Notation and Units

Complete Symbol Reference for Planck Core Thermodynamics

Primary Thermodynamic Quantities

Symbol	Name	Units	Dimensions	Definition
sigma_theta	Drift Scalar / Entropy Production	s^-1	T^-1	sigma_theta = D(1 – L)
T_ITT	ITT Temperature	K	Theta	T_ITT = T_0 * sigma_theta
S_theta	Recursive Entropy	J/K	ML^2 T^-2 Theta^-1	S_theta = integral k_sigma sigma_theta d_tau
S_theta_max	Maximum Entropy	J/K	ML^2 T^-2 Theta^-1	S_theta_max = n_max * ell_P^2 * N_folds

Symbol	Name	Units	Range	Definition
D	Drift Magnitude	s^-1	[0, infinity)	Rate of glyph field evolution
L	Shell-Lock	—	[0, 1]	Recursive stability coefficient
1 – L	Unlock Factor	—	[0, 1]	Fraction available for drift

D(x, t) = alpha_M ||dM_ij/dt||_F + alpha_Phi ||d(grad Phi)/dt||_2

L(x, t) = <C(x,t), C_ref(x)> / (||C|| * ||C_ref||)

Symbol	Name	Type	Units	Role
Phi	Intent Potential	Scalar field	—	Latent permission field
F_i = d_i Phi	Intent Gradient	Vector field	L^-1	Directional intent
C_i	Curvent	Vector field	L^-1	Recursive fold direction
M_ij	Memory Tensor	Rank-2 tensor	L^2	Coherence structure
Psi	Field Stack	Tuple	—	{Phi, F_i, C_i, M_ij}

Symbol	Name	Units	Range	Definition
gamma_ITT	Dilation Factor	—	(0, 1]	gamma = sqrt(1 – A^2 * mu)
A	Alignment Functional	—	[0, 1]	Substrate load fraction
Tr(M)	Memory Trace	L^2	[0, infinity)	Total memory load
mu	Memory Saturation	—	[0, 1]	Tr(M)/Tr(M)_max

Symbol	Name	Units	Range	Description
n	Recursion Index	—	Z+ union {0}	Current recursive depth
n_max	Maximum Recursion	—	(0, infinity)	Computational ceiling
tau	Recursion Parameter	s	[0, infinity)	Continuous recursion time
t_P	Planck Time	s	—	5.391 x 10^-44 s
R_hat	Recursive Operator	—	—	Psi_{n+1} = R_hat(Psi_n)

Symbol	Name	Value	Units
hbar	Reduced Planck constant	1.055 x 10^-34	J*s
G	Gravitational constant	6.674 x 10^-11	m^3/(kg*s^2)
c	Speed of light	2.998 x 10^8	m/s
k_B	Boltzmann constant	1.381 x 10^-23	J/K
t_P	Planck time	5.391 x 10^-44	s
ell_P	Planck length	1.616 x 10^-35	m
m_P	Planck mass	2.176 x 10^-8	kg
E_P	Planck energy	1.956 x 10^9	J
T_P	Planck temperature	1.417 x 10^32	K

Symbol	Name	Units	Role
alpha_M	Memory Coupling	—	Weight of d_t M in drift
alpha_Phi	Intent Coupling	—	Weight of d_t grad Phi in drift
k_sigma	Entropy Coupling	J/(K*s^-1)	dS/d_tau = k_sigma sigma_theta
T_0	Reference Temperature	K	T_ITT = T_0 sigma_theta

Symbol	Name	Units	Definition
M	Mass	kg	Total gravitational mass
r_s	Schwarzschild radius	m	r_s = 2GM/c^2
r_PC	Planck Core radius	m	r_PC ~ sqrt(n_max) * ell_P
A	Horizon area	m^2	A = 4 pi r_s^2
T_H	Hawking temperature	K	T_H = hbar c^3 / (8 pi G M k_B)
N_folds	Fold site count	—	Resolution-dependent info sites

sigma_theta = D(1 - L)

T_ITT = T_0 * sigma_theta

L = 1   =>   sigma_theta = 0   =>   T_ITT = 0

S_theta_max = n_max * ell_P^2 * N_folds

gamma_ITT = sqrt(1 - A^2 * Tr(M)/Tr(M)_max)

S_BH = k_B c^3 A / (4 G hbar) = k_B A / (4 ell_P^2)

T_H = hbar c^3 / (8 pi G M k_B)

Notation	Name	Definition	Application
\|\|v\|\|_2	Euclidean norm	sqrt(sum_i v_i^2)	Vectors
\|\|A\|\|_F	Frobenius norm	sqrt(sum_ij A_ij^2)	Matrices/Tensors
<u, v>	Inner product	sum_i u_i v_i	Dot product
Tr(*)	Trace	sum_i A_ii	Sum of diagonal
d_i	Spatial derivative	d/dx_i	i in {1,2,3}
d_t	Time derivative	d/dt	With respect to tau
grad	Gradient	(d_1, d_2, d_3)	Spatial gradient

Index Type	Symbols	Range	Usage
Spatial	i, j, k	{1, 2, 3}	Vector/tensor components
Recursion	n, m	Z+ union {0}	Discrete state labels
Summation	—	—	Einstein convention (repeated indices summed)

All equations in this documentation use SI units unless otherwise specified.

In Planck units: t_P = 1, ell_P = 1, E_P = 1, T_P = 1

Simplifies equations but obscures physical magnitudes.

Common in general relativity. Length and time have same units.