From 8cc1f4a84db11105413cc787f16f8f1d767f6a4f Mon Sep 17 00:00:00 2001
From: Allaun Silverfox <28494262+allaunthefox@users.noreply.github.com>
Date: Sat, 16 May 2026 13:24:06 -0500
Subject: [PATCH] Add Semantic Mass Z-domain accelerator documentation

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+# 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:
+
+```text
+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:
+
+```math
+\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:
+
+```math
+M(z)=\sum_{k=0}^{\infty}\mu[k]z^{-k}
+```
+
+## Recurrence compression
+
+Instead of carrying the full history, fit a causal recurrence:
+
+```math
+\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:
+
+```math
+H_\mu(z)
+=
+\frac{M(z)}{U(z)}
+=
+\frac{B(z)}{A(z)}
+```
+
+with:
+
+```math
+A(z)=1-\sum_{i=1}^{p}a_i z^{-i}
+```
+
+The stored object becomes:
+
+```text
+coefficients + state vector + residual seal
+```
+
+not the entire history.
+
+## Acceleration rule
+
+Naive history carry:
+
+```text
+O(n) scan of semantic history
+```
+
+Z-domain carry:
+
+```text
+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` | stable semantic memory | carry recurrence |
+| 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
+
+```math
+\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
+
+```text
+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.