{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:BV2IDITOCUXHN2DU73EXY2KFSJ","short_pith_number":"pith:BV2IDITO","canonical_record":{"source":{"id":"1902.04330","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-02-12T11:10:07Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"db15f442c1652f6cf200c0b9d4785c4fdc51f3f460af8dc7f69597531b1b8631","abstract_canon_sha256":"dd02d9b87772632a4d779de5af37fbf6e33ad9575c3819b2c12c6ff11ec58e8c"},"schema_version":"1.0"},"canonical_sha256":"0d7481a26e152e76e874fec97c6945925ee7fc6a94b183537a5da0ee35b422a9","source":{"kind":"arxiv","id":"1902.04330","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.04330","created_at":"2026-05-17T23:54:12Z"},{"alias_kind":"arxiv_version","alias_value":"1902.04330v1","created_at":"2026-05-17T23:54:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.04330","created_at":"2026-05-17T23:54:12Z"},{"alias_kind":"pith_short_12","alias_value":"BV2IDITOCUXH","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"BV2IDITOCUXHN2DU","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"BV2IDITO","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:BV2IDITOCUXHN2DU73EXY2KFSJ","target":"record","payload":{"canonical_record":{"source":{"id":"1902.04330","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-02-12T11:10:07Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"db15f442c1652f6cf200c0b9d4785c4fdc51f3f460af8dc7f69597531b1b8631","abstract_canon_sha256":"dd02d9b87772632a4d779de5af37fbf6e33ad9575c3819b2c12c6ff11ec58e8c"},"schema_version":"1.0"},"canonical_sha256":"0d7481a26e152e76e874fec97c6945925ee7fc6a94b183537a5da0ee35b422a9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:12.552117Z","signature_b64":"CzIDBKdi/p/1PEakxJgIRJsQF+ubfn1q7IRZXzc2XjWJ2nDwuCEBoae1LFNvdQvI/HavZskuWP752458M428AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d7481a26e152e76e874fec97c6945925ee7fc6a94b183537a5da0ee35b422a9","last_reissued_at":"2026-05-17T23:54:12.551511Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:12.551511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.04330","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":"2026-05-17T23:54:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fZ+uWE/xIEOJJrVtRvizFww3DI17xhXrn5Fg8537nj5aFcVMTSiiv4cROcqhlmG/XEFtR2zovCGLpvwuGwOgAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:19:06.971253Z"},"content_sha256":"867bcb4782b6edad25eaf4032a8333c4d9f16abe13a4a69dce1144621372e44a","schema_version":"1.0","event_id":"sha256:867bcb4782b6edad25eaf4032a8333c4d9f16abe13a4a69dce1144621372e44a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:BV2IDITOCUXHN2DU73EXY2KFSJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Identifying logarithmic tracts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"James Waterman","submitted_at":"2019-02-12T11:10:07Z","abstract_excerpt":"We show that a direct tract bounded by a simple curve is a logarithmic tract and further give sufficient conditions for a direct tract to contain logarithmic tracts. As an application of these results, an example of a function with infinitely many direct singularities, but no logarithmic singularity over any finite value, is shown to be in the Eremenko-Lyubich class."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.04330","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":"2026-05-17T23:54:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KQvlfBsOywFqO/sL9CmBE7R6QBqwalY2IlaaEBivCHjUl3CinAvhaJpRdry5H/wwjXa2FdMLA1uUlCp3yglTAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:19:06.971625Z"},"content_sha256":"1f3a0247b43375f520d04daf8b03fa6633e61a627e111d8776ebce34c28ebe27","schema_version":"1.0","event_id":"sha256:1f3a0247b43375f520d04daf8b03fa6633e61a627e111d8776ebce34c28ebe27"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BV2IDITOCUXHN2DU73EXY2KFSJ/bundle.json","state_url":"https://pith.science/pith/BV2IDITOCUXHN2DU73EXY2KFSJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BV2IDITOCUXHN2DU73EXY2KFSJ/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":"2026-06-01T23:19:06Z","links":{"resolver":"https://pith.science/pith/BV2IDITOCUXHN2DU73EXY2KFSJ","bundle":"https://pith.science/pith/BV2IDITOCUXHN2DU73EXY2KFSJ/bundle.json","state":"https://pith.science/pith/BV2IDITOCUXHN2DU73EXY2KFSJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BV2IDITOCUXHN2DU73EXY2KFSJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:BV2IDITOCUXHN2DU73EXY2KFSJ","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":"dd02d9b87772632a4d779de5af37fbf6e33ad9575c3819b2c12c6ff11ec58e8c","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-02-12T11:10:07Z","title_canon_sha256":"db15f442c1652f6cf200c0b9d4785c4fdc51f3f460af8dc7f69597531b1b8631"},"schema_version":"1.0","source":{"id":"1902.04330","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.04330","created_at":"2026-05-17T23:54:12Z"},{"alias_kind":"arxiv_version","alias_value":"1902.04330v1","created_at":"2026-05-17T23:54:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.04330","created_at":"2026-05-17T23:54:12Z"},{"alias_kind":"pith_short_12","alias_value":"BV2IDITOCUXH","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"BV2IDITOCUXHN2DU","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"BV2IDITO","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:1f3a0247b43375f520d04daf8b03fa6633e61a627e111d8776ebce34c28ebe27","target":"graph","created_at":"2026-05-17T23:54:12Z","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 show that a direct tract bounded by a simple curve is a logarithmic tract and further give sufficient conditions for a direct tract to contain logarithmic tracts. As an application of these results, an example of a function with infinitely many direct singularities, but no logarithmic singularity over any finite value, is shown to be in the Eremenko-Lyubich class.","authors_text":"James Waterman","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-02-12T11:10:07Z","title":"Identifying logarithmic tracts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.04330","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":"sha256:867bcb4782b6edad25eaf4032a8333c4d9f16abe13a4a69dce1144621372e44a","target":"record","created_at":"2026-05-17T23:54:12Z","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":"dd02d9b87772632a4d779de5af37fbf6e33ad9575c3819b2c12c6ff11ec58e8c","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-02-12T11:10:07Z","title_canon_sha256":"db15f442c1652f6cf200c0b9d4785c4fdc51f3f460af8dc7f69597531b1b8631"},"schema_version":"1.0","source":{"id":"1902.04330","kind":"arxiv","version":1}},"canonical_sha256":"0d7481a26e152e76e874fec97c6945925ee7fc6a94b183537a5da0ee35b422a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d7481a26e152e76e874fec97c6945925ee7fc6a94b183537a5da0ee35b422a9","first_computed_at":"2026-05-17T23:54:12.551511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:12.551511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CzIDBKdi/p/1PEakxJgIRJsQF+ubfn1q7IRZXzc2XjWJ2nDwuCEBoae1LFNvdQvI/HavZskuWP752458M428AQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:12.552117Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.04330","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:867bcb4782b6edad25eaf4032a8333c4d9f16abe13a4a69dce1144621372e44a","sha256:1f3a0247b43375f520d04daf8b03fa6633e61a627e111d8776ebce34c28ebe27"],"state_sha256":"609551a4fd7380907ef8a0691f98af6dab57147e7f878ff20a9eabde17626820"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jN0dWENeno5xXMHbzxXmzkp0qUUVGpuFasv34nsSff+V9ciWa1kz+nzBUcOJHosJWjePVrJDR7UOeS/jn5L8AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T23:19:06.973593Z","bundle_sha256":"e7f460d764d5ad676c859dcfa7e64d9986221c747a7e5dc975593e29662a7f87"}}