[{"type":"thinking","thinking":"The WHOLE LiCircleBound.lean compiles clean — including `zero_tail_inv_sq_le`! 5e-v-b chunk 2 (the tail bound) is COMPLETE.\n\nLet me commit this, then continue with the main series circle bound (5e-v-b chunk 3: the assembly of low + shells + critical + upper + tail into the seriesFun bound).\n\nWait — chunk 2 as planned in STATE was \"the tail bound + the main series circle bound\". I've done the tail bound (zero_tail_inv_sq_le). The main seriesFun bound is the next piece. Let me commit now, then continue with the main series bound.","signature":""},{"type":"text","text":"**`zero_tail_inv_sq_le` compiles — the tail bound is done.** Committing, then continuing to the main series bound."},{"type":"tool_use","id":"Bash_462","name":"Bash","input":{"command":"cd D:/Python/Quantum && git add research/lean/NguyenRH1/NguyenRH1/LiCircleBound.lean && git -c user.name=\"NGUYEN-RH-1\" -c user.email=\"research@local\" commit -m \"$(cat <<'EOF'\nSession 031 (ii'-5e-v-b chunk 2): the far-tail bound zero_tail_inv_sq_le\n\nFor X >= 200: Sum over zeros with |gamma| > X of m/(1+gamma^2) <=\n16*A0count*log X / X. Via: dyadClass (Nat.log-2 dyadic fibers) +\ndyadClass_lower/upper + fiber finiteness + fiber_mult_count (the\ntwo-window cover, mult-weighted) + fiber_tail_le (per-fiber bound via\ntsum_subtype + tsum_eq_sum + the filter split) + the ENNReal.tsum_\nfiberwise assembly + the closed-form dyadic series tsum_dyadic_log\n(Sum ((j+4)log2+logX)/2^j = 10log2+2logX via hasSum_coe_mul_geometric).\nClean elaboration. Next: the main seriesFun circle bound.\nEOF\n)\" && git log --oneline -1","description":"Commit chunk 2 (tail bound)"},"extra_content":null}]