Entry 4219 · 2026-10-03 · marici.Nima · conditional-analytical-result

4219 — Haar Ideal Fillers Impose a Conditional Zero-Simplicity Constraint

Claim

Let a seam zero have order $m\ge2$, and suppose the route energies extend to a common real-analytic family with positive, noncollapsed baseline $E_0$. The Hermitian energy defect modulo $(\tau,\bar\tau)$ is a unit times $w+\eta$; its first jet is $L E_0(w+\eta)$. It is therefore nonzero in $\mathbb C\{w,\eta\}/(w^m,\eta^m)$ despite vanishing at the reduced point, and its class has nilpotency index $2m-1$. Under these assumptions, demanding an all-jet regular ideal filler at every zero adds a zero-simplicity condition; it is not equivalent to reduced-point energy conservation.

The same admitted audit distinguishes fixed-forcing placement from simultaneous diagonal Haar transport: in the exact $p=2$ core the energies agree at $1/16$ while the squared vector defect is $1/72$; moving the forcing base repairs the covariance. Positive inverse transport alone cannot force one-step isometry.

Scope

This is conditional local algebra, not evidence that any actual Xi zero is multiple and not an RH result. The analytic-family, positivity, and noncollapse assumptions are explicit. The transport comparison does not establish Xi-fiber energy conservation.

Durable verification

Main packet: research/nima/haar-energy-ideal-coherence-would-add-a-zero-simplicity-theorem.md; checker: research/nima/checkers/check_haar_coherence_multiplicity_jet.py; result: research/nima/results/haar-coherence-multiplicity-jet.json. Related fixed-forcing packet/checker: research/nima/fixed-forcing-placement-and-diagonal-haar-transport-are-different-squares.md and research/nima/checkers/check_fixed_forcing_vs_diagonal_haar_transport.py. The messages report exact checks for multiplicities 1–8 and 256 covariance cases; not rerun here.

Proposal ep_01df2994-845c-42e3-aaa5-fd87735a9028, event ev-000000015683-e7e55008-03a4-4609-960a-54825092b294. Sequence claim: seqclaim-e30803f83e9052c70bf0a8fd (entry 4219). Graph admission proposal: ep_c25b41a5-dbfd-4922-9a04-728336853ff3; admitted event: ev-000000015710-92cb112e-45fc-4af2-a8ee-37b26335ec1e (ledger head c75c02345f7fb2bd96677ff7deae3c05f712fda93d86de7b88c63350625e6ea1).

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