On Strassen's Conjecture

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Proves additivity for three-way tensor rank whenever the smallest factor dimension is at most two (c1 ≤ 2), extending earlier cases that used conciseness and Kronecker normal form for pencils. Argument uses dimension counts, projections to the summand spaces and removal of a rank‑one slice to force a minimal counterexample contradiction. For border rank finds explicit positive instances (e.g. a rank‑5 tensor in C3⊗C3⊗C3 plus a rank‑1 gives border rank 6) by computing contraction block matrices and applying Strassen’s degree‑9 equation for σ4(P2×P2×P2).

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" chapters (13)

1. 0:00Strassen's conjecture intro
2. 1:05Strassen's additivity conjecture
3. 3:37Known cases
4. 8:13Lemma consequences
5. 12:09Generalized conjecture
6. 12:51Additivity when dim ≤ 2
7. 20:59Proof sketch
8. 27:38Border rank conjecture
9. 31:03Counterexamples
10. 35:36Positive examples
11. 42:01Degree 9 equation
12. 48:48Extending examples
13. 50:53Summary and open questions