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71 lines
1.5 KiB
Markdown
71 lines
1.5 KiB
Markdown
# NUVMAP Delta-DAG Sharding Spec
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## Goal
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Make search traces shardable, replayable, and independently verifiable.
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## Shard ID format
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```text
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famm-ddag://<problem_hash>/<shard_type>/<hash>
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```
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## Required hashes
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```json
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{
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"problem_hash": "sha256(base instance)",
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"rule_hash": "sha256(route rule + weights)",
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"projection_hash": "sha256(NUVMAP projection config)",
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"node_hash": "sha256(projected node payload)",
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"edge_hash": "sha256(parent_hash + delta + child_hash)",
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"receipt_hash": "sha256(final verifier payload)"
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}
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```
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## Edge verification
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Every delta-edge shard must verify:
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```text
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apply_delta(parent_state, delta, route_rule)
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→ child_state
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hash(project(child_state))
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= child_node_hash
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```
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## DAG merge condition
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Two states may share a node if their NUVMAP projections match:
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```math
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h_{\mathrm{NUV}}(s_a)=h_{\mathrm{NUV}}(s_b)
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```
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The merge is safe only for the selected projection level. Exact receipt still replays an explicit solution path.
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## Projection levels
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| Level | Meaning | Use |
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|---|---|---|
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| `exact` | raw canonical state | safest; fewer merges |
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| `frontier` | frontier + domains + scars + residual | normal FAMM use |
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| `symmetry` | frontier plus symmetry/canonical color relabeling | aggressive merge |
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| `semantic` | semantic-mass basin only | routing prior, not proof |
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## Receipt rule
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The DAG may guide and compress search, but the final solution must be verified by a domain exact gate.
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For graph coloring:
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```math
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R(c)=|\{(u,v)\in E:c_u=c_v\}|=0
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```
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For exact cover:
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```math
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R(x)=\|Ax-\mathbf 1\|_1=0
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```
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