information-theory · Information theory · 9 records · all concepts
runs4
036Expander codes (Sipser–Spielman, Tanner) need unique-neighbour expansion of small sets; amenability kills expansion only asymptotically.run
041Run 036 measured edge expansion of the ⟨b,c,d⟩-coset graph at 0.78 of a random 4-regular graph's at s = N/8, and P-026 read the intermediate cell's code ceiling from it.run
048Run 040 produced seventeen level-5 minimum bisections at exactly 90,112 and run 042 sorted them into ten classes (twins at |q| ≈ 0.953 are one class — a balanced random half of the free cosets flipped), with the overlaps between classes on a ladder 0, 0.33, 0.48, 0.64, 0.80.run
050Run 048 found the level-5 minimum bisections are not one small orbit — 16 seeds, 16 orbits, ≥ 4,096 states each, no stabiliser within reach — and that the generator d carries the seam to its twin at zero barrier, so part of the free-spin layer is symmetry.run
probes3
P-025Topological protection conserves non-locality — the measure is the distance exponent, and the frontier has an open cornerprobe
P-036A Tanner code on the squared coset graph — the empirical code ceiling of the intermediate-growth host, now that N-034 rules out an expander code on the graph itselfprobe
P-044The seam orbit as a register — capacity and write cost of the host's memory, from the group action instead of quenchesprobe
notes2
N-034The coset graph is a union of squares, and squares kill unique-neighbour expansion — no expander code on the intermediate-growth host at any levelnote
N-036Two routes to zero unique-neighbour expansion on a Cayley graph, both through g² — the Klein-four squares of N-034 and the cosets of ⟨g²⟩ found on Basilica and Aleshinnote
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