{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:NSRWI4PEENSRM2ZWAJOBTCURXP","short_pith_number":"pith:NSRWI4PE","canonical_record":{"source":{"id":"1902.03474","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-09T19:06:01Z","cross_cats_sorted":[],"title_canon_sha256":"82e79953d48b9662090c249dddc4b998a273458f9d8b5a7debfa93f62ba8a20f","abstract_canon_sha256":"3a5575d6f0cbee997d54d87fe65e136d764118b0ee98470effb0080cbdd37a48"},"schema_version":"1.0"},"canonical_sha256":"6ca36471e42365166b36025c198a91bbc4994a907f0860675973517a6c22fb46","source":{"kind":"arxiv","id":"1902.03474","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03474","created_at":"2026-05-17T23:45:52Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03474v7","created_at":"2026-05-17T23:45:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03474","created_at":"2026-05-17T23:45:52Z"},{"alias_kind":"pith_short_12","alias_value":"NSRWI4PEENSR","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NSRWI4PEENSRM2ZW","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NSRWI4PE","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:NSRWI4PEENSRM2ZWAJOBTCURXP","target":"record","payload":{"canonical_record":{"source":{"id":"1902.03474","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-09T19:06:01Z","cross_cats_sorted":[],"title_canon_sha256":"82e79953d48b9662090c249dddc4b998a273458f9d8b5a7debfa93f62ba8a20f","abstract_canon_sha256":"3a5575d6f0cbee997d54d87fe65e136d764118b0ee98470effb0080cbdd37a48"},"schema_version":"1.0"},"canonical_sha256":"6ca36471e42365166b36025c198a91bbc4994a907f0860675973517a6c22fb46","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:52.081514Z","signature_b64":"hQpU7c8weAUawDwCmqUYLThoGVPaYoeu5z6jtA0VSq9SNW2Fn1ylHTvis0+eHo/DVmIpQwbd2ZrlrsLZmnG0DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ca36471e42365166b36025c198a91bbc4994a907f0860675973517a6c22fb46","last_reissued_at":"2026-05-17T23:45:52.081072Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:52.081072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.03474","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4l5r8SAZWvcV/+8ZhFztFyugeZvXHrTBPbwZsrbB7eVHc4mnUJJRhfGlT7pt16RciekbZTuMPUYhVm3JVcJGCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:10:17.078971Z"},"content_sha256":"f2b1140412b41f65281aebd749073ec27b4bd7d3c76a0a1d21f7d0aba3b9a528","schema_version":"1.0","event_id":"sha256:f2b1140412b41f65281aebd749073ec27b4bd7d3c76a0a1d21f7d0aba3b9a528"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:NSRWI4PEENSRM2ZWAJOBTCURXP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reiterative $m_{n}$-distributional chaos of type $s$ in Fr\\' echet spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Marko Kosti\\'c","submitted_at":"2019-02-09T19:06:01Z","abstract_excerpt":"The main aim of this paper is to consider various notions of (dense) $m_{n}$-distributional chaos of type $s$ and (dense) reiterative $m_{n}$-distributional chaos of type $s$ for general sequences of linear not necessarily continuous operators in Fr\\' echet spaces. Here, $(m_{n})$ is an increasing sequence in $[1,\\infty)$ satisfying $\\liminf_{n\\rightarrow \\infty}\\frac{m_{n}}{n}>0$ and $s$ could be $0,1,2,2+,2\\frac{1}{2},3,1+,2-,2_{Bd},2_{Bd}+.$ We investigate $m_{n}$-distributionally chaotic properties and reiteratively $m_{n}$-distributionally chaotic properties of some special classes of ope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03474","kind":"arxiv","version":7},"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":"2026-05-17T23:45:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0yfFXdNbvut9f1QroQAqts2QFN/Y6dNUtaby6zrsshdDHA99koINyqkuFsaDyRhZ0s9Whsx43g8+qCNcoeaTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:10:17.079330Z"},"content_sha256":"07b11128124f36a788279cfea79a4c07758257e475a6c291457971f5b023bc2c","schema_version":"1.0","event_id":"sha256:07b11128124f36a788279cfea79a4c07758257e475a6c291457971f5b023bc2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NSRWI4PEENSRM2ZWAJOBTCURXP/bundle.json","state_url":"https://pith.science/pith/NSRWI4PEENSRM2ZWAJOBTCURXP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NSRWI4PEENSRM2ZWAJOBTCURXP/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":"2026-06-22T20:10:17Z","links":{"resolver":"https://pith.science/pith/NSRWI4PEENSRM2ZWAJOBTCURXP","bundle":"https://pith.science/pith/NSRWI4PEENSRM2ZWAJOBTCURXP/bundle.json","state":"https://pith.science/pith/NSRWI4PEENSRM2ZWAJOBTCURXP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NSRWI4PEENSRM2ZWAJOBTCURXP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NSRWI4PEENSRM2ZWAJOBTCURXP","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":"3a5575d6f0cbee997d54d87fe65e136d764118b0ee98470effb0080cbdd37a48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-09T19:06:01Z","title_canon_sha256":"82e79953d48b9662090c249dddc4b998a273458f9d8b5a7debfa93f62ba8a20f"},"schema_version":"1.0","source":{"id":"1902.03474","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03474","created_at":"2026-05-17T23:45:52Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03474v7","created_at":"2026-05-17T23:45:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03474","created_at":"2026-05-17T23:45:52Z"},{"alias_kind":"pith_short_12","alias_value":"NSRWI4PEENSR","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NSRWI4PEENSRM2ZW","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NSRWI4PE","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:07b11128124f36a788279cfea79a4c07758257e475a6c291457971f5b023bc2c","target":"graph","created_at":"2026-05-17T23:45:52Z","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 main aim of this paper is to consider various notions of (dense) $m_{n}$-distributional chaos of type $s$ and (dense) reiterative $m_{n}$-distributional chaos of type $s$ for general sequences of linear not necessarily continuous operators in Fr\\' echet spaces. Here, $(m_{n})$ is an increasing sequence in $[1,\\infty)$ satisfying $\\liminf_{n\\rightarrow \\infty}\\frac{m_{n}}{n}>0$ and $s$ could be $0,1,2,2+,2\\frac{1}{2},3,1+,2-,2_{Bd},2_{Bd}+.$ We investigate $m_{n}$-distributionally chaotic properties and reiteratively $m_{n}$-distributionally chaotic properties of some special classes of ope","authors_text":"Marko Kosti\\'c","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-09T19:06:01Z","title":"Reiterative $m_{n}$-distributional chaos of type $s$ in Fr\\' echet spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03474","kind":"arxiv","version":7},"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:f2b1140412b41f65281aebd749073ec27b4bd7d3c76a0a1d21f7d0aba3b9a528","target":"record","created_at":"2026-05-17T23:45:52Z","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":"3a5575d6f0cbee997d54d87fe65e136d764118b0ee98470effb0080cbdd37a48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-09T19:06:01Z","title_canon_sha256":"82e79953d48b9662090c249dddc4b998a273458f9d8b5a7debfa93f62ba8a20f"},"schema_version":"1.0","source":{"id":"1902.03474","kind":"arxiv","version":7}},"canonical_sha256":"6ca36471e42365166b36025c198a91bbc4994a907f0860675973517a6c22fb46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ca36471e42365166b36025c198a91bbc4994a907f0860675973517a6c22fb46","first_computed_at":"2026-05-17T23:45:52.081072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:52.081072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hQpU7c8weAUawDwCmqUYLThoGVPaYoeu5z6jtA0VSq9SNW2Fn1ylHTvis0+eHo/DVmIpQwbd2ZrlrsLZmnG0DQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:52.081514Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.03474","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2b1140412b41f65281aebd749073ec27b4bd7d3c76a0a1d21f7d0aba3b9a528","sha256:07b11128124f36a788279cfea79a4c07758257e475a6c291457971f5b023bc2c"],"state_sha256":"463f86fc5531fe457ea32314d60bdd72f525a92bba121ddfff44e1642590b5d0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8FzG8bkP6bcDNecrT67EDyitYr6Jrzuz0rbsoNq1kEdCL0a8F5jYGUMaBdgAeP83yXvkGT6sN8Y+WbODnizRAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T20:10:17.081347Z","bundle_sha256":"4689b43cb70ce489516c2c22dfa362a9ee5f3670e92ac80664d29b90087d5bee"}}