Depth-Generated Geometry: Ordered Quaternionic Response Quotients, Flat Cores, and Residual Descent

Depth-Generated Geometry Research Snapshot 2026-09-07, audit revision 1, presents an independent finite-algebra account of ordered quaternionic response quotients. It builds on the frozen Free Numbers Core v1.0.0 artifact and is a separate research publication unit, not a replacement of that Core release. Research navigation for readers and AI agents This work develops a quaternionic exact-response framework for finite ordered words in the Free Numbers Program. Note 25 establishes a flat, 144-dimensional stationary-edge core connection on the reduced two-spectator spacing-word graph, with identity holonomy I_144. Note 26 studies the three-internal-spectator word 222. Its quotient has dimension 444, with a 432-dimensional outer-edge core and a 12-dimensional residual quotient. A specified central-slot right decoder induces an isomorphism of residual quotients, while its full descent obstruction has image equal to the entire 432-dimensional core. For exact rational verification, run the following from the extracted DGG snapshot directory: python3 certificates/n8_222_redetection_certificate.py --certificate See CLAIMS_LEDGER.md for theorem scope and REPRODUCIBILITY.md for dependencies and verification records. The archive contains a PDF manuscript and editable sources, the complete DGG source-note series through Note 26, exact computational certificates, a claim ledger, verification records, reproduction instructions and checksums. Rational theorems are distinguished from finite-field checks and from constructions that require the stated choice of comparison operator. The snapshot does not claim a complete three-spectator atlas, an all-length interior transport theorem, nonzero core curvature, a physical interpretation, or a time-update law. The evidence record identifies which certificates were run for this snapshot and which are retained from the source theorem chain. The audit revision clarifies the selected extension on the exceptional residual, corrects the full common-face projection description, and strengthens cached rank certification. It includes fresh historical theorem-chain runs and an independent third-prime and exhaustive component-product check for the latest object and its parents.