Draft for PROBLEM.md Status, WALKTHROUGH “proved vs open”, and the README covering row after leftover SAT cubes finish. N is the last leftover order whose every needed k≥d cube has a stored replayed DRAT; do not invent N. F₄ on disk is already c=0.34640 (f4_or_new_certificate.json; hunt_threshold.json certified_c=0.34640; CKLS 2015 fork, published β<0.8616γ). Replay: worst F=−0.4190333660, Q≽0. Prior stored F₄ is 0.34645; HKN is 0.3465. The same hunt fails at 0.346, 0.340, and 0.3388. The 0.34640 step closes no leftover n that 0.34645 left open; first leftover after q3 stays n=73, d=25 until SAT. (a) If leftover SAT cubes close through some N and F₄ is 0.34640: Status: open — F₄ certificate c=0.34640 (CKLS 2015 fork; HKN 0.3465; prior stored 0.34645). DRAT exact CH at n=12,15,16,17,18 and every leftover hole through n=N (in-degree ≥d cubes). First leftover hole n=N+1. Did not beat 0.3388. Conjecture 1/3 open. README (a): Exact CH-triangle at n=18, 21, 24, 26, 27, 29, 30, 32, 33, 35, 36 and every leftover order through n=N. F4 certificate c=0.34640, below HKN 0.3465. Did not beat 0.3388. Conjecture 1/3 open. (b) If leftover SAT cubes leave residue and F₄ moved: Status: open — F₄ certificate c=0.34640 (CKLS fork). Leftover from n=73 is residue: covering empties only high-k (n=73: k=34–46; n=73–120: 792 of 1464 cubes); survivors k=d .. n-3-d-floor((d-1)/2) (n=73: k=25–33) have no stored replayed DRAT. Incomplete search, not a lower bound. First leftover hole n=73. README (b): First remaining hole n=73. F4 certificate c=0.34640 (CKLS 2015 fork; prior 0.34645). Leftover cubes from n=73 incomplete (covering kills high-k only). Conjecture 1/3 open. (c) If both (holes close through N and F₄ moved): Status: open — F₄ certificate c=0.34640 (CKLS 2015 fork; HKN 0.3465) and DRAT exact CH through leftover n=N; first leftover hole n=N+1. Numerical move vs Combinatorica; finite close only through verified N. Covering is not a DRAT. Did not beat 0.3388. Conjecture 1/3 open. README (c): Exact leftover CH through n=N; first remaining hole n=N+1. F4 certificate c=0.34640, below HKN 0.3465 and the stored 0.34645. Did not beat 0.3388. Conjecture 1/3 open.