{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:DYT5SHZHOHNAM6F32KTROLSYJ6","short_pith_number":"pith:DYT5SHZH","canonical_record":{"source":{"id":"1703.05888","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-17T04:42:25Z","cross_cats_sorted":[],"title_canon_sha256":"d6d9a26cd92c329ab0d9e00f02af6b733885b0f1ad005fa82c833b09264ac579","abstract_canon_sha256":"03dd8ed9e4b4b372cce9ca38d1fc42fe27e85cec0dfae5a5c05f7a6c156bc841"},"schema_version":"1.0"},"canonical_sha256":"1e27d91f2771da0678bbd2a7172e584f853369bfd36bd1ac63597a07722fa519","source":{"kind":"arxiv","id":"1703.05888","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05888","created_at":"2026-05-18T00:48:31Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05888v1","created_at":"2026-05-18T00:48:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05888","created_at":"2026-05-18T00:48:31Z"},{"alias_kind":"pith_short_12","alias_value":"DYT5SHZHOHNA","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DYT5SHZHOHNAM6F3","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DYT5SHZH","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:DYT5SHZHOHNAM6F32KTROLSYJ6","target":"record","payload":{"canonical_record":{"source":{"id":"1703.05888","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-17T04:42:25Z","cross_cats_sorted":[],"title_canon_sha256":"d6d9a26cd92c329ab0d9e00f02af6b733885b0f1ad005fa82c833b09264ac579","abstract_canon_sha256":"03dd8ed9e4b4b372cce9ca38d1fc42fe27e85cec0dfae5a5c05f7a6c156bc841"},"schema_version":"1.0"},"canonical_sha256":"1e27d91f2771da0678bbd2a7172e584f853369bfd36bd1ac63597a07722fa519","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:31.861020Z","signature_b64":"MHZqU0C3/5Rpen1MhrOQTCTUZ3QQyWHCLzIg1QGUWw1xF/LhWR/87hNZsG7FW8/aABMOQfyQ9JoaZXQPrqkxBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e27d91f2771da0678bbd2a7172e584f853369bfd36bd1ac63597a07722fa519","last_reissued_at":"2026-05-18T00:48:31.860027Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:31.860027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.05888","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":"2026-05-18T00:48:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gdfbihZrqmo+tgRkhs9P8+4OKFtZUcWcDDg8W1BAZXqo0SRTFOR4wdjmqQuV4hbk45yYGdYQpLdZ9q9FZv27DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:34:23.096376Z"},"content_sha256":"763a7165454aaa752114120032d9be663b84b1616ae6e24f22e9a21fcc3bbf42","schema_version":"1.0","event_id":"sha256:763a7165454aaa752114120032d9be663b84b1616ae6e24f22e9a21fcc3bbf42"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:DYT5SHZHOHNAM6F32KTROLSYJ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological entropy and IE-tuples of indecomposable continua","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hisao Kato","submitted_at":"2017-03-17T04:42:25Z","abstract_excerpt":"In this paper, we define a new notion of \"freely tracing property by free chains\" on $G$-like continua and we prove that a positive topological entropy homeomorphism on a $G$-like continuum admits a Cantor set $Z$ such that every tuple of finite points in $Z$ is an $IE$-tuple of $f$ and $Z$ has the freely tracing property by free chains. Also, by use of this notion, we prove the following theorem: If $G$ is any graph and a homeomorphism $f$ on a $G$-like continuum $X$ has positive topological entropy, then there is a Cantor set $Z$ which is related to both the chaotic behaviors of Kerr and Li "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05888","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":"2026-05-18T00:48:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ftTJ3krup6074D5FZ+WoD5W1HI8gPE6vjXUyXbq4h/t3gM3Lg0mJHCrQaT3a7lyoYl19V6fWbZnrHddzgiztAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:34:23.097162Z"},"content_sha256":"aef8d8ed7021fcbd65fd0f769aea0e960df57393a961b1f7fd1a049dbdc77f25","schema_version":"1.0","event_id":"sha256:aef8d8ed7021fcbd65fd0f769aea0e960df57393a961b1f7fd1a049dbdc77f25"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DYT5SHZHOHNAM6F32KTROLSYJ6/bundle.json","state_url":"https://pith.science/pith/DYT5SHZHOHNAM6F32KTROLSYJ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DYT5SHZHOHNAM6F32KTROLSYJ6/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":"2026-06-06T18:34:23Z","links":{"resolver":"https://pith.science/pith/DYT5SHZHOHNAM6F32KTROLSYJ6","bundle":"https://pith.science/pith/DYT5SHZHOHNAM6F32KTROLSYJ6/bundle.json","state":"https://pith.science/pith/DYT5SHZHOHNAM6F32KTROLSYJ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DYT5SHZHOHNAM6F32KTROLSYJ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DYT5SHZHOHNAM6F32KTROLSYJ6","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":"03dd8ed9e4b4b372cce9ca38d1fc42fe27e85cec0dfae5a5c05f7a6c156bc841","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-17T04:42:25Z","title_canon_sha256":"d6d9a26cd92c329ab0d9e00f02af6b733885b0f1ad005fa82c833b09264ac579"},"schema_version":"1.0","source":{"id":"1703.05888","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05888","created_at":"2026-05-18T00:48:31Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05888v1","created_at":"2026-05-18T00:48:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05888","created_at":"2026-05-18T00:48:31Z"},{"alias_kind":"pith_short_12","alias_value":"DYT5SHZHOHNA","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DYT5SHZHOHNAM6F3","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DYT5SHZH","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:aef8d8ed7021fcbd65fd0f769aea0e960df57393a961b1f7fd1a049dbdc77f25","target":"graph","created_at":"2026-05-18T00:48:31Z","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":"In this paper, we define a new notion of \"freely tracing property by free chains\" on $G$-like continua and we prove that a positive topological entropy homeomorphism on a $G$-like continuum admits a Cantor set $Z$ such that every tuple of finite points in $Z$ is an $IE$-tuple of $f$ and $Z$ has the freely tracing property by free chains. Also, by use of this notion, we prove the following theorem: If $G$ is any graph and a homeomorphism $f$ on a $G$-like continuum $X$ has positive topological entropy, then there is a Cantor set $Z$ which is related to both the chaotic behaviors of Kerr and Li ","authors_text":"Hisao Kato","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-17T04:42:25Z","title":"Topological entropy and IE-tuples of indecomposable continua"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05888","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":"sha256:763a7165454aaa752114120032d9be663b84b1616ae6e24f22e9a21fcc3bbf42","target":"record","created_at":"2026-05-18T00:48:31Z","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":"03dd8ed9e4b4b372cce9ca38d1fc42fe27e85cec0dfae5a5c05f7a6c156bc841","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-17T04:42:25Z","title_canon_sha256":"d6d9a26cd92c329ab0d9e00f02af6b733885b0f1ad005fa82c833b09264ac579"},"schema_version":"1.0","source":{"id":"1703.05888","kind":"arxiv","version":1}},"canonical_sha256":"1e27d91f2771da0678bbd2a7172e584f853369bfd36bd1ac63597a07722fa519","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e27d91f2771da0678bbd2a7172e584f853369bfd36bd1ac63597a07722fa519","first_computed_at":"2026-05-18T00:48:31.860027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:31.860027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MHZqU0C3/5Rpen1MhrOQTCTUZ3QQyWHCLzIg1QGUWw1xF/LhWR/87hNZsG7FW8/aABMOQfyQ9JoaZXQPrqkxBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:31.861020Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.05888","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:763a7165454aaa752114120032d9be663b84b1616ae6e24f22e9a21fcc3bbf42","sha256:aef8d8ed7021fcbd65fd0f769aea0e960df57393a961b1f7fd1a049dbdc77f25"],"state_sha256":"9740212823ffea865bffbd58583dd13a37b8289726faa31d4ac3e1ccfc644aa3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RZlx03vmB0YpOGpfSbmvaOggdB+BGBwFSPjbvJyIkHAbHFnTc5oBaTgXYlSkmIPlmLBOmWNonDYHQv2kXbwZCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T18:34:23.101168Z","bundle_sha256":"81d3c8c9a552405ed2fa84d62e2aac8d767d37a7a3fa136754133ef85fc68a93"}}