{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:R3KMGDP4YRFC653T6MCH4G65C4","short_pith_number":"pith:R3KMGDP4","canonical_record":{"source":{"id":"1003.5321","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-03-27T21:06:25Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"ef5f35894bdab347620fe804935c71282cda280b40efba2221f77191b616fcab","abstract_canon_sha256":"697b324de7079a5ae458962a538c26b0f0460b59a6f1e8761ca7422ca991934d"},"schema_version":"1.0"},"canonical_sha256":"8ed4c30dfcc44a2f7773f3047e1bdd171179dbbd09e74fc7c938ebaefc1161bf","source":{"kind":"arxiv","id":"1003.5321","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.5321","created_at":"2026-05-18T03:10:46Z"},{"alias_kind":"arxiv_version","alias_value":"1003.5321v3","created_at":"2026-05-18T03:10:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5321","created_at":"2026-05-18T03:10:46Z"},{"alias_kind":"pith_short_12","alias_value":"R3KMGDP4YRFC","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"R3KMGDP4YRFC653T","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"R3KMGDP4","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:R3KMGDP4YRFC653T6MCH4G65C4","target":"record","payload":{"canonical_record":{"source":{"id":"1003.5321","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-03-27T21:06:25Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"ef5f35894bdab347620fe804935c71282cda280b40efba2221f77191b616fcab","abstract_canon_sha256":"697b324de7079a5ae458962a538c26b0f0460b59a6f1e8761ca7422ca991934d"},"schema_version":"1.0"},"canonical_sha256":"8ed4c30dfcc44a2f7773f3047e1bdd171179dbbd09e74fc7c938ebaefc1161bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:46.194162Z","signature_b64":"8d9ciiJTgZKWfk6Eo6FKimifeixpVUqkEdial9JcP9ih3eVNvSNk3UAcAwOidpeRx4ytaJNazflzYK9Am3KICA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ed4c30dfcc44a2f7773f3047e1bdd171179dbbd09e74fc7c938ebaefc1161bf","last_reissued_at":"2026-05-18T03:10:46.193596Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:46.193596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.5321","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:10:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8HpKG8Y7Ln0WMavl7yyzpdCgkpHhO2BxZ/B+++jHYGT2U+CJnWr660h8we9IIjan5MCCheO4g4k7UT1IB8+aAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:04:46.243106Z"},"content_sha256":"850bef0e12ecb8e598fa18c369c830b9339e55eaca8dfb185d1103f5acf1b7e2","schema_version":"1.0","event_id":"sha256:850bef0e12ecb8e598fa18c369c830b9339e55eaca8dfb185d1103f5acf1b7e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:R3KMGDP4YRFC653T6MCH4G65C4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamics of tuples of matrices in Jordan form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"George Costakis, Ioannis Parissis","submitted_at":"2010-03-27T21:06:25Z","abstract_excerpt":"A tuple (T_1,...,T_k) of (n x n) matrices over R is called hypercyclic if for some x in R^n the set {T^{m_1} T^{m_2}...T^{m_k} x : m_1,m_2,...,m_k in N} is dense in R^n. We prove that the minimum number of (n x n) matrices in Jordan form over R which form a hypercyclic tuple is n+1. This answers a question of Costakis, Hadjiloucas and Manoussos."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5321","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:10:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IgZk+Y1Hwt1cgLkcgYwGwGaoFa82hDE3dTezEE87U4fdMK4yCdjmBpxZWH19t8niwFV7QE0+6k2aESYRG2i7DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:04:46.243757Z"},"content_sha256":"39c77aeaf11d58ad6185b485873f06b893a30dd861307930e2018be0df2b1d4c","schema_version":"1.0","event_id":"sha256:39c77aeaf11d58ad6185b485873f06b893a30dd861307930e2018be0df2b1d4c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R3KMGDP4YRFC653T6MCH4G65C4/bundle.json","state_url":"https://pith.science/pith/R3KMGDP4YRFC653T6MCH4G65C4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R3KMGDP4YRFC653T6MCH4G65C4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T22:04:46Z","links":{"resolver":"https://pith.science/pith/R3KMGDP4YRFC653T6MCH4G65C4","bundle":"https://pith.science/pith/R3KMGDP4YRFC653T6MCH4G65C4/bundle.json","state":"https://pith.science/pith/R3KMGDP4YRFC653T6MCH4G65C4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R3KMGDP4YRFC653T6MCH4G65C4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:R3KMGDP4YRFC653T6MCH4G65C4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"697b324de7079a5ae458962a538c26b0f0460b59a6f1e8761ca7422ca991934d","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-03-27T21:06:25Z","title_canon_sha256":"ef5f35894bdab347620fe804935c71282cda280b40efba2221f77191b616fcab"},"schema_version":"1.0","source":{"id":"1003.5321","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.5321","created_at":"2026-05-18T03:10:46Z"},{"alias_kind":"arxiv_version","alias_value":"1003.5321v3","created_at":"2026-05-18T03:10:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5321","created_at":"2026-05-18T03:10:46Z"},{"alias_kind":"pith_short_12","alias_value":"R3KMGDP4YRFC","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"R3KMGDP4YRFC653T","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"R3KMGDP4","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:39c77aeaf11d58ad6185b485873f06b893a30dd861307930e2018be0df2b1d4c","target":"graph","created_at":"2026-05-18T03:10:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"A tuple (T_1,...,T_k) of (n x n) matrices over R is called hypercyclic if for some x in R^n the set {T^{m_1} T^{m_2}...T^{m_k} x : m_1,m_2,...,m_k in N} is dense in R^n. We prove that the minimum number of (n x n) matrices in Jordan form over R which form a hypercyclic tuple is n+1. This answers a question of Costakis, Hadjiloucas and Manoussos.","authors_text":"George Costakis, Ioannis Parissis","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-03-27T21:06:25Z","title":"Dynamics of tuples of matrices in Jordan form"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5321","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:850bef0e12ecb8e598fa18c369c830b9339e55eaca8dfb185d1103f5acf1b7e2","target":"record","created_at":"2026-05-18T03:10:46Z","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":"697b324de7079a5ae458962a538c26b0f0460b59a6f1e8761ca7422ca991934d","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-03-27T21:06:25Z","title_canon_sha256":"ef5f35894bdab347620fe804935c71282cda280b40efba2221f77191b616fcab"},"schema_version":"1.0","source":{"id":"1003.5321","kind":"arxiv","version":3}},"canonical_sha256":"8ed4c30dfcc44a2f7773f3047e1bdd171179dbbd09e74fc7c938ebaefc1161bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ed4c30dfcc44a2f7773f3047e1bdd171179dbbd09e74fc7c938ebaefc1161bf","first_computed_at":"2026-05-18T03:10:46.193596Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:46.193596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8d9ciiJTgZKWfk6Eo6FKimifeixpVUqkEdial9JcP9ih3eVNvSNk3UAcAwOidpeRx4ytaJNazflzYK9Am3KICA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:46.194162Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.5321","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:850bef0e12ecb8e598fa18c369c830b9339e55eaca8dfb185d1103f5acf1b7e2","sha256:39c77aeaf11d58ad6185b485873f06b893a30dd861307930e2018be0df2b1d4c"],"state_sha256":"f9b0af520e51551203daeef7f1dd8d34564e3186a2c9a73742b4038cc760b5ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TFYQTgNXBb0GCBYNyF78QrvFJDUQ+Ih207GYRR7lDkBGSsUJ3HTTdtWyWNevVkEo9HqMQ6DWbOQ9Mj35k5zLAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T22:04:46.246987Z","bundle_sha256":"c44909d8780c26b82c703c6d6c2f27683a0c01ccabfafe71641bb97f8656577a"}}