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145 lines
2.9 KiB
Markdown
145 lines
2.9 KiB
Markdown
# NUVMAP Delta-DAG Search Compressor
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## Purpose
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Make the NP-search acceleration stack explicitly shardable.
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The stack is now:
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```text
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SEMANTIC_MASS_ROUTE_PLOW
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→ 16D_CHAOS_GAME_FIELD_SHRINKER
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→ DELTA_STREAM
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→ NUVMAP_DAG
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→ NOGOOD_SCAR_CACHE
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→ EXACT_RECEIPT
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```
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The key distinction:
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```text
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Delta compression shrinks the path.
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NUVMAP DAG shrinks the search topology.
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```
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## Why this tilts the needle
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A normal backtracking solver creates a tree. Many branches can produce equivalent remaining subproblems. A tree repeats them.
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A NUVMAP DAG stores projected state addresses and merges equivalent frontier basins:
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```math
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D_{\mathrm{NUVMAP}}
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=
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(V_{\mathrm{state}},E_{\Delta},h)
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```
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Each node is an addressed projected state:
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```math
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\nu_t
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=
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h(
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G,
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\text{assignment frontier},
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\text{domains},
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\text{scars},
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\text{residual}
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)
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```
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Each edge is only a legal delta:
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```math
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e_t=(\nu_t,\Delta_t,\nu_{t+1})
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```
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## FAMM object
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```math
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\mathfrak C_{\Delta\mathrm{DAG}}
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=
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A_{16}(u_G)
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\otimes
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[
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\Sigma_G
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+
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\Sigma_{\Delta}
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+
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\Sigma_{\mathrm{NUV}}
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+
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\Sigma_{\mathrm{DAG}}
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+
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\Sigma_{\mathrm{nogood}}
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+
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\Sigma_{\mathrm{resid}}
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+
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\Sigma_{\mathrm{receipt}}
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]
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```
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## NUVMAP address
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```math
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h_{\mathrm{NUV}}(s)
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=
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h(
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\Pi_{\mathrm{frontier}}(s),
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\Pi_{\mathrm{domain}}(s),
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\Pi_{\mathrm{scar}}(s),
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\Pi_{\mathrm{residual}}(s),
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\Pi_{\mathrm{sym}}(s)
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)
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```
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This is stronger than raw memoization because it does not ask only whether the state is byte-identical. It asks whether the projected route basin is equivalent.
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## Sharding model
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| Shard | Contents | Local verification |
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|---|---|---|
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| Base instance shard | graph / exact-cover / SAT instance | hash matches manifest |
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| Route-rule shard | deterministic FAMM route rule and weights | rule hash matches manifest |
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| NUVMAP node shard | projected frontier/domain/scar/residual address | node hash recomputes |
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| Delta-edge shard | legal operation from parent to child | replay parent + delta → child |
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| Nogood/scar shard | failed basin, contradiction, or forbidden transition | scar hash and projection match |
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| Solution-path shard | ordered edge hashes | path joins from root to receipt |
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| Exact receipt shard | final verifier output | residual = 0 |
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## Multiplicative gain
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```math
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G_{\mathrm{total}}
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=
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G_{\mathrm{route}}
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\cdot
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G_{\Delta}
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\cdot
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G_{\mathrm{DAG}}
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```
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The earlier estimate was:
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```text
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FAMM route shortening: >= 393.7×
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delta trace shrink: ~30×
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```
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So before DAG merging:
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```text
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>= 11,800× effective route-trace shrink
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```
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With NUVMAP DAG merging:
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```text
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40% redundant frontier states → ~20,000×
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70% redundant frontier states → ~39,000×
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```
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These are architecture estimates, not proof of general-case NP collapse.
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## No-drift boundary
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This is not a P vs NP claim. It is a route/topology/receipt compression layer. Exactness still comes from the final verifier: graph coloring conflict count zero, exact cover residual zero, SAT formula satisfied, Lean proof accepted, or other domain-specific receipt.
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