10. Proof of work and difficulty

• Compact bits as in Bitcoin. A set sign bit, a zero mantissa, or overflow beyond 256 bits is invalid.
• ASERT (aserti3-2d), anchored at genesis:

  exponent = ((parent.ts − genesis.ts − spacing × parent.height) × 65536) // halflife   (floor)
  shifts   = exponent >> 16;   frac = exponent & 0xFFFF
  factor   = 65536 + ((195766423245049·frac + 971821376·frac² + 5127·frac³ + 2⁴⁷) >> 48)
  target   = (genesis_target × factor) << shifts (or >> −shifts), then >> 16
  target   = clamp(target, 1, pow_limit);  expected_bits = compact(target)
  

• Regtest uses no retargeting: expected_bits = genesis_bits.