{
  "packet_id": "marked_moment_section17",
  "scope_summary": "Audited the marked inverse moment estimate, including the canonical family reduction via two Poisson transformations, the exact character and coprimality tracking, the finite propagation of seminorm and height orders, the parameter selection scheme, and the sixth-power amplification.",
  "audited_steps": [
    {
      "anchor": "Equation (17.13) and (17.14)",
      "result": "checked",
      "evidence": "The inclusion-exclusion and priority identities for the slot assignments are exact and correctly partition the prime conditions."
    },
    {
      "anchor": "Equation (17.26) and (17.27)",
      "result": "checked",
      "evidence": "The retained fourth-power label from the cubes correctly identifies the primes with exponent 4 as $s J_2 = J$ and the remaining primes of $\\mathfrak B$ as dividing $q_0$, perfectly matching the zero-extended character identity."
    },
    {
      "anchor": "Equation (17.35) and (17.36)",
      "result": "checked",
      "evidence": "The new canonical data $k_{\\rm new}$ and $f_{\\rm new}$ exactly absorb the moving characters, and the new puncture $\\operatorname{rad}(q_0 t' r_g)$ correctly accounts for all residual coprimality conditions."
    },
    {
      "anchor": "Equation (17.42) and (17.43)",
      "result": "checked",
      "evidence": "The formal center identity $\\kappa_i + \\lambda_c + C_c + 2 F_c = F$ is algebraically exact, and the energy exponent bound correctly incorporates the clipping errors $\\delta_N$ and the margin tolerances."
    },
    {
      "anchor": "Equation (17.51) and (17.57)",
      "result": "checked",
      "evidence": "The initialization identity for the common extraction and the formal center identity $\\kappa_c^{\\rm init} + P_1 + 2 F_c^{\\rm init} = m$ are algebraically exact."
    },
    {
      "anchor": "Equation (17.60) and (17.61)",
      "result": "checked",
      "evidence": "The sixth-power amplification correctly uses the injectivity of $(u, a) \\mapsto u a^6$ on sixth-power-free ideals to bound the amplified moment."
    },
    {
      "anchor": "Lemma 17.3 and Corollary 17.4",
      "result": "checked",
      "evidence": "The finite propagation of seminorm and height orders correctly uses reverse induction on the acyclic graph, ensuring all internal orders are fixed before any external cutoff."
    }
  ],
  "objections": [],
  "unverified_obligations": [],
  "assessment": "no_demonstrated_error_found"
}