Harmonic filter diagnostic
Stub README (2026-09-28): this directory predates the README convention. The summary below was reconstructed from its files; see them for detail.
Question. Do position-distribution 'chord' features of trie substrings separate on-path from off-path query/key pairs, and which operator and frequency set separates them best?
Answer. Pooled over all pairs, symmetric chord-vs-chord scores (E3/E4) separate weakly or not at all. Stratified by key mass, the signal sits at low-mass keys. The asymmetric K-at-p_Q operator with DFT frequencies separates best: at key mass 2-9 (HD=48, W=64) the gap is 1.60 pooled-IQR units on Shakespeare and 1.68 on Gutenberg, falling to about 0.04 at mass ≥1000.
- ASYM DFT operator, HD=48 W=64, Shakespeare, key mass 2-9: on/off-path separation (pooled-IQR units) = 1.6
- ASYM DFT operator, HD=48 W=64, Gutenberg, key mass 2-9: on/off-path separation (pooled-IQR units) = 1.68
Sources. notes/seq-len-extension/harmonic-filter-asymmetric.md ('diagnostic-validated 2026-05-25', stratified tables); stratified/shake_dft_HD48_W64.txt and gut_dft_HD48_W64.txt 'ASYM aggregate score' rows; shakespeare*/summary.md E3/E4 all-pairs separations (-0.03 to +0.23).
Caveats. The headline values are in stratified/.The training follow-up (harmonic-bias-prototype) is listed in rnd/TRIAGE.md as a null result. The design notes live in notes/seq-len-extension/harmonic-filter-.md.