{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DE3CMSHTXSWOWPWBWVUN6LPUXP","short_pith_number":"pith:DE3CMSHT","canonical_record":{"source":{"id":"1306.5331","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-22T15:48:55Z","cross_cats_sorted":[],"title_canon_sha256":"b6c9d6a1ff0d08af5e8495ca98592a563348f962a784f031afee8617c149edf5","abstract_canon_sha256":"81b60c415d9ca261a380264f9fdc5f99734563cabc684e2be71b23d52487251d"},"schema_version":"1.0"},"canonical_sha256":"19362648f3bcaceb3ec1b568df2df4bbd0349b2a52a4a3113b9cf00666b5da64","source":{"kind":"arxiv","id":"1306.5331","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5331","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5331v2","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5331","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"pith_short_12","alias_value":"DE3CMSHTXSWO","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DE3CMSHTXSWOWPWB","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DE3CMSHT","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DE3CMSHTXSWOWPWBWVUN6LPUXP","target":"record","payload":{"canonical_record":{"source":{"id":"1306.5331","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-22T15:48:55Z","cross_cats_sorted":[],"title_canon_sha256":"b6c9d6a1ff0d08af5e8495ca98592a563348f962a784f031afee8617c149edf5","abstract_canon_sha256":"81b60c415d9ca261a380264f9fdc5f99734563cabc684e2be71b23d52487251d"},"schema_version":"1.0"},"canonical_sha256":"19362648f3bcaceb3ec1b568df2df4bbd0349b2a52a4a3113b9cf00666b5da64","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:24.019428Z","signature_b64":"3zZONklOxa71Pj6gDHH80vut4B+zwBOhmJcfG9BuhaMJobTvthTtsDnMTYoPSJKjtEupXgdgMRa26Ofu0c+sCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19362648f3bcaceb3ec1b568df2df4bbd0349b2a52a4a3113b9cf00666b5da64","last_reissued_at":"2026-05-18T03:19:24.018671Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:24.018671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.5331","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:19:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DVAVAARDp54abICi7IV5ovQD/4dbZzA/eAYaYpMdrPN8+RWcPR+uhMrAe3180yGdMjZ3NlTTyLL+IfmYKnYBAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:06:28.907883Z"},"content_sha256":"ced28057c62ec6451e0fa989db94780d509b2b4d35e15e602e5144f1c9b96c2a","schema_version":"1.0","event_id":"sha256:ced28057c62ec6451e0fa989db94780d509b2b4d35e15e602e5144f1c9b96c2a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DE3CMSHTXSWOWPWBWVUN6LPUXP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coarse topological transitivity on open cones and coarsely J-class and D-class operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Antonios Manoussos","submitted_at":"2013-06-22T15:48:55Z","abstract_excerpt":"We generalize the concept of coarse hypercyclicity, introduced by Feldman in \\cite{Fe1}, to that of coarse topological transitivity on open cones. We show that a bounded linear operator acting on an infinite dimensional Banach space with a coarsely dense orbit on an open cone is hypercyclic and a coarsely topologically transitive (mixing) operator on an open cone is topologically transitive (mixing resp.). We also \"localize\" these concepts by introducing two new classes of operators called coarsely $J$-class and coarsely $D$-class operators and we establish some results that may make these cla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5331","kind":"arxiv","version":2},"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":"2026-05-18T03:19:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OifjuNbj3WdSXSD1UNiOkZR+GLP14q7ULIO5FIPRMo+WBEZmtIDuP0qNp4q+iyDr0l0RgOW2ggWzyOdleVJsBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:06:28.908230Z"},"content_sha256":"4eb477c28e6622e05d4b6bbc72910e50e8a423d0e544b9ce4a22e53d92ec1316","schema_version":"1.0","event_id":"sha256:4eb477c28e6622e05d4b6bbc72910e50e8a423d0e544b9ce4a22e53d92ec1316"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DE3CMSHTXSWOWPWBWVUN6LPUXP/bundle.json","state_url":"https://pith.science/pith/DE3CMSHTXSWOWPWBWVUN6LPUXP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DE3CMSHTXSWOWPWBWVUN6LPUXP/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":"2026-06-03T20:06:28Z","links":{"resolver":"https://pith.science/pith/DE3CMSHTXSWOWPWBWVUN6LPUXP","bundle":"https://pith.science/pith/DE3CMSHTXSWOWPWBWVUN6LPUXP/bundle.json","state":"https://pith.science/pith/DE3CMSHTXSWOWPWBWVUN6LPUXP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DE3CMSHTXSWOWPWBWVUN6LPUXP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DE3CMSHTXSWOWPWBWVUN6LPUXP","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":"81b60c415d9ca261a380264f9fdc5f99734563cabc684e2be71b23d52487251d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-22T15:48:55Z","title_canon_sha256":"b6c9d6a1ff0d08af5e8495ca98592a563348f962a784f031afee8617c149edf5"},"schema_version":"1.0","source":{"id":"1306.5331","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5331","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5331v2","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5331","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"pith_short_12","alias_value":"DE3CMSHTXSWO","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DE3CMSHTXSWOWPWB","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DE3CMSHT","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:4eb477c28e6622e05d4b6bbc72910e50e8a423d0e544b9ce4a22e53d92ec1316","target":"graph","created_at":"2026-05-18T03:19:24Z","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":"We generalize the concept of coarse hypercyclicity, introduced by Feldman in \\cite{Fe1}, to that of coarse topological transitivity on open cones. We show that a bounded linear operator acting on an infinite dimensional Banach space with a coarsely dense orbit on an open cone is hypercyclic and a coarsely topologically transitive (mixing) operator on an open cone is topologically transitive (mixing resp.). We also \"localize\" these concepts by introducing two new classes of operators called coarsely $J$-class and coarsely $D$-class operators and we establish some results that may make these cla","authors_text":"Antonios Manoussos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-22T15:48:55Z","title":"Coarse topological transitivity on open cones and coarsely J-class and D-class operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5331","kind":"arxiv","version":2},"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:ced28057c62ec6451e0fa989db94780d509b2b4d35e15e602e5144f1c9b96c2a","target":"record","created_at":"2026-05-18T03:19:24Z","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":"81b60c415d9ca261a380264f9fdc5f99734563cabc684e2be71b23d52487251d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-22T15:48:55Z","title_canon_sha256":"b6c9d6a1ff0d08af5e8495ca98592a563348f962a784f031afee8617c149edf5"},"schema_version":"1.0","source":{"id":"1306.5331","kind":"arxiv","version":2}},"canonical_sha256":"19362648f3bcaceb3ec1b568df2df4bbd0349b2a52a4a3113b9cf00666b5da64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19362648f3bcaceb3ec1b568df2df4bbd0349b2a52a4a3113b9cf00666b5da64","first_computed_at":"2026-05-18T03:19:24.018671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:24.018671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3zZONklOxa71Pj6gDHH80vut4B+zwBOhmJcfG9BuhaMJobTvthTtsDnMTYoPSJKjtEupXgdgMRa26Ofu0c+sCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:24.019428Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.5331","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ced28057c62ec6451e0fa989db94780d509b2b4d35e15e602e5144f1c9b96c2a","sha256:4eb477c28e6622e05d4b6bbc72910e50e8a423d0e544b9ce4a22e53d92ec1316"],"state_sha256":"0f0930d5efdeed23f161d0d73a20c04540c3c2a504e43732af58df80afa5e33b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dPVwd+9umtqL9S38jwGTSI5PksOLeU3MpV1kiSTacB0vztO96CaF0Rww3mi0v85rlc9TRZml+idqYYzm7gszAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T20:06:28.910162Z","bundle_sha256":"175ef05e1cd0ce229cc993cc8a7c6a7bf5cee0251f3f793115dc180a58b5523e"}}