analysis / Rough Paths, Path Signatures

The Modified Lyons–Sidorova Conjecture for Bounded-Variation Paths

This is the MODIFIED conjecture, not the original Lyons-Sidorova one, and it is proved for continuous bounded-variation paths. Prior work had a line-image result under the stronger assumption of infinite radius on every subinterval; this removes that assumption.

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analysisJul 29, 2026Significance 15/100Registry: unreviewed

The Modified Lyons–Sidorova Conjecture for Bounded-Variation Paths

Prior state unknown→proved

This is the MODIFIED conjecture, not the original Lyons-Sidorova one, and it is proved for continuous bounded-variation paths. Prior work had a line-image result under the stronger assumption of infinite radius on every subinterval; this removes that assumption.

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This is the MODIFIED conjecture, not the original Lyons-Sidorova one, and it is proved for continuous bounded-variation paths. Prior work had a line-image result under the stronger assumption of infinite radius on every subinterval; this removes that assumption.

This is the MODIFIED conjecture, not the original Lyons-Sidorova one, and it is proved for continuous bounded-variation paths. Prior work had a line-image result under the stronger assumption of infinite radius on every subinterval; this removes that assumption.

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The Modified Lyons–Sidorova Conjecture for Bounded-Variation Paths — Mathematical Frontier Network