This research release proposes a compact identity behind multiplication of two binary forms. Multiplication loses one direction: scaling the first factor up while scaling the second down leaves their product unchanged. The paper identifies that lost direction explicitly. It claims that if one adds any final row to the rectangular multiplication Jacobian, the resulting determinant is exactly one signed resultant multiplied by the pairing of that row with the scaling direction. The formula is stated over the integers for every pair of positive degrees, including equal degrees. Choosing the derivative of the resultant as the final row recovers the earlier degree-difference formula. The same argument explains why equal degrees collapse, when the map is etale in positive characteristic, and why no function of the product alone can repair the missing direction. The evidence package contains a twelve-page proof, exact SymPy and FLINT computations, ninety-three deep checks, five deliberate failure controls, source hashes, citation and novelty audits, reviews, and machine-readable claim records. Those computations test finite bidegrees and implementation behaviour. The all-degree statement rests on the written proof. Mathlib contains related resultant and monic-factorisation ingredients, but the complete bordered identity has not been formalised. This remains an anonymous, unrefereed candidate. It has not been independently reproduced or editorially peer reviewed, and the recorded novelty search is bounded. This is an Evidence Press audio briefing, released 8 August 2026. The full manuscript and exact archive are linked on this page. The audio uses an AI-generated voice and is not additional mathematical evidence.