Research-Stack/6-Documentation/famm/SEMANTIC_MASS_Z_ACCELERATOR.md

Semantic Mass Z-Domain Accelerator

Purpose

Apply the Z-transform to Semantic Mass Numbers so repeated semantic-history scans can be replaced by compact recurrence receipts.

The core move:

semantic mass stream
→ Z-domain recurrence
→ pole / ROC / residual receipt
→ low-cost state update

This turns Semantic Mass from a per-event scalar into a transfer object.

Canonical sequence

Let a routed object, chat thread, proof route, token lane, or signal path emit a typed semantic mass stream:

\mu[k]
=
w_H H[k]
+
w_L L[k]
+
w_I I[k]
+
w_R R[k]
+
w_C C[k]

Where the lanes may represent entropy/load, Landauer or compute cost, invariant pressure, residual scar, and closure/context cost.

The one-sided Z-transform is:

M(z)=\sum_{k=0}^{\infty}\mu[k]z^{-k}

Recurrence compression

Instead of carrying the full history, fit a causal recurrence:

\mu[k]
=
\sum_{i=1}^{p}a_i\mu[k-i]
+
\sum_{j=0}^{q}b_j u[k-j]
+
r[k]

or in transfer form:

H_\mu(z)
=
\frac{M(z)}{U(z)}
=
\frac{B(z)}{A(z)}

with:

A(z)=1-\sum_{i=1}^{p}a_i z^{-i}

The stored object becomes:

coefficients + state vector + residual seal

not the entire history.

Acceleration rule

Naive history carry:

O(n) scan of semantic history

Z-domain carry:

O(p+q) recurrence update

This is the same compression doctrine as DELTA_MEM, but for Semantic Mass Numbers.

ROC / stability gate

The poles of A(z) are semantic memory scars.

Pole behavior	FAMM meaning	Route action
all `	p_i	< 1`
pole near unit circle	long-memory / high inertia	use DELTA_MEM or seal
pole outside unit circle	unstable route	quarantine / closure test
repeated poles	strong recurrence basin	promote as eigensolid candidate

The ROC is the admissible chart region.

Integration with existing shortcuts

Existing shortcut	Z-domain role
DELTA_MEM	stores online recurrence state instead of full history
HESSIAN_EIGEN	decides whether recurrence basin is stiff, flat, or saddle-like
E_TAIL_BOUND	seals bounded residual tails
SYSTEM_CLOSURE	tests whether bad poles mean missing boundary/context
OISC	executes recurrence using load/delay/accumulate/branch
Coulomb compression boundary	stops pressing when recurrence residual is cheaper to seal

FAMM object

\mathfrak C_{\mathrm{MassZ}}
=
A_{16}(u_{\mu})
\otimes
[
\Sigma_{\mu}
+
\Sigma_{Z}
+
\Sigma_{\mathrm{pole}}
+
\Sigma_{\mathrm{ROC}}
+
\Sigma_{\mathrm{rec}}
+
\Sigma_{\mathrm{resid}}
+
\epsilon_{\mathrm{fit}}
]

Where:

• Σ_mu = typed semantic mass sequence.
• Σ_Z = Z-domain transform.
• Σ_pole = recurrence pole structure.
• Σ_ROC = admissible convergence chart.
• Σ_rec = recurrence coefficients/state.
• Σ_resid = residual seal.
• ε_fit = fit/model uncertainty.

Updated compression spine

SEMANTIC_MASS
→ Z_DOMAIN_GATE
→ DELTA_MEM
→ HESSIAN_EIGEN
→ E_TAIL_BOUND
→ SYSTEM_CLOSURE

Project sentence

Semantic Mass Numbers become faster when treated as a Z-domain recurrence: store the pole/ROC law and residual seal, not every historical mass sample.