NUVMAP Delta-DAG Search Compressor

Purpose

Make the NP-search acceleration stack explicitly shardable.

The stack is now:

SEMANTIC_MASS_ROUTE_PLOW
→ 16D_CHAOS_GAME_FIELD_SHRINKER
→ DELTA_STREAM
→ NUVMAP_DAG
→ NOGOOD_SCAR_CACHE
→ EXACT_RECEIPT

The key distinction:

Delta compression shrinks the path.
NUVMAP DAG shrinks the search topology.

Why this tilts the needle

A normal backtracking solver creates a tree. Many branches can produce equivalent remaining subproblems. A tree repeats them.

A NUVMAP DAG stores projected state addresses and merges equivalent frontier basins:

D_{\mathrm{NUVMAP}}
=
(V_{\mathrm{state}},E_{\Delta},h)

Each node is an addressed projected state:

\nu_t
=
h(
G,
\text{assignment frontier},
\text{domains},
\text{scars},
\text{residual}
)

Each edge is only a legal delta:

e_t=(\nu_t,\Delta_t,\nu_{t+1})

FAMM object

\mathfrak C_{\Delta\mathrm{DAG}}
=
A_{16}(u_G)
\otimes
[
\Sigma_G
+
\Sigma_{\Delta}
+
\Sigma_{\mathrm{NUV}}
+
\Sigma_{\mathrm{DAG}}
+
\Sigma_{\mathrm{nogood}}
+
\Sigma_{\mathrm{resid}}
+
\Sigma_{\mathrm{receipt}}
]

NUVMAP address

h_{\mathrm{NUV}}(s)
=
h(
\Pi_{\mathrm{frontier}}(s),
\Pi_{\mathrm{domain}}(s),
\Pi_{\mathrm{scar}}(s),
\Pi_{\mathrm{residual}}(s),
\Pi_{\mathrm{sym}}(s)
)

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.

Sharding model

Shard	Contents	Local verification
Base instance shard	graph / exact-cover / SAT instance	hash matches manifest
Route-rule shard	deterministic FAMM route rule and weights	rule hash matches manifest
NUVMAP node shard	projected frontier/domain/scar/residual address	node hash recomputes
Delta-edge shard	legal operation from parent to child	replay parent + delta → child
Nogood/scar shard	failed basin, contradiction, or forbidden transition	scar hash and projection match
Solution-path shard	ordered edge hashes	path joins from root to receipt
Exact receipt shard	final verifier output	residual = 0

Multiplicative gain

G_{\mathrm{total}}
=
G_{\mathrm{route}}
\cdot
G_{\Delta}
\cdot
G_{\mathrm{DAG}}

The earlier estimate was:

FAMM route shortening: >= 393.7×
delta trace shrink:    ~30×

So before DAG merging:

>= 11,800× effective route-trace shrink

With NUVMAP DAG merging:

40% redundant frontier states → ~20,000×
70% redundant frontier states → ~39,000×

These are architecture estimates, not proof of general-case NP collapse.

No-drift boundary

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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