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Add MarkovJunior 16D PIST rewrite shim documentation
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6-Documentation/famm/MARKOVJUNIOR_16D_PIST_REWRITE_SHIM.md
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6-Documentation/famm/MARKOVJUNIOR_16D_PIST_REWRITE_SHIM.md
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# MarkovJunior 16D PIST Rewrite Shim
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## Purpose
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Add a shim that treats MarkovJunior-style rewrite programs as 16D FAMM/PIST/NUVMAP objects.
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This is an adapter, not a replacement for MarkovJunior. MarkovJunior provides the rewrite-rule grammar and constraint-propagation style. The shim projects those rules into the current project stack:
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```text
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MarkovJunior rule
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→ 16D rewrite anchor
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→ PIST transition candidate
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→ FAMM scar/residual accounting
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→ NUVMAP rewrite-basin address
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→ Delta-DAG replay edge
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→ BJW cleanup / exact receipt
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```
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## Why MarkovJunior fits
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MarkovJunior programs are built from rewrite rules. In basic form, a program is an ordered list of rewrite rules. A rule match is selected and applied on the grid, and the process halts when no rules match. MarkovJunior also supports probabilistic inference through constraint propagation.
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Project translation:
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```text
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rewrite rule = PIST surface-transition operator
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rule match = local state crossing
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changed cells = delta edge
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failed constraint = FAMM scar
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inference field = Semantic Mass / route pressure
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trace = NUVMAP Delta-DAG
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```
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## 16D rewrite state
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```math
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X_{\mathrm{MJ}}
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=
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[
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\nu,
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s,
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m_L,
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m_\Delta,
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h_{\mathrm{rule}},
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p_{\mathrm{obs}},
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\chi,
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\mu,
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z,
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\Delta_{\mathrm{mem}},
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\Omega,
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R,
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I,
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C,
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\rho,
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\pi
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]
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```
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| Axis | Meaning |
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|---:|---|
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| 0 | NUVMAP rewrite-state address |
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| 1 | S3C shell / dimensional shell |
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| 2 | left-pattern mass |
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| 3 | rewrite delta mass |
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| 4 | rule hash / rule-order pressure |
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| 5 | observation / constraint pressure |
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| 6 | chirality / orientation |
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| 7 | semantic mass |
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| 8 | recurrence / Z-domain lane |
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| 9 | delta-memory state |
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| 10 | FAMM scar pressure |
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| 11 | residual / unsatisfied constraint |
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| 12 | invariant overlap |
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| 13 | route cost |
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| 14 | receipt strength |
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| 15 | projection / display gauge |
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## Rule anchor
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```math
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A_r
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=
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\operatorname{Embed}_{16D}
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(
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H(L_r),
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H(R_r),
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\|L_r\|,
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\|R_r-L_r\|,
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\mathrm{wildcards},
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\mathrm{weight},
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\mathrm{constraints}
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)
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```
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Where `L_r` is the left pattern and `R_r` is the right pattern.
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## PIST transition law
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```math
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X_{t+1}
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=
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\Pi_{\mathrm{adm}}
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\left[
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\mathrm{PIST}_{r_t}(X_t)
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+
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\Delta_{\mathrm{MJ}}(r_t,m_t)
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\right]
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```
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## Rule score
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```math
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P(r_t=i\mid X_t)
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\propto
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\exp[
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-\alpha d_i
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-\beta\Omega_i
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-\kappa K_i
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+\gamma I_i
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-\eta C_i
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+\lambda\mu_i
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+\rho R_i
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+\chi H_i
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]
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```
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This makes MarkovJunior rule selection compatible with semantic mass, scar pressure, coarsening pressure, invariant overlap, route cost, receipt strength, and chirality compatibility.
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## Coarsening-agent behavior
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```text
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failed rewrite
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→ residual measured
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→ scar written
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→ basin coarsened
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→ future matching downweighted
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→ route reopened only if new evidence changes the boundary
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```
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## Boundary
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This shim does not execute full MarkovJunior XML semantics. It is a projection layer. It maps MarkovJunior-style rewrite rules and traces into the 16D project state so they can be routed, scored, replayed, and receipted.
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## Project sentence
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The MarkovJunior shim lets the project treat local rewrite rules as 16D surface-transition anchors: MarkovJunior supplies the rewrite grammar, PIST supplies lawful motion, FAMM tracks scars and residuals, NUVMAP stores rewrite basins, and Delta-DAG receipts the replay path.
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