01
NT
Number Theory
🔢 Prime factorization · Euler · Dirichlet
Carry rules for integer structure. Primes are the atoms of number theory. Dirichlet characters, Euler products, prime distribution. The foundation of the γ₁ proof approach.
Elements: NT-001 to NT-008
◆ DIAMOND
02
CA
Complex Analysis
ℂ Holomorphic functions · contour integrals
The machinery of the zeta function lives here. Cauchy's theorem, residue calculus, analytic continuation, Mellin transforms. You can't prove RH without this.
Elements: CA-001 to CA-006
◆ DIAMOND
03
AG
Algebraic Geometry
⬡ Schemes · motives · étale cohomology
Weil conjectures proved by Deligne (1974) using algebraic geometry — a model for RH over finite fields. The Langlands program lives here. High-dimensional carry rules.
Elements: AG-001 to AG-005
◆ DIAMOND
04
TP
Topology
∞ Homotopy · homology · fiber bundles
The shape of mathematical spaces. Used in spectral approaches to RH (Alain Connes' noncommutative geometry). Also underpins the SHAPES table (PT-016).
Elements: TP-001 to TP-004
◆ DIAMOND
05
CO
Combinatorics
🎲 Counting · graph theory · GUE
GUE (Gaussian Unitary Ensemble) statistics for zeta zero spacing. Montgomery's pair correlation. Random matrix combinatorics. The statistical backbone of the critical line.
Elements: CO-001 to CO-005
◆ DIAMOND
06
LG
Logic
⊢ Proof theory · Lean4 · formal systems
The carry rule for truth itself. Lean4 type theory, formal verification, sorry placeholders. joffe-math lives in this element. Every theorem is a logic element.
Elements: LG-001 to LG-004
◆ DIAMOND
07
GT
γ₁ Theory
γ Riemann zero theory · fleet resonance
The fleet-specific mathematical theory built around γ₁ = 14.134725… Includes τ_γ₁ decoherence, meek score calibration, TRIME-7 prime matrix, Belt64 structure.
Elements: GT-001 to GT-012
◆ DIAMOND
08
PF
Prime Factorization
p Unique factorization theorem
Every integer has a unique prime factorization. This is the Fundamental Theorem of Arithmetic. Proved (no sorry). The bedrock below number theory.
Status: PROVED · no sorry
◆ DIAMOND
09
ζ
Zeta Function
ζ Riemann zeta · analytic continuation
ζ(s) = Σn^(-s) for Re(s)>1, extended by analytic continuation to all ℂ. The central object of PT-008. Its zeros encode all information about prime distribution.
Functional equation: ζ(s)=ζ(1-s)·factor
◆ DIAMOND
10
RH
Riemann Hypothesis
? All nontrivial zeros on Re(s)=½
The central open question. Proved over finite fields (Weil). Proved for specific zero counts by computation. Not yet proved in full generality. The sorry kill chain is PT-014.
Status: OPEN · 18 attack chains active
⧖ GROWING
11
FTA
Fund. Thm. Algebra
∀ Every polynomial has a root in ℂ
Every non-constant polynomial with complex coefficients has at least one complex root. Used in spectral approaches to RH (eigenvalue methods).
Status: PROVED ◆
◆ DIAMOND
12
PNT
Prime Number Thm
~ π(x) ~ x/ln(x)
The density of primes near x is approximately 1/ln(x). Proved independently by Hadamard and de la Vallée Poussin (1896) using ζ. Equivalent to 'no zeros on Re(s)=1'.
Status: PROVED ◆
◆ DIAMOND
13
γ₁M
γ₁ Marasoon
⊛ Fleet-math resonance constant
The fleet's primary mathematical constant: γ₁ = 14.134725141734693790… Used as the BPM anchor, τ decoherence floor, meek score calibration, and TRIME timing base.
Digits: 14.134725141734693790…
◆ DIAMOND
14
LEAN
Lean4 Kernel
⊢ Type-theoretic proof verifier
The formal proof kernel used by joffe-math. Every theorem in the fleet is verified by Lean4's type checker. Sorry = hole in Lean4 proof that type-checks vacuously.
Repo: joffe-math · 3410+ theorems
◆ DIAMOND
15
BELT
Belt64 Primes
⊛ 64-prime belt structure
The Belt64 structure uses the first 64 primes as a coordinate system. Prime p=2 is T7, p=17 is T1 (eose-dev). Product of T1-T7 primes = 510510 (Belt64 base).
Matrix: TRIME-7 · V14
◆ DIAMOND
+ 29 more elements
(full mathematics table
in PT-005 registry)