TITLE: EVEN PARITY IN R FOUR [STYLE: Avant-Garde Choral Metal with Progressive Math Rock Undercurrent] [TEMPO: Begins at 172 BPM, fluctuates irrationally] [METER: Alternating 13/8, 7/8, 5/4, sudden fermatas] [INSTRUMENTATION: Pipe organ clusters, distorted seven-string guitars, modular synth noise, full SATB choir, manic baritone lead] [MOOD: Exultant, unhinged, hyper-intellectual ecstasy] [OVERTURE – Prestissimo Furioso, organ cluster glissandi, polyrhythmic percussion] Low brass intone a tritone drone. Choir whispers “orientation… orientation…” [VERSE ONE – Driving 13/8 riff, staccato strings doubling guitar line] I fix an orientation in R four! Choose a basis: x, y, z, w — Positively ordered, cyclically adored, Determinant strictly greater than zero! Levi Civita tensor in combustion, Epsilon i j k l equals plus one When permutation is even — Alternating tensor eruption! Wedge them! x wedge y wedge z wedge w! Four form sovereign! Volume element enthroned above! [PRE-CHORUS – Tempo modulation, syncopated accents] Contract with partial with respect to w! Interior product tears the silence! Induce the three form on x y z — But count the sign! Negative one raised to k minus one! Parity stalks the omission! [CHORUS – Full choir fortissimo, blast beats underneath] Even parity! Even parity! Product of hyperplane orientations equals plus one! Multiply the signs! Negative times negative redeems the sum! Sixteen naïve assignments collapse to eight — Exterior algebra forbids your rebellion! [VERSE TWO – 7/8 groove, angular melodic leaps] Omit w — inherit the sign! Omit z — inherit the sign! Omit y — inherit the sign! Omit x — inherit the sign! Compute the product! Two negatives annihilate in symmetry! The determinant does not negotiate! The four dimensional volume form Laughs in multilinear ecstasy! [BRIDGE – Sudden drop to 5/4, eerie synth pad, whispered counterpoint] In R three you cling to handedness, Left versus right in mirror opposition, Chirality trapped in fundamental groups. But ascend — Embed in R four! Ambient isotopy devours asymmetry! Knots untwist in higher freedom! Handedness is provincial. Orientation is imperial. [FINAL CHORUS – Accelerando, choir in layered canon] Even parity! Even parity! Product of all induced orientations equals plus one! You may permute! You may contract! You may dualize with the Hodge star! But you shall not violate the four form! [CODA – Rubato, organ sustained cluster fading into silence] All projections are shadows. All shadows inherit constraint. There is only the volume form. And it does not forgive.
