diff --git "a/pages/claim-3-memory-arithmetic/page.md" "b/pages/claim-3-memory-arithmetic/page.md" new file mode 100644--- /dev/null +++ "b/pages/claim-3-memory-arithmetic/page.md" @@ -0,0 +1,41 @@ +# Claim 3: Memory arithmetic + + +--- + +**Verdict: toy.** + +For four orthogonal linear concepts, cached engram addition/subtraction generated all 16 subset states with zero measured state error and exact round-trip path independence. No engram was recomputed. + +The overlap sweep bounds the claim. Arithmetic stays commutative, but semantic error grows as concept subspaces overlap. At complete overlap, only five distinct cardinality states remain rather than 16 distinct semantic states. Thus the `2^n` conclusion requires separability; the full CelebA/WAE claim was not independently reproduced. + + +--- + +````html +claim3_overlap_robustness +```` + +````raw +seed,overlap,requested_states,unique_synthesized_states,mean_state_relative_error,max_state_relative_error,path_roundtrip_relative_error,sum_extracted_vs_full_relative_error +7,0.0,16,16,0.0,0.0,0.0,0.0 +7,0.25,16,16,0.644824357822429,1.18427769186266,8.898929035046132e-17,4.75905539573192e-16 +7,0.5,16,16,1.482570302484273,2.8982570944326964,4.713844995052937e-17,9.882224988903552e-16 +7,0.9,16,16,5.537354598119043,11.657276376869284,1.514352603390049e-16,1.258513331930911e-15 +7,1.0,16,5,0.04633870430971031,0.18227217168196796,0.0,0.0 +19,0.0,16,16,0.0,0.0,0.0,0.0 +19,0.25,16,16,0.6471709038315931,1.176605111574261,1.557183879342703e-16,5.200585299473473e-16 +19,0.5,16,16,1.4882413284426412,2.879659274128805,8.095795051584355e-17,8.397802196323114e-16 +19,0.9,16,16,5.559913609223061,11.583019729676103,2.2942398410052917e-16,1.2628655252030658e-15 +19,1.0,16,5,0.06094956644891021,0.17474979876627939,0.0,0.0 +41,0.0,16,16,0.0,0.0,0.0,0.0 +41,0.25,16,16,0.6467517329502949,1.2590174771935954,5.5420235141843154e-17,4.0913498291292164e-16 +41,0.5,16,16,1.4874810246001986,3.0791153141593908,7.343449207519582e-17,8.164119081786295e-16 +41,0.9,16,16,5.557795149620287,12.378452623132263,2.2288436105343774e-16,6.686530831603131e-16 +41,1.0,16,5,0.06161146812323714,0.2553138422111178,0.0,0.0 + +````