{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:B6XQGELTSD6LWLRIVL32RLNTTB","short_pith_number":"pith:B6XQGELT","canonical_record":{"source":{"id":"2505.24657","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-05-30T14:46:12Z","cross_cats_sorted":[],"title_canon_sha256":"d593ec5bfa896312b677aff50e85cee47312fad6e367f14dc4042572060e630a","abstract_canon_sha256":"cf5b2ba43899f2fb89e07b6a3bb47f517823719db5b87c5f783f7670e45e1917"},"schema_version":"1.0"},"canonical_sha256":"0faf03117390fcbb2e28aaf7a8adb3985a0f4082f6577fd631f0bec629a936e8","source":{"kind":"arxiv","id":"2505.24657","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.24657","created_at":"2026-07-05T11:12:54Z"},{"alias_kind":"arxiv_version","alias_value":"2505.24657v1","created_at":"2026-07-05T11:12:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.24657","created_at":"2026-07-05T11:12:54Z"},{"alias_kind":"pith_short_12","alias_value":"B6XQGELTSD6L","created_at":"2026-07-05T11:12:54Z"},{"alias_kind":"pith_short_16","alias_value":"B6XQGELTSD6LWLRI","created_at":"2026-07-05T11:12:54Z"},{"alias_kind":"pith_short_8","alias_value":"B6XQGELT","created_at":"2026-07-05T11:12:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:B6XQGELTSD6LWLRIVL32RLNTTB","target":"record","payload":{"canonical_record":{"source":{"id":"2505.24657","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-05-30T14:46:12Z","cross_cats_sorted":[],"title_canon_sha256":"d593ec5bfa896312b677aff50e85cee47312fad6e367f14dc4042572060e630a","abstract_canon_sha256":"cf5b2ba43899f2fb89e07b6a3bb47f517823719db5b87c5f783f7670e45e1917"},"schema_version":"1.0"},"canonical_sha256":"0faf03117390fcbb2e28aaf7a8adb3985a0f4082f6577fd631f0bec629a936e8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:12:54.115140Z","signature_b64":"Y8o8vygQD+674rgVuCZOG24gTT2/+ev5AIe1yOLzMMIZ2dFVUtjSBT3631PW6sIBNKQs6NlL0knL5e+crCwkCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0faf03117390fcbb2e28aaf7a8adb3985a0f4082f6577fd631f0bec629a936e8","last_reissued_at":"2026-07-05T11:12:54.114609Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:12:54.114609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.24657","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":"2026-07-05T11:12:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HbTkZ4HTadUtmVALCCWh5RmY9ub7SQyrAW6Q14GCxQ7ByJ0qC9kHw3xvuhKgi+jHvrUXfFhb2+Iabi3fnxyaBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T17:42:39.419971Z"},"content_sha256":"c79ab79c73da3c1e7dd9c2c62ca8fe503cef23e699cc4cd8a791c91eb87170c2","schema_version":"1.0","event_id":"sha256:c79ab79c73da3c1e7dd9c2c62ca8fe503cef23e699cc4cd8a791c91eb87170c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:B6XQGELTSD6LWLRIVL32RLNTTB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on multi-transitivity in non-autonomous discrete systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hongbo Zeng","submitted_at":"2025-05-30T14:46:12Z","abstract_excerpt":"This paper is concerned with some stronger forms of transitivity in non-autonomous discrete systems$(f_{ 1,\\infty})$ generated by a uniformly convergent sequence of continuous self maps. Firstly, we present two counterexamples to show that Theorem 3.1 obtained by Salman and Das in [Multi-transitivity in nonautonomous discrete systems Topol. Appl. 278(2020)107237] is not true. Then, we introduce and study mildly mixing in non-autonomous discrete systems, which is stronger than mixing. We obtain that multi-transitivity implies Li-Yorke chaos and that mildly mixing implies multi-transitivity, whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24657","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.24657/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:12:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jk0QuZp9kY1nLmzKu35SJ2zqPJ9M/w0F51/PlA+1I/degZqPGwcS3wVZhojrrydxGaOA3z7EN0hrNDnwcVovAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T17:42:39.420457Z"},"content_sha256":"85ce0ebe08a3b3b2c402334698f3badd34b291cec414c1ce1fce79016b1e6454","schema_version":"1.0","event_id":"sha256:85ce0ebe08a3b3b2c402334698f3badd34b291cec414c1ce1fce79016b1e6454"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B6XQGELTSD6LWLRIVL32RLNTTB/bundle.json","state_url":"https://pith.science/pith/B6XQGELTSD6LWLRIVL32RLNTTB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B6XQGELTSD6LWLRIVL32RLNTTB/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":"2026-08-08T17:42:39Z","links":{"resolver":"https://pith.science/pith/B6XQGELTSD6LWLRIVL32RLNTTB","bundle":"https://pith.science/pith/B6XQGELTSD6LWLRIVL32RLNTTB/bundle.json","state":"https://pith.science/pith/B6XQGELTSD6LWLRIVL32RLNTTB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B6XQGELTSD6LWLRIVL32RLNTTB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:B6XQGELTSD6LWLRIVL32RLNTTB","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":"cf5b2ba43899f2fb89e07b6a3bb47f517823719db5b87c5f783f7670e45e1917","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-05-30T14:46:12Z","title_canon_sha256":"d593ec5bfa896312b677aff50e85cee47312fad6e367f14dc4042572060e630a"},"schema_version":"1.0","source":{"id":"2505.24657","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.24657","created_at":"2026-07-05T11:12:54Z"},{"alias_kind":"arxiv_version","alias_value":"2505.24657v1","created_at":"2026-07-05T11:12:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.24657","created_at":"2026-07-05T11:12:54Z"},{"alias_kind":"pith_short_12","alias_value":"B6XQGELTSD6L","created_at":"2026-07-05T11:12:54Z"},{"alias_kind":"pith_short_16","alias_value":"B6XQGELTSD6LWLRI","created_at":"2026-07-05T11:12:54Z"},{"alias_kind":"pith_short_8","alias_value":"B6XQGELT","created_at":"2026-07-05T11:12:54Z"}],"graph_snapshots":[{"event_id":"sha256:85ce0ebe08a3b3b2c402334698f3badd34b291cec414c1ce1fce79016b1e6454","target":"graph","created_at":"2026-07-05T11:12:54Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.24657/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is concerned with some stronger forms of transitivity in non-autonomous discrete systems$(f_{ 1,\\infty})$ generated by a uniformly convergent sequence of continuous self maps. Firstly, we present two counterexamples to show that Theorem 3.1 obtained by Salman and Das in [Multi-transitivity in nonautonomous discrete systems Topol. Appl. 278(2020)107237] is not true. Then, we introduce and study mildly mixing in non-autonomous discrete systems, which is stronger than mixing. We obtain that multi-transitivity implies Li-Yorke chaos and that mildly mixing implies multi-transitivity, whi","authors_text":"Hongbo Zeng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-05-30T14:46:12Z","title":"A note on multi-transitivity in non-autonomous discrete systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24657","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:c79ab79c73da3c1e7dd9c2c62ca8fe503cef23e699cc4cd8a791c91eb87170c2","target":"record","created_at":"2026-07-05T11:12:54Z","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":"cf5b2ba43899f2fb89e07b6a3bb47f517823719db5b87c5f783f7670e45e1917","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-05-30T14:46:12Z","title_canon_sha256":"d593ec5bfa896312b677aff50e85cee47312fad6e367f14dc4042572060e630a"},"schema_version":"1.0","source":{"id":"2505.24657","kind":"arxiv","version":1}},"canonical_sha256":"0faf03117390fcbb2e28aaf7a8adb3985a0f4082f6577fd631f0bec629a936e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0faf03117390fcbb2e28aaf7a8adb3985a0f4082f6577fd631f0bec629a936e8","first_computed_at":"2026-07-05T11:12:54.114609Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:12:54.114609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y8o8vygQD+674rgVuCZOG24gTT2/+ev5AIe1yOLzMMIZ2dFVUtjSBT3631PW6sIBNKQs6NlL0knL5e+crCwkCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:12:54.115140Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.24657","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c79ab79c73da3c1e7dd9c2c62ca8fe503cef23e699cc4cd8a791c91eb87170c2","sha256:85ce0ebe08a3b3b2c402334698f3badd34b291cec414c1ce1fce79016b1e6454"],"state_sha256":"3667ca31cb1d1933a2f525a456f5e1b0e4aaf29b4ce49fbd3cf2717b4cdd15b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uYJQ8rXQp4pz0EGzqAuk5ZmSIDhUWQ8JhazjBCbiCJduBOHH9bb4r8CgUxt68llSsRQWvzIIEbumye4qNeGZDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T17:42:39.424052Z","bundle_sha256":"51cd7c3e4a05cacdcf43a7c6da9135c8003de1fdff96aa4e12309a22a334c78d"}}