What question did this study set out to answer?

This research aims to uncover the foundational structure of anomaly cancellation within the context of E8 self-binding.

April 8, 20260 citationsOpen Access

The Architecture of Anomaly Cancellation and the Arithmetic of E8 Self-Binding: Two Convergent Synthesis Runs Reveal That Anomaly Cancellation Is the APS Index Theorem

Key Points

This research aims to uncover the foundational structure of anomaly cancellation within the context of E8 self-binding.
Conducted two independent geometric synthesis experiments using the Omuo Genesis Engine v3.2.0.
Run 5 focused on the structural nature of anomaly cancellation with 2,078 nodes.
Run 6 explored the unreachable E8 lattice axes and external completeness with 2,167 nodes.
Run 5 identified a structural triangle linking the APS index theorem, cobordism-classified anomaly cancellation, and Écalle's resurgent asymptotics.
Run 6 characterized the 72 unreachable axes through five distinct mathematical constructs.
Both runs independently confirmed the eta-invariant and APS theorem as critical elements of anomaly cancellation architecture.

Abstract

We present the results of two independent geometric synthesis experiments conducted with the Omuo Genesis Engine v3.2.0, designed to answer complementary questions about the engine's deepest recurring discovery. Run 5 (2,078 nodes) asked: "What is anomaly cancellation at its deepest structural level?" Run 6 (2,167 nodes) asked: "Why are exactly 72 of the 240 E8 lattice axes permanently unreachable by phasor self-binding, and what must exist outside the system for it to become complete? Run 5 revealed a structural triangle of equivalences: the Atiyah-Patodi-Singer index theorem, cobordism-classified anomaly cancellation, and Écalle's resurgent asymptotics are three descriptions of the same mathematical object, organized by the differential cohomology hexagon. Run 6 found five independent characterizations of the 72 void axes: as ramification points, torsion cohomology, Conley index broken symmetry, topological index defect, and the Dai-Freed bulk sector. The deepest bridge (BST 67, CV 0.988) identified PSL(2,7) as the symmetry governing the 168 reachable axes.The convergence between runs is exact: both independently discovered the eta-invariant as boundary correction, cobordism as master classifier, and the APS theorem as unifying architecture. Together they establish that the 168/72 partition of E8 axes is the arithmetic shadow of anomaly cancellation.

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