Established in scope
Declared recursive SOM update alone prefers no absolute code orientation
In the question: Common clock sectors, quartic geometry and operational reconstruction
Exact mathematical symmetry of the chosen update plus finite numerical checks. Generic U(35) does NOT preserve native tensor powers/field products;not a countermodel to full TFPT origin. Given native initial alignment may be justified upstream.
Read the exact result, assumptions and evidence
Result
For every U in U(35),the stipulated update is exactly covariant under X->XU,W->WU: norms,distances,winners,means and normalization are preserved. After5000 directly executed steps the relative signal error is1.36e-14. Original code weight.9809168 becomes.1324321 for actively rotated input with FIXED readout; passive readout transport restores.9809168.128 orientations transported by the proved covariance give mean.1417688 near5/35. Three generic complex starts also compress without the high native code weight.
Required assumptions
- Explicitly chosen recursive SOM rule on60 native signal cells
Given solely for the authorized model study is the60x35 complex update of RECURSIVE-SOM-AUDIT.txt section1,with native K60,fixed neighbors,row normalization,Euclidean winners,batch means and chosen c,beta,eta. The code basis is readout only. This update and its initial alignment are not primitive TFPT laws.
- Symmetric quartic and actual erasure intertwiner
Use Sym^4 of the native four-representation, the actual five codeword sums, and the existing one-register erasure intertwiner. The symmetric tensor rule and its physical selection are not silently inferred from the full tensor product.
- Existing even E8 lattice, Gaussian J and sign lifts
Given existing even unimodular E8 with actual J(x0,x1,...)=(-x1,x0,...) and J²=-I, and the original ordered sign lattice cocycle. Sign automorphisms have kernel Hom(L,F2). Retain original integral ordered basis and generator phases; no enlargement to U1 characters except explicitly defined scalar pushouts.
Original evidence
- RECURSIVE-SOM-AUDIT.txt lines 1–101
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/collective-native-marginal-origin-20261026/RECURSIVE-SOM-AUDIT.txt
d52d1cbb7b88572d4ee097fd412e8e611c3f7019baace049eb3ee6d1a6476c1c
- fundamental_audit.py lines 1–134
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/collective-native-marginal-origin-20261026/recursive_machine_audit/fundamental_audit.py
94e0bfa42f6e8442668ed3c7b0baa239e80229b7090ff7e8e706811f60f3d77e
finding:declared-recursive-native-som-is-u35-equivariant