{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:2MEP3TNU763FZ3RAAP5RNB7HON","short_pith_number":"pith:2MEP3TNU","canonical_record":{"source":{"id":"1109.4648","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-09-21T20:20:04Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"09cc625d0f7bd6016ed119c6f1f83edce6db42d3514d75abaddde5bb7b4b5860","abstract_canon_sha256":"0b61587b176188157d9c56b472f79be0df2133d736e0ac0b1255f1e561e1820d"},"schema_version":"1.0"},"canonical_sha256":"d308fdcdb4ffb65cee2003fb1687e7734db2ceddac201e5a77cf2e0ea29374d3","source":{"kind":"arxiv","id":"1109.4648","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4648","created_at":"2026-05-18T04:12:33Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4648v1","created_at":"2026-05-18T04:12:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4648","created_at":"2026-05-18T04:12:33Z"},{"alias_kind":"pith_short_12","alias_value":"2MEP3TNU763F","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2MEP3TNU763FZ3RA","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2MEP3TNU","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:2MEP3TNU763FZ3RAAP5RNB7HON","target":"record","payload":{"canonical_record":{"source":{"id":"1109.4648","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-09-21T20:20:04Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"09cc625d0f7bd6016ed119c6f1f83edce6db42d3514d75abaddde5bb7b4b5860","abstract_canon_sha256":"0b61587b176188157d9c56b472f79be0df2133d736e0ac0b1255f1e561e1820d"},"schema_version":"1.0"},"canonical_sha256":"d308fdcdb4ffb65cee2003fb1687e7734db2ceddac201e5a77cf2e0ea29374d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:33.278287Z","signature_b64":"S2smz5CqfgFieMGxTWSBvj6dTmfQMyPKEpH9DaNMS3Thkqho2uXPR8azgR96oB2ibroHfYnREIr0C4nyLt0LDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d308fdcdb4ffb65cee2003fb1687e7734db2ceddac201e5a77cf2e0ea29374d3","last_reissued_at":"2026-05-18T04:12:33.277663Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:33.277663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.4648","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:12:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gaHVU7zKjx1dP7kOKZ3AGPUWhIDWdEPHfFvo3umJ796IAzu/FH9FeVavEBUai+6rDj4n7RonsbdYXHDnIRNHAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:07:26.092372Z"},"content_sha256":"44ab3e6118c65ead7494b275b91bcd843a6721556913046d2d0a5c9fe1ac5174","schema_version":"1.0","event_id":"sha256:44ab3e6118c65ead7494b275b91bcd843a6721556913046d2d0a5c9fe1ac5174"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:2MEP3TNU763FZ3RAAP5RNB7HON","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rank one matrices do not contribute to the failure of the finiteness property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.SP","authors_text":"Ian D. Morris","submitted_at":"2011-09-21T20:20:04Z","abstract_excerpt":"The joint spectral radius of a bounded set of d times d real or complex matrices is defined to be the maximum exponential rate of growth of products of matrices drawn from that set. A set of matrices is said to satisfy the finiteness property if this maximum rate of growth occurs along a periodic infinite sequence. In this note we give some sufficient conditions for a finite set of matrices to satisfy the finiteness property in terms of its rank one elements. We show in particular that if a finite set of matrices does not satisfy the finiteness property, then the subset consisting of all matri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4648","kind":"arxiv","version":1},"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":"2026-05-18T04:12:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w1rAh4FJnz6Pap7jKuniVDdT4RZ/ZNwNSZ5qGbdCfUEC3WEGW57xBnisBMFbr4WWWGmiC9DnQa/TlLVHjZ1ZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:07:26.092704Z"},"content_sha256":"326f534d08e569578c01c8dd47669690950287ef3f618ff91e72a624ad5723aa","schema_version":"1.0","event_id":"sha256:326f534d08e569578c01c8dd47669690950287ef3f618ff91e72a624ad5723aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2MEP3TNU763FZ3RAAP5RNB7HON/bundle.json","state_url":"https://pith.science/pith/2MEP3TNU763FZ3RAAP5RNB7HON/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2MEP3TNU763FZ3RAAP5RNB7HON/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":"2026-06-20T06:07:26Z","links":{"resolver":"https://pith.science/pith/2MEP3TNU763FZ3RAAP5RNB7HON","bundle":"https://pith.science/pith/2MEP3TNU763FZ3RAAP5RNB7HON/bundle.json","state":"https://pith.science/pith/2MEP3TNU763FZ3RAAP5RNB7HON/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2MEP3TNU763FZ3RAAP5RNB7HON/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2MEP3TNU763FZ3RAAP5RNB7HON","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":"0b61587b176188157d9c56b472f79be0df2133d736e0ac0b1255f1e561e1820d","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-09-21T20:20:04Z","title_canon_sha256":"09cc625d0f7bd6016ed119c6f1f83edce6db42d3514d75abaddde5bb7b4b5860"},"schema_version":"1.0","source":{"id":"1109.4648","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4648","created_at":"2026-05-18T04:12:33Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4648v1","created_at":"2026-05-18T04:12:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4648","created_at":"2026-05-18T04:12:33Z"},{"alias_kind":"pith_short_12","alias_value":"2MEP3TNU763F","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2MEP3TNU763FZ3RA","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2MEP3TNU","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:326f534d08e569578c01c8dd47669690950287ef3f618ff91e72a624ad5723aa","target":"graph","created_at":"2026-05-18T04:12:33Z","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":"The joint spectral radius of a bounded set of d times d real or complex matrices is defined to be the maximum exponential rate of growth of products of matrices drawn from that set. A set of matrices is said to satisfy the finiteness property if this maximum rate of growth occurs along a periodic infinite sequence. In this note we give some sufficient conditions for a finite set of matrices to satisfy the finiteness property in terms of its rank one elements. We show in particular that if a finite set of matrices does not satisfy the finiteness property, then the subset consisting of all matri","authors_text":"Ian D. Morris","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-09-21T20:20:04Z","title":"Rank one matrices do not contribute to the failure of the finiteness property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4648","kind":"arxiv","version":1},"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":"sha256:44ab3e6118c65ead7494b275b91bcd843a6721556913046d2d0a5c9fe1ac5174","target":"record","created_at":"2026-05-18T04:12:33Z","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":"0b61587b176188157d9c56b472f79be0df2133d736e0ac0b1255f1e561e1820d","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-09-21T20:20:04Z","title_canon_sha256":"09cc625d0f7bd6016ed119c6f1f83edce6db42d3514d75abaddde5bb7b4b5860"},"schema_version":"1.0","source":{"id":"1109.4648","kind":"arxiv","version":1}},"canonical_sha256":"d308fdcdb4ffb65cee2003fb1687e7734db2ceddac201e5a77cf2e0ea29374d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d308fdcdb4ffb65cee2003fb1687e7734db2ceddac201e5a77cf2e0ea29374d3","first_computed_at":"2026-05-18T04:12:33.277663Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:33.277663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S2smz5CqfgFieMGxTWSBvj6dTmfQMyPKEpH9DaNMS3Thkqho2uXPR8azgR96oB2ibroHfYnREIr0C4nyLt0LDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:33.278287Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4648","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44ab3e6118c65ead7494b275b91bcd843a6721556913046d2d0a5c9fe1ac5174","sha256:326f534d08e569578c01c8dd47669690950287ef3f618ff91e72a624ad5723aa"],"state_sha256":"5b0370d7fef2622ddf11925f752530e2383ddde744669255491b7085da3493be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S28Usm3B5XwqVdF0eV6hQFOr34W/QmfIjS8mbpbzsO+mnkO88Q+YxC91ZkKnjJFeyFmdgXORKGdDapW98UtZDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:07:26.094575Z","bundle_sha256":"a70b6a592008bf2221983e6a2a08e3b85cdf2c4629edd046520387a2e1e99414"}}