Unified Theory of Everything Research Program: TOE-N00AK-r1 - Exact Tree-Level Majorana Kernels and a Dimension-Seven Scope Correction

This research and reproducibility update documents the sequential Type-I seesaw effective-field-theory branch of the project. It retains exact tree-level identities and corrects the interpretation of the earlier local TOE-N00AK dimension-seven loop claims.

Established mathematical content: the lepton-number-violating finite-pole Majorana tree kernel, its local moments and exact remainder, a spectral-norm error bound, and finite-pole reconstruction from the first c effective-node moments when those nodes are known. For a single nonzero removed pole at a probe-to-heavy mass ratio r below one, retaining dimension five gives relative tree-kernel error r^2; retaining dimensions five and seven gives r^4. These are tree-kernel approximation errors, not uncertainties on measured neutrino masses.

Scope correction: the proposed dimension-seven bubble was obtained by multiplying a published dimension-five result by a common external momentum squared. The derivative LLHH vertex has distinct Wick pairings with different composite momenta; one pairing carries loop momentum. The supplied argument therefore does not establish the dimension-seven ultraviolet pole. The proposed +3 A2 and -3 A2 components, their higher-odd extensions, and their finite-ratio cancellation are retained only as conditional algebra, not established loop coefficients. A common coefficient other than 3 also cancels, demonstrating why algebraic replay cannot determine that physical coefficient. This identifies a gap in the derivation; it does not calculate a replacement coefficient or prove the eventual physical cancellation false.

The release contains a corrected technical note, a readable PDF overview, frozen benchmark data, a focused numerical implementation, fresh verification results, and file checksums. Code checks establish reproducibility of the stated mathematical and conditional formulas. AI-assisted checks are not independent expert peer review. Historical parent archives and private chat exports are excluded.

The next calculation is an independently routed off-shell dimension-seven mixed-bubble evaluation with all Wick contractions and complete sourced-equation-of-motion reduction. The full dimension-seven operator packet, hard and finite one-loop matching, and connection to low-energy observables remain open. This release does not demonstrate a complete Theory of Everything, a new experimentally validated prediction, or a physical bridge joining the earlier epsilon-lattice construction to a complete ultraviolet theory.