{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CCCHGKTURATDOJGBM4PMFYX3GJ","short_pith_number":"pith:CCCHGKTU","canonical_record":{"source":{"id":"1612.09364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-30T01:23:52Z","cross_cats_sorted":[],"title_canon_sha256":"4556b9ef5fcb22adcdf67098ae3b2a3654128b08dcedafa37438b43644314091","abstract_canon_sha256":"efb36b7243c96af0fb5249225b13ddd83b19d2d3ecfa373d7270ddc208114972"},"schema_version":"1.0"},"canonical_sha256":"1084732a7488263724c1671ec2e2fb327166a61abb52dc38b7ad3c62188036b5","source":{"kind":"arxiv","id":"1612.09364","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09364","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09364v1","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09364","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"pith_short_12","alias_value":"CCCHGKTURATD","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CCCHGKTURATDOJGB","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CCCHGKTU","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CCCHGKTURATDOJGBM4PMFYX3GJ","target":"record","payload":{"canonical_record":{"source":{"id":"1612.09364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-30T01:23:52Z","cross_cats_sorted":[],"title_canon_sha256":"4556b9ef5fcb22adcdf67098ae3b2a3654128b08dcedafa37438b43644314091","abstract_canon_sha256":"efb36b7243c96af0fb5249225b13ddd83b19d2d3ecfa373d7270ddc208114972"},"schema_version":"1.0"},"canonical_sha256":"1084732a7488263724c1671ec2e2fb327166a61abb52dc38b7ad3c62188036b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:41.700299Z","signature_b64":"JXnzMNPeqPnnSMdlh95KdV3ku+kPxiKj65k3LzdkV3vZUzmKwyYDJkuE/5l4FMSG7TcuNcEGDH5JzmWvjMk+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1084732a7488263724c1671ec2e2fb327166a61abb52dc38b7ad3c62188036b5","last_reissued_at":"2026-05-18T00:53:41.699932Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:41.699932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.09364","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":"2026-05-18T00:53:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qCs1kq3tDqrA4FleGPqSTxYIp8L+sQ3MOxH833Th8ewaudXfl9QNMDCNXgvDQ1CwLWg5nThm7LMOQq6NeHO9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:27:27.780825Z"},"content_sha256":"375be663a163623215767e446fc03fdcf2b0dfbee5db6c680f2d39161d0e7a59","schema_version":"1.0","event_id":"sha256:375be663a163623215767e446fc03fdcf2b0dfbee5db6c680f2d39161d0e7a59"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CCCHGKTURATDOJGBM4PMFYX3GJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Slow entropy for some smooth flows on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Adam Kanigowski","submitted_at":"2016-12-30T01:23:52Z","abstract_excerpt":"We study slow entropy in some classes of smooth mixing flows on surfaces. The flows we study can be represented as special flows over irrational rotations and under roof functions which are $C^2$ everywhere except one point (singularity). If the singularity is logarithmic asymmetric (Arnol'd flows) we show that in the scale $a_n(t)=n(logn)^t$ slow entropy equals 1 (the speed of orbit growth is nlogn) for a.e. irrational $\\alpha$. If the singularity is of power type ($x^{-\\gamma}$, $\\gamma\\in (0,1)$) (Kochergin flows) we show that in the scale $a_n(t)=n^t$ slow entropy equals $1+\\gamma$ for a.e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09364","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":"2026-05-18T00:53:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yghrt4lI6DaxjbWGJ315DpDsGAN2pq4Nl9xBqgahJ2LzgGDPOIu2DqoC8EyTxZsU8iAkVSySqcL2/KUY/fCqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:27:27.781171Z"},"content_sha256":"547574778854f49d9d80a163284ce6796eccf042477956af4e0c679791f607d9","schema_version":"1.0","event_id":"sha256:547574778854f49d9d80a163284ce6796eccf042477956af4e0c679791f607d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CCCHGKTURATDOJGBM4PMFYX3GJ/bundle.json","state_url":"https://pith.science/pith/CCCHGKTURATDOJGBM4PMFYX3GJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CCCHGKTURATDOJGBM4PMFYX3GJ/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":"2026-06-23T12:27:27Z","links":{"resolver":"https://pith.science/pith/CCCHGKTURATDOJGBM4PMFYX3GJ","bundle":"https://pith.science/pith/CCCHGKTURATDOJGBM4PMFYX3GJ/bundle.json","state":"https://pith.science/pith/CCCHGKTURATDOJGBM4PMFYX3GJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CCCHGKTURATDOJGBM4PMFYX3GJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CCCHGKTURATDOJGBM4PMFYX3GJ","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":"efb36b7243c96af0fb5249225b13ddd83b19d2d3ecfa373d7270ddc208114972","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-30T01:23:52Z","title_canon_sha256":"4556b9ef5fcb22adcdf67098ae3b2a3654128b08dcedafa37438b43644314091"},"schema_version":"1.0","source":{"id":"1612.09364","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09364","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09364v1","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09364","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"pith_short_12","alias_value":"CCCHGKTURATD","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CCCHGKTURATDOJGB","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CCCHGKTU","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:547574778854f49d9d80a163284ce6796eccf042477956af4e0c679791f607d9","target":"graph","created_at":"2026-05-18T00:53:41Z","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 study slow entropy in some classes of smooth mixing flows on surfaces. The flows we study can be represented as special flows over irrational rotations and under roof functions which are $C^2$ everywhere except one point (singularity). If the singularity is logarithmic asymmetric (Arnol'd flows) we show that in the scale $a_n(t)=n(logn)^t$ slow entropy equals 1 (the speed of orbit growth is nlogn) for a.e. irrational $\\alpha$. If the singularity is of power type ($x^{-\\gamma}$, $\\gamma\\in (0,1)$) (Kochergin flows) we show that in the scale $a_n(t)=n^t$ slow entropy equals $1+\\gamma$ for a.e","authors_text":"Adam Kanigowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-30T01:23:52Z","title":"Slow entropy for some smooth flows on surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09364","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":"sha256:375be663a163623215767e446fc03fdcf2b0dfbee5db6c680f2d39161d0e7a59","target":"record","created_at":"2026-05-18T00:53:41Z","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":"efb36b7243c96af0fb5249225b13ddd83b19d2d3ecfa373d7270ddc208114972","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-30T01:23:52Z","title_canon_sha256":"4556b9ef5fcb22adcdf67098ae3b2a3654128b08dcedafa37438b43644314091"},"schema_version":"1.0","source":{"id":"1612.09364","kind":"arxiv","version":1}},"canonical_sha256":"1084732a7488263724c1671ec2e2fb327166a61abb52dc38b7ad3c62188036b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1084732a7488263724c1671ec2e2fb327166a61abb52dc38b7ad3c62188036b5","first_computed_at":"2026-05-18T00:53:41.699932Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:41.699932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JXnzMNPeqPnnSMdlh95KdV3ku+kPxiKj65k3LzdkV3vZUzmKwyYDJkuE/5l4FMSG7TcuNcEGDH5JzmWvjMk+CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:41.700299Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.09364","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:375be663a163623215767e446fc03fdcf2b0dfbee5db6c680f2d39161d0e7a59","sha256:547574778854f49d9d80a163284ce6796eccf042477956af4e0c679791f607d9"],"state_sha256":"958b9ea05baf1094ffc34d6081877c81bb59a3ccd2b45731b982ed9d8a0d907f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bNnlFBCOWgHEH9PQ9q2cMa4py1xTVJrfc93UfARQVLJmUtTHF6MjW/MCUxdrOesvg46voiBsdPCR1DSxc9SBCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T12:27:27.783118Z","bundle_sha256":"9a800cfb75e466bf19ad53f5a38b8d4a883c0c40576fc351d3889be630fec5bf"}}