Baseline: 5434d96f0034f842b0229f1d69dbbf3fb7fea270 (merged PR73). Remote refreshed; no open PRs. Coordinator freshly reviewed all 104 node scope/status/evidence/dependency notes, 14 continuation demands, current README, NEXT_STEPS freezes and evidence/MISSING.md (unchanged original recovery groups OPEN), plus the current PR72/73 findings. Node records are byte-for-byte semantically unchanged from the preceding full review. This is not a historical proof/certificate replay.
Read current AGENTS.md, PROPOSAL_TEMPLATE.md, relevant ZERO-GEOMETRY map scope, and the current reports below before your assigned work.
User explicitly requests continuation with six agents. Seek a concrete estimating method for the COMPLETE original theta two-factor expression, or a useful independent partial estimate with a fully stated transfer. Default wall check: Same open gap (ZERO-GEOMETRY, NS100/101, PR72/73). Do not count identities, alternate notation, finite tables, or unexcluded possibilities as arithmetic progress. Prior art only from arXiv, with actual hypotheses/normalizations checked. State original arithmetic beyond symmetry. No numerical or symbolic scan, certificate, new research row, manuscript version, outreach, push or commits by agents. Admission/proof applicability and paper derivations only. No new computation until a concrete dependency and matched controls are specified and assessed. A screen can be on paper.
NS100 excludes positivity of every unintegrated slice for the original kernel. NS101 reciprocal mixture fails the original normalized Jacobi ODE (PR72); its off-axis zeros alone do NOT settle its first Laguerre sign. PR73 excludes all-height nonnegative certificates based on a fixed finite sum reflected at zero: its nonzero odd boundary derivative forces L1[X_M]=-8delta_M^2r^-6+O_M(r^-8). It does not exclude smooth completions, growing M(r), or the exact original nonlinear evolution. Do not reopen that fixed-prefix strategy or a finite constant-matrix moment closure.
phi(u) is the smooth even COMPLETE original theta kernel; for u>=0, phi(u)=sum_(n>=1) (2pi^2n^4exp(9u/2)-3pin^2exp(5u/2)) exp(-pin^2exp(2u)). X(r)=integral_R phi(u)exp(iru)du=xi(1/2+ir)/2. C(t)=integral_R s^2phi(s+t)phi(s-t)ds. L1(r)=X’(r)^2-X(r)X’‘(r)=4integral_R C(t)cos(2rt)dt. Want L1>=0 for ALL real r; equivalent to C positive definite. This is only first Laguerre, not the full all-order criterion.
Original state has L=2u, a’=(U+a^2-1)/2, U’=2U(a+chi), chi’=achi-U, a(0)=chi(0)=0, U(0)=Gamma(1/4)^8/(64pi^4). Define d=U+1.5(a^2-1), P=a/4+[2U(a+chi)+1.5a(U+a^2-1)]/d, P1=V(P). K_tt=4[(Pplus-Pminus)^2+P1plus+P1minus]K, clocks 2(s+-t).
The mixed form for arbitrary finite real x_i, complex c_i is Q=sum c_i conj(c_j) C((x_i-x_j)/2) =||E||^2+0.5 Re<D2,D0>-0.5||D1||^2, f_i(y)=phi(y-x_i), Dk=sum c_ix_i^kf_i, E=sum c_i(y-x_i)f_i. No lower bound follows from this identity alone.
Write only your assigned internal review note. Start with reviewed commit, wall classification, exact question and dependency. Separate what you actually derived/checked from guesses or conditional statements. Give a precise estimate with domains and method if one survives; otherwise say which missing comparison remains and why. Name matched controls and hypothesis mismatches, success/failure consequence and bounded next budget. Do not recommend further scans without an independently estimating method. You are not alone in the worktree; preserve all other agents’ edits.