NUVMAP Delta-DAG Sharding Spec

Goal

Make search traces shardable, replayable, and independently verifiable.

Shard ID format

famm-ddag://<problem_hash>/<shard_type>/<hash>

Required hashes

{
  "problem_hash": "sha256(base instance)",
  "rule_hash": "sha256(route rule + weights)",
  "projection_hash": "sha256(NUVMAP projection config)",
  "node_hash": "sha256(projected node payload)",
  "edge_hash": "sha256(parent_hash + delta + child_hash)",
  "receipt_hash": "sha256(final verifier payload)"
}

Edge verification

Every delta-edge shard must verify:

apply_delta(parent_state, delta, route_rule)
→ child_state

hash(project(child_state))
= child_node_hash

DAG merge condition

Two states may share a node if their NUVMAP projections match:

h_{\mathrm{NUV}}(s_a)=h_{\mathrm{NUV}}(s_b)

The merge is safe only for the selected projection level. Exact receipt still replays an explicit solution path.

Projection levels

Level	Meaning	Use
`exact`	raw canonical state	safest; fewer merges
`frontier`	frontier + domains + scars + residual	normal FAMM use
`symmetry`	frontier plus symmetry/canonical color relabeling	aggressive merge
`semantic`	semantic-mass basin only	routing prior, not proof

Receipt rule

The DAG may guide and compress search, but the final solution must be verified by a domain exact gate.

For graph coloring:

R(c)=|\{(u,v)\in E:c_u=c_v\}|=0

For exact cover:

R(x)=\|Ax-\mathbf 1\|_1=0

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