[{"type":"thinking","thinking":"§2 complete and green — the level-2 EM identity `integral_b1_cpow_eq` is proved. Commit this increment (crash-safe), then continue with §3 (hasDerivAt of the B₂ parameter integral) + §4 (identity extension) + §5 (disc bound).","signature":""},{"type":"text","text":"§2 green — the IBP identity `integral_b1_cpow_eq` is proved. Committing this increment before the analyticity section."},{"type":"tool_use","id":"Bash_250","name":"Bash","input":{"command":"cd D:/Python/Quantum && git add research/lean/NguyenRH1/NguyenRH1/LiRBound.lean && git -c user.name=\"NGUYEN-RH-1\" -c user.email=\"research@local\" commit -m \"$(cat <<'EOF'\nSession 022 (ii'-5b WIP1): LiRBound.lean — B2 machinery + level-2 IBP identity\n\nb2Fun (periodic Bernoulli primitive, continuous via comp_fract'',\nrange [-1/8, 0], HasDerivAt fract−1/2 off Z) + the unit-interval IBP\n(boundary vanishing at integers) + the level-2 Euler–Maclaurin identity\nintegral_b1_cpow_eq: ∫₁^∞ B̃₁·x^{−s−1} = (s+1)∫₁^∞ B̃₂·x^{−s−2} (re s > 0).\nSingle-file compile green. Next: parameter-integral analyticity +\nidentity-principle extension + the disc bound.\nEOF\n)\"","description":"Commit ii′-5b WIP1"},"extra_content":null}]