionary: Module Structure of VZD and the Dark Sector Partition v1
- Paper 23 — The ZD Dirac Operator and Fermionic Sector S₄ v1
- Paper 22-B — Fano Incidence and the Level-3 Tripling v1
- Paper 22-A — Two-Loop Renormalization of a Sedenion Scalar Field and Gravitational Coupling v1
- Paper 21 — The Level-2 Sector of the Black Circle v2
- Paper 20 — One-Loop Stability and Backreaction of the Black Circle v2
- Paper 19 — The Majorana Sector of the Black Circle v3
- Paper 18 — Vacuum Instability and Majorana Spinors of the Black Circle v3
- Paper 17 — The Physical Boundary Condition at r=0 for the Black Circle v1
- Paper 16 — The Limit-Circle Obstacle for Black Circle Quasi-Normal Modes v1
- Paper 15 — The Kummer Connection Matrix for the Black Circle v1
- Paper 14 — Black Circle Hypergeometric Reduction and Cavity Bound v1
- Paper 13 — Quasi-Normal Modes of the Black Circle Interior v1
- Paper 12 — Boundary Conditions and Spinorial Statistics of the Black Circle Interior v1
- Paper 11 — Canonical Quantisation of the Black Circle Interior v1
- Paper 10 — Loop, Threshold and Residue: The Algebraic Structure of the A₃–A₄ Transition v1
- Paper 9 — A Quartic Contact Interaction with Fano–CSS Structure v1
- Paper 8 — Fano Duality, Projective Orthogonality and the CSS Bridge v1
- Paper 7 — A Clifford Representation of the Fano Zero-Divisors v1
- Paper 6 — The Factorization Threshold in Cayley–Dickson Integer Algebras v1
- Paper 5 — Active Stabilizers in Reed–Muller CSS Codes from Cayley–Dickson Zero-Divisors v1
- Paper 4 — Fano Geometry, Automorphisms and the Weil Zeta Function of Cayley–Dickson Zero-Divisors v10
- Paper 3 — Sign Structure, Automorphism Groups, and the ZD Zeta Function of Cayley–Dickson Algebras v4
- Paper 2 — The Informational Identity Boundary: Algebraic Foundations and Physical Conjectures v5
- Paper 1 — Sign-Parity Classification of Zero-Divisors in Cayley–Dickson Algebras v2 Under Peer Review • Communications in Algebra