ya, tricky staying balanced between coding & math & making accessible
skimmed gist / one concept that stood out is your notion of coherence basin, may borrow with credit in next paper
one reason is readable accessibility in that our core thesis with hypertokens is every system has what we might call a family of fidelity windows or less formally an eyeball entropy
we have to respect that & keep model in fidelity limits to achieve balanced optimal parallel transport (OPT)
that of course immediately suggests we apply spherical harmonics, which leads to sphere packing, multipath, & channel code subspaces, which of course leads to Fourier families
our initial release is more wavelet driven since we are outside the model using tokens to drive the process; we interleave a topological skewed lattice code every k content tokens
skipping how we do that rn, it is specifically built in fixed or adaptive sense to keep model in fidelity window and we can show it exactly functions as pre/post Fourier interferometer aka means max filter signal capture & dithered denoising.
To be precise our context compiler is a robust software defined amplifier that presamples prior signal Hamiltonian like, evolves few tokens Lagrange like and post samples with same code to get interferometry differential. We get the Fourier lift because the codes themselves are *strictly drawn* from skewed lattice where pre sample and postsample amount to:
pre-sample FFT
co-evolve in freq & time domains
post-sample iFFT
differential
code is locally & globally nested & also locally & globally unique, so we get all sorts of nice info theory, group theory & other properties, e.g., self-syncing, prefix-free & suffix-free
which going back to practical coding and what first inspired our work is that we can define K:V & V:K associative memory in-context just like you’d program spreadsheet it just happens to be classic-quantum in that we are in balanced transport regime
if you think about those projections to from FFT and iFFT, we are essentially walking model from coherence basin to coherence basin. There’s nice adjacent visual I saw last night that gets in this direction they assume uniform lattice and get to skewed were as our work is like playing that movie backward.