A domain-separated semantic header ID commits to every consensus field except nonce, while the canonical block ID includes it. The miner proves the complete transition once, searches many nonce-bearing headers and reconnects the winner through native PoW and exact boundary checks.
Where should the nonce enter the proof?
State is the authenticated set of current unspent outputs and consensus counters. HistoryStep is the recursive proof of one block's exact transition from its parent State to its child State. It certifies the expensive semantic work, while proof of work changes only a 128-bit nonce—the header value miners vary during search. If the nonce is included in the recursive statement, every candidate changes that statement and the expensive proof cannot be prepared before search.
A nonce-free semantic header
The construction defines two domain-separated identifiers:
| Identifier | Domain | Fields | Role |
|---|---|---|---|
| Semantic header ID | SEMHDR__ | Every consensus header field except nonce | HistoryStep statement |
| Block ID | BLOCKHDR | Every header field including nonce | PoW, parent link and canonical identity |
The semantic projection preserves the exact block-header field order and skips only the nonce. Mutation tests change every field independently: changing nonce must preserve the semantic ID; changing any other field must change it.
Prove once, search many
When a nonce meets the target, the node performs one native PoW check and verifies that the nonce-bearing header names the same proved parent and child State boundary as the semantic template. It then commits the complete block and terminal atomically.
Why the split does not free other fields
The recursive proof omits the nonce, not the mining target or any semantic transition field. Native acceptance requires the terminal's semantic ID and the candidate header to agree on every non-nonce field. The nonce-bearing block ID remains the chain-link identity.
Domain separation prevents the same absorb schedule from being interpreted interchangeably as a semantic ID and a canonical block ID.
Result
Expensive proof work is performed once per fixed block template. Cheap nonce search may vary the only field deliberately excluded from that statement.
The pattern applies whenever a costly proof certifies a deterministic object and a separate search varies one explicitly non-semantic field. The acceptance rule must reconnect the winning search result to every field the proof fixed.