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We complement this by a near-matching fine-grained lower bound: for constant dimensions d ≥ 3, there is no O((ε^{2/d}(n/ε)^{2-2/d})^{1-δ}) algorithm for any δ>0 unless the Orthogonal Vector Hypothesis fails.","weakest_assumption":"The Orthogonal Vector Hypothesis must hold for the conditional lower bound to apply; the curves must be simple paths on the grid graph."}},"verdict_id":"0a38e0fb-5494-4656-bda0-9704170eab89"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:47ac74b388eaf7046a0add1e0c155a75666db304bf64ba6bd63d276b0b841e9e","target":"record","created_at":"2026-05-20T00:00:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2fc967aea039ca9a9fdf3abbce2d18ca4283a8d7a47e50ec892a01a03f0de749","cross_cats_sorted":["cs.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2026-04-27T07:42:51Z","title_canon_sha256":"7476946eccdb7c3c2a2c2797a0bb6a87c3e8f1bcc40612244ba9a7f6076882ff"},"schema_version":"1.0","source":{"id":"2604.24135","kind":"arxiv","version":1}},"canonical_sha256":"133c045bc8b43c5037402a0a0fb473b66387288873c47ec957ee82f0532d0c3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"133c045bc8b43c5037402a0a0fb473b66387288873c47ec957ee82f0532d0c3f","first_computed_at":"2026-05-20T00:00:39.429366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:00:39.429366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I+mtB+w4lnTvSpTxOG0K/sfFouLQM0BKmE3Vq96xZtJDXOJ0Tdjx6hjKIfOGZsCLQV392iC13QEY0l0FqGJFDw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:00:39.430081Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.24135","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47ac74b388eaf7046a0add1e0c155a75666db304bf64ba6bd63d276b0b841e9e","sha256:4a3fce59e8cfea75952155cd853b16f4d2469e211017114bf069898d6103948d"],"state_sha256":"7461137b5d4fbb9bec331e2ef95bea92df11989f6a4292ce3e0b11000829da11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UiqSk3P4cJNJM9QN+JHTyJqAHXYmiv8z++L8MG+KOccnPYbyVxesKxL3QFXkba0RIns5H41zGG/2yy8thhLECA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T00:39:27.157763Z","bundle_sha256":"8b6c27aff83f746cd4304fc90594611d8273b9f2d86bdb98b7ae8a7d19385ae5"}}