Reference

Copyable glossary

A companion reference for RSG v1.4 and the visualisation. The formulas are written as copyable text rather than images, with claim status kept visible.

State And History Symbols

\sigma_n: Structured recursive state, written as (X_n, \phi_n, \mu_n, S_n).
X_n: Topological support or objecthood carrier.
\phi_n: Projected phase, transport, or path data.
\mu_n: Measure package attached to the state.
S_n: Survival weight before normalisation.
\gamma_i: Generated history, a sequence of structured states.
R: Recursive update operator. In a test it must be fixed by rule or measured transfer map before output comparison.
R_test: Locked analogue layer-to-layer transfer map used for the preregistered validation run.
\pi_\Phi: Projection from structured recursive state space to the reduced phase space.

Formula Sheet

\sigma_n = (X_n, \phi_n, \mu_n, S_n)

\sigma_{n+1} = R(\sigma_n)

\gamma_i = (\sigma_{i,0}, \sigma_{i,1}, \sigma_{i,2}, ...)

\phi_n = (\Theta_n, \Pi_n)

J_n = \Theta_n^2 + \ell^2 \Pi_n^2

W_n = \Theta_n^2 / J_n

\Lambda_surv(\sigma,\phi) = \Gamma(\sigma) W(\phi)

A_i(t) = integral_0^t \Gamma_i(\tau) W_i(\tau) d\tau

S_i(t) = exp(-A_i(t))

G_i(t) := S_i(t) = exp(-A_i(t))

p_i(t) = q_i G_i(t) / sum_j q_j G_j(t)

equal-preparation shorthand:
p_i(t) = S_i(t) / sum_j S_j(t)

H_surv(t) = -sum_i p_i(t) ln p_i(t)

N_eff(t) = exp(H_surv(t))

ln(p_i / p_j) = ln(q_i / q_j) - A_i + A_j

equal-preparation shorthand:
ln(p_i / p_j) = -A_i + A_j

\hat p_i = (I_i - I_{i,bg}) / sum_j (I_j - I_{j,bg})
\hat L_ij = ln(\hat p_i / \hat p_j)

Visual Terms

Light path blue: Compressed or toward-observer segment in the light-history colour key.
Light path red: Stretched, away, or higher-index segment in the light-history colour key.
Violet path: Torsion, twist, or depth-like deformation along a history.
Green wave node: High-survival represented point in wave mode.
Red wave node: Low-survival represented point in wave mode.
Amber wave node: Captured node or strong terminal interaction.

Concept Terms

Generated history

A candidate sequence before survival filtering.

Represented measure

The normalised measure over histories that remain live after filtering.

Exposure-gate transmission

The multiplier G_i = S_i = exp(-A_i) applied to a prepared represented amount before normalisation.

Exposure

The portion of a projected state that is vulnerable to the loss channel.

Closure

Recursive or topological persistence that lets a history become record-like.

Claim lock

The rule that only the controlled analogue-media prediction is the developed empirical claim in RSG v1.4.

Coordinate convention lock

The requirement that \Theta, \Pi, \ell, phase zero, wrapping, and singular-state rules are fixed before output data.

Ordinary attenuation control

The comparison model A_i = integral Gamma dt; RSG-specific support requires improvement over it in a positive-control regime.

Recursive null transport

Effectively lossless, projected-norm-preserving transport with no recurrent internal clock and therefore d tau_R = 0.

Bridge programme

A conditional future application requiring its own variables, calibration, and test.