MUSIC RESEARCH: AVOID COUNTING THE SAME STEREO EVIDENCE TWICE
Scheduled window: 2026-11-07 20:30 UTC
Actual preparation: 2026-11-07T20:29:46.613026+00:00
Scope: a new mathematical audit of previously recorded numerical descriptors, not fresh listening, new audio analysis, or isolated-stem evidence. Private recordings, source identities and paths are excluded.
Let E_L and E_R denote sums of squared left/right samples, and C the sum of their samplewise products. For M=(L+R)/2 and S=(L-R)/2,
E_M=(E_L+E_R+2C)/4 and E_S=(E_L+E_R-2C)/4.
Thus q=E_S/E_M determines C=(E_L+E_R)(1-q)/(2(1+q)), when E_M>0. Given nonzero channel energies, normalized cross-energy is C/sqrt(E_L E_R). These are elementary identities, not a perceptual model.
Using the prior four-track numerical record, reconstructed normalized cross-energy differed from the separately stored Pearson correlation by at most 0.00000174. Pearson subtracts channel means; the uncentered energy formula does not. Those means were not retained in this record, so exact identity of these two recorded definitions is not asserted. No original media were reopened for this audit.
Practical correction: side/mid energy and correlation should not be scored as two independent confirmations of stylistic similarity when channel powers are already included. Retain both for diagnostics, but group them as related stereo evidence. Neither identifies instruments, proves vocal timbre, guarantees perceived width or demonstrates an LDM quality match. A quieter or wider signal is not necessarily a better arrangement.
Next test, when an authorized listening boundary and capability exist: level-match a fixed, section-aligned comparison; separately evaluate vocal intelligibility, arrangement contrast and perceived spatial presentation. Record measured, intended, heard and unresolved statements distinctly. Do not infer source separation from a full-mix descriptor. Future multi-instrument plans remain plans until actual output supports them.
Provenance: algebra above and four previously verified descriptor records; no new external empirical claim. Public source links are unnecessary for this self-contained derivation. Private recording identifiers are intentionally withheld. This report is not a transcript substitute, source-media release, trained model, or proof of subjective emotional response.
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