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TauLib Reference
Canonical
Key terms, symbols, constants, and structures used throughout TauLib.
TauLib Glossary
Key terms, symbols, constants, and structures used throughout TauLib.
Constants
| Symbol |
Value |
Lean Name |
Description |
| iota_tau |
2/(pi + e) = 0.341304 |
iota_tau_float |
Master constant; governs all quantitative predictions |
| kappa_D |
1 - iota_tau = 0.658696 |
— |
Complementary constant (D-sector coupling) |
| kappa_omega |
iota_tau/(1 + iota_tau) = 0.254485 |
— |
Omega coupling constant |
| W_3(4) |
5 |
— |
Continued-fraction window sum (3 partial quotients from index 4); governs NLO corrections |
| W_3(3) |
17 |
— |
Continued-fraction window sum (3 partial quotients from index 3) |
| W_4(3) |
18 |
— |
Continued-fraction window sum (4 partial quotients from index 3) |
| W_5(3) |
19 |
— |
Continued-fraction window sum (5 partial quotients from index 3); equals N_e/3 |
Generators
| Generator |
Symbol |
Index |
Role |
alpha |
alpha |
0 |
Radial seed — its orbit becomes TauIdx (natural numbers) |
pi |
pi |
1 |
Prime base / multiplicative spine |
gamma |
gamma |
2 |
Exponent channel |
eta |
eta |
3 |
Tetration channel |
omega |
omega |
4 |
Fixed-point absorber / closure beacon |
Core Structures
| Lean Type |
Module |
Description |
Generator |
BookI/Kernel/Signature |
The 5-element generator type |
TauObj |
BookI/Kernel/Axioms |
Objects in Category τ (seed + depth) |
TauIdx |
BookI/Denotation/TauIdx |
Internal natural numbers (= Nat, earned from O_alpha) |
SplitComplex |
BookI/Boundary/SplitComplex |
Split-complex numbers (boundary ring) |
Key Spaces
| Symbol |
Description |
Lean Module |
| tau^3 |
The tau-fibration: tau^1 x_f T^2 |
BookII/Interior/Tau3Fibration |
| tau^1 |
Base circle (macrocosm) |
BookV/Temporal/BaseCircle |
| T^2 |
Fiber torus (microcosm) |
BookIV/Arena/Tau3Arena |
| L |
Lemniscate boundary: S^1 v S^1 |
BookI/Polarity/Lemniscate |
Axioms (K0-K6)
| Axiom |
Name |
One-Line Description |
| K0 |
Universe Postulate |
tau exists as a universe of discourse |
| K1 |
Strict Order |
The 5 generators are strictly totally ordered: alpha < pi < gamma < eta < omega |
| K2 |
Omega Fixed Point |
rho(omega) = omega — omega is the unique fixed point |
| K3 |
Orbit-Seeded |
rho(g) is seeded by g for all non-omega generators |
| K4 |
No-Jump (Cover) |
rho advances depth by exactly 1 |
| K5 |
Beacon Non-Successor |
omega is never reached by iterating rho |
| K6 |
Object Closure |
Every TauObj is a generator or rho-generated |
| Prefix |
Meaning |
Example |
I. - VII. |
Book number |
IV.T140 = Book IV |
K |
Axiom |
I.K1 = Axiom K1 |
D |
Definition |
V.D317 |
T |
Theorem |
IV.T66 |
P |
Proposition |
V.P176 |
R |
Remark |
IV.R260 |
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