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We show an optimal (up to logarithms) ``Frobenius light cone\" obeying $t\\sim r^{\\min(\\alpha-1,1)}$ for $\\alpha>1$ in one-dimensional power-law interacting systems with finite local dimension: this controls, among other physical properties, the butterfly"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2105.09960","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2021-05-20T18:00:03Z","cross_cats_sorted":["cond-mat.str-el","math-ph","math.MP"],"title_canon_sha256":"39d654c5167a1974250b8c3ac6ac8039e94800202beca0bcd51c16458c4a3674","abstract_canon_sha256":"1b49129e270db82d5a2032fa8e3f7f2977298550641fdca94e517b8e08762e38"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:39:59.218337Z","signature_b64":"uGLCq4HR0Ie0xpVsBWypmapm84FChelhOzjwMHmjyVCXek5gRyfWd9DxyixvedcBwZ9EsNi3MN2occ/8OHINCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82a3ec968bc7dc3267a29e0d329c59c9cb393ff4173c4cb5115a21f0814cfa88","last_reissued_at":"2026-07-05T03:39:59.217837Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:39:59.217837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Frobenius light cone in spin chains with power-law interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Andrew Lucas, Chi-Fang Chen","submitted_at":"2021-05-20T18:00:03Z","abstract_excerpt":"In many-body quantum systems with spatially local interactions, quantum information propagates with a finite velocity, reminiscent of the ``light cone\" of relativity. 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