SSUM Observatory — 01 Newton Root Finding (Baseline)

Structured Numbers • Classical Correctness • Universal Behavioural Insight

What this demonstrates

Classical layer: Newton’s method computes the usual iterate x_k and residual f(x_k).
SSUM layer: we attach structure to each step as x_k = (m_k, a_k, s_k) without changing m_k.
Guarantee: phi((m_k,a_k,s_k)) = m_k at every step.

This page runs two initializations: one “stable” start and one “unstable” start, so you can see how identical math can behave differently across iterations.

Inputs

Legend: m classical value (unchanged) · a bounded step health · s bounded step contrast · phi_ok must remain true

Status / Guards

If a near-zero derivative or NaN/Inf would occur, the demo can report it here (instead of failing silently).

ok

Run Output

Each row is one Newton iteration step.

run	k	m = x_k (classical)	f(m)	dx	a (alignment)	s (signature)	phi_ok

Interpretation

m is the classical iterate x_k (unchanged).
a is bounded in (-1,+1) and tracks step “health” (good progress → higher a, poor step → lower a).
s is bounded in (-1,+1) and tracks step “contrast” (large jumps / sharp changes → higher |s|).
phi_ok must remain true. If it ever becomes false, the SSUM implementation is invalid.

SSUM here provides structural observability, not prediction. Any forecasting or inference is done above SSUM.