[Cryptography] Prime-based proof-of-work and Nashian cooperative mining

[Ovanes Oganisian]

  Hi all,

   I wanted to share a short follow-up to the Primechain/PRIME testnet note.

   The current public testnet is still running as an ordered 
integer-classification chain: each record certifies the next frontier 
integer as prime or composite, using Pratt-style certificates for primes 
and divisor/cofactor evidence for composites.

   I have now written a short addendum describing the next protocol 
direction: an evidence layer around mined primes. The idea is that once 
a prime p is mined, it can become an anchor for additional verifiable 
arithmetic evidence, such as:

   - irreducible polynomials over F_p and explicit finite-field 
constructions;
   - splitting, non-splitting, partial splitting, and ramification 
evidence in finite-degree algebraic extensions;
   - later, more difficult ring/class-group evidence, initially manual 
or tool-assisted.

   The intended implementation is staged and forward-only: first a 
manual evidence registry, then automatic verifiers for simple evidence 
types, then optional evidence events in later records, derived evidence 
indexes for lookup, and only later a small capped evidence reward pool, 
likely in the 1-5% range of future newly mined prime issuance. Existing 
chain history and wallet balances would not be rewritten.

   The evidence addendum is here:

https://midlincoln.com/opportunities/prime-mining/launch-proof/primechain-evidence-addendum.html

The project home:

https://midlincoln.com/opportunities/prime-mining/

  Comments are welcome, especially on whether the proposed evidence 
types are mathematically well-scoped enough for staged verification, and 
where the boundary should be between validator-checkable evidence and 
manually reviewed/tool-assisted evidence.

   Best,
   Ovanes Oganisian