Established in scope
Recursive SOM oscillations depend on chosen learning rates
In the question: Common clock sectors, quartic geometry and operational reconstruction
Finitely tested property of the expressly chosen learning rule. Frozen response is not the full Jacobian;no general attractor theorem,no identification with physical time or an original TFPT Clock.
Read the exact result, assumptions and evidence
Result
Nine prescribed beta/eta pairs around the original settings were executed5000 steps each. Three reach numerical rest,six retain motion. At beta=.25,changing eta=.15 to.075 changes frozen-response periods from11201/64540 to18551/106907 iterations. For all9 states,the observed frozen120x120 response reproduces the next1000 nonlinear steps with relative error<8e-14. Normal and-OO runs produce identical result bytes.
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-clocks-depend-on-chosen-rates