{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PFHDPKOUTIR7RFEHMPFEJXUMDJ","short_pith_number":"pith:PFHDPKOU","canonical_record":{"source":{"id":"1609.07977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2016-09-26T14:14:35Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"58a053de9a78ae622c0356e22ac15fed4548712f5f20fa7c203ab2b9d642fa99","abstract_canon_sha256":"2c876c8ceaaf938b8056bdcb1397a76339ab0d4c7de56fb1b1a3dc826ce92f70"},"schema_version":"1.0"},"canonical_sha256":"794e37a9d49a23f8948763ca44de8c1a4d2c373307124ebebd44994fc7eb48c6","source":{"kind":"arxiv","id":"1609.07977","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07977","created_at":"2026-05-18T00:55:20Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07977v1","created_at":"2026-05-18T00:55:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07977","created_at":"2026-05-18T00:55:20Z"},{"alias_kind":"pith_short_12","alias_value":"PFHDPKOUTIR7","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PFHDPKOUTIR7RFEH","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PFHDPKOU","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PFHDPKOUTIR7RFEHMPFEJXUMDJ","target":"record","payload":{"canonical_record":{"source":{"id":"1609.07977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2016-09-26T14:14:35Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"58a053de9a78ae622c0356e22ac15fed4548712f5f20fa7c203ab2b9d642fa99","abstract_canon_sha256":"2c876c8ceaaf938b8056bdcb1397a76339ab0d4c7de56fb1b1a3dc826ce92f70"},"schema_version":"1.0"},"canonical_sha256":"794e37a9d49a23f8948763ca44de8c1a4d2c373307124ebebd44994fc7eb48c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:20.599914Z","signature_b64":"qknd8Tj3X+2zm1SMsAnyeGSD+L+TuUEUhIk940m6+hfPTD7NN63vnRapOkffBTMTWFwp4yH622HaCdLDbtI2DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"794e37a9d49a23f8948763ca44de8c1a4d2c373307124ebebd44994fc7eb48c6","last_reissued_at":"2026-05-18T00:55:20.599346Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:20.599346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.07977","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":"2026-05-18T00:55:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/cPpGREujgivbLADMKs5vMf5ErUZOKDcmNug2+RwBuXE/oZjT36jLn/Ya/1PFzLlW9UBEJw1W5F1/3wGyOxgDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:56:09.817008Z"},"content_sha256":"24ff3571c58e258805346340bd53e6b221c55eb3134b0514c0641bba54d912bd","schema_version":"1.0","event_id":"sha256:24ff3571c58e258805346340bd53e6b221c55eb3134b0514c0641bba54d912bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PFHDPKOUTIR7RFEHMPFEJXUMDJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"What is the mechanism of power-law distributed Poincar\\'e recurrences in higher-dimensional systems?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"nlin.CD","authors_text":"2), 2) ((1) Institut f\\\"ur Theoretische Physik, Arnd B\\\"acker (1, Center for Dynamics, Roland Ketzmerick (1, Steffen Lange (1), Technische Universit\\\"at Dresden (2) Max-Planck-Institut f\\\"ur Physik komplexer Systeme)","submitted_at":"2016-09-26T14:14:35Z","abstract_excerpt":"The statistics of Poincar\\'e recurrence times in Hamiltonian systems typically shows a power-law decay with chaotic trajectories sticking to some phase-space regions for long times. For higher-dimensional systems the mechanism of this power-law trapping is still unknown. We investigate trapped orbits of a generic 4D symplectic map in phase space and frequency space and find that, in contrast to 2D maps, the trapping is (i) not due to a hierarchy in phase space. Instead, it occurs at the surface of the regular region, (ii) outside of the Arnold web. The chaotic dynamics in this sticky region is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07977","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":"2026-05-18T00:55:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4H4BnXN3NwPhG7DhUYJhDTb2tyJxpsywiuO4fULggMcYzdtHuWSx096jsOGvmv36gYorLQ0g/UJk0JUPjPyABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:56:09.817372Z"},"content_sha256":"1c95d6661531a1b41599afe6216771b08a790223a74250b0ebfb20150b868f04","schema_version":"1.0","event_id":"sha256:1c95d6661531a1b41599afe6216771b08a790223a74250b0ebfb20150b868f04"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PFHDPKOUTIR7RFEHMPFEJXUMDJ/bundle.json","state_url":"https://pith.science/pith/PFHDPKOUTIR7RFEHMPFEJXUMDJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PFHDPKOUTIR7RFEHMPFEJXUMDJ/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":"2026-06-24T05:56:09Z","links":{"resolver":"https://pith.science/pith/PFHDPKOUTIR7RFEHMPFEJXUMDJ","bundle":"https://pith.science/pith/PFHDPKOUTIR7RFEHMPFEJXUMDJ/bundle.json","state":"https://pith.science/pith/PFHDPKOUTIR7RFEHMPFEJXUMDJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PFHDPKOUTIR7RFEHMPFEJXUMDJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PFHDPKOUTIR7RFEHMPFEJXUMDJ","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":"2c876c8ceaaf938b8056bdcb1397a76339ab0d4c7de56fb1b1a3dc826ce92f70","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2016-09-26T14:14:35Z","title_canon_sha256":"58a053de9a78ae622c0356e22ac15fed4548712f5f20fa7c203ab2b9d642fa99"},"schema_version":"1.0","source":{"id":"1609.07977","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07977","created_at":"2026-05-18T00:55:20Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07977v1","created_at":"2026-05-18T00:55:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07977","created_at":"2026-05-18T00:55:20Z"},{"alias_kind":"pith_short_12","alias_value":"PFHDPKOUTIR7","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PFHDPKOUTIR7RFEH","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PFHDPKOU","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:1c95d6661531a1b41599afe6216771b08a790223a74250b0ebfb20150b868f04","target":"graph","created_at":"2026-05-18T00:55:20Z","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 statistics of Poincar\\'e recurrence times in Hamiltonian systems typically shows a power-law decay with chaotic trajectories sticking to some phase-space regions for long times. For higher-dimensional systems the mechanism of this power-law trapping is still unknown. We investigate trapped orbits of a generic 4D symplectic map in phase space and frequency space and find that, in contrast to 2D maps, the trapping is (i) not due to a hierarchy in phase space. Instead, it occurs at the surface of the regular region, (ii) outside of the Arnold web. The chaotic dynamics in this sticky region is","authors_text":"2), 2) ((1) Institut f\\\"ur Theoretische Physik, Arnd B\\\"acker (1, Center for Dynamics, Roland Ketzmerick (1, Steffen Lange (1), Technische Universit\\\"at Dresden (2) Max-Planck-Institut f\\\"ur Physik komplexer Systeme)","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2016-09-26T14:14:35Z","title":"What is the mechanism of power-law distributed Poincar\\'e recurrences in higher-dimensional systems?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07977","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":"sha256:24ff3571c58e258805346340bd53e6b221c55eb3134b0514c0641bba54d912bd","target":"record","created_at":"2026-05-18T00:55:20Z","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":"2c876c8ceaaf938b8056bdcb1397a76339ab0d4c7de56fb1b1a3dc826ce92f70","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2016-09-26T14:14:35Z","title_canon_sha256":"58a053de9a78ae622c0356e22ac15fed4548712f5f20fa7c203ab2b9d642fa99"},"schema_version":"1.0","source":{"id":"1609.07977","kind":"arxiv","version":1}},"canonical_sha256":"794e37a9d49a23f8948763ca44de8c1a4d2c373307124ebebd44994fc7eb48c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"794e37a9d49a23f8948763ca44de8c1a4d2c373307124ebebd44994fc7eb48c6","first_computed_at":"2026-05-18T00:55:20.599346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:20.599346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qknd8Tj3X+2zm1SMsAnyeGSD+L+TuUEUhIk940m6+hfPTD7NN63vnRapOkffBTMTWFwp4yH622HaCdLDbtI2DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:20.599914Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.07977","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24ff3571c58e258805346340bd53e6b221c55eb3134b0514c0641bba54d912bd","sha256:1c95d6661531a1b41599afe6216771b08a790223a74250b0ebfb20150b868f04"],"state_sha256":"30d3993f4638dcabd8fb6ad250e8b48f71f059fcc12cda2ee950000ef87c495f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zg0miYhRGlcDl6sR6FtCqBRrStxg0FSaC6wTzKwgLl/c5R/Mnfb6D9aTCPqCGWrukjHkMbnz/rnZLotzYqNdCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T05:56:09.819293Z","bundle_sha256":"d70bdf28e43c069140e1eac31c4b2533d4d91a13a34ef3ce280a1c3355ded0ce"}}