{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FXXSSUSLTOZ6MTHFGYSGWQ7RHB","short_pith_number":"pith:FXXSSUSL","canonical_record":{"source":{"id":"1510.07449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-26T11:59:36Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"58ed67079c62a7dc197631d33eccf32e2d028012db957e9f1cb47dadfaef0ac8","abstract_canon_sha256":"35c09c8e2845e961efe303f7fa9c38491f72149794d6e3c85da8e9fb15b1cb9d"},"schema_version":"1.0"},"canonical_sha256":"2def29524b9bb3e64ce536246b43f1387134072a0ecde90d73c8f3394143a868","source":{"kind":"arxiv","id":"1510.07449","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07449","created_at":"2026-05-18T01:29:14Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07449v1","created_at":"2026-05-18T01:29:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07449","created_at":"2026-05-18T01:29:14Z"},{"alias_kind":"pith_short_12","alias_value":"FXXSSUSLTOZ6","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FXXSSUSLTOZ6MTHF","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FXXSSUSL","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FXXSSUSLTOZ6MTHFGYSGWQ7RHB","target":"record","payload":{"canonical_record":{"source":{"id":"1510.07449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-26T11:59:36Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"58ed67079c62a7dc197631d33eccf32e2d028012db957e9f1cb47dadfaef0ac8","abstract_canon_sha256":"35c09c8e2845e961efe303f7fa9c38491f72149794d6e3c85da8e9fb15b1cb9d"},"schema_version":"1.0"},"canonical_sha256":"2def29524b9bb3e64ce536246b43f1387134072a0ecde90d73c8f3394143a868","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:14.049014Z","signature_b64":"6VlDrFx6WyZLHACPhmsef9b50HmVkA354XdBC80/Ed42Htt8prlu6tTZSe2bO4haBp0xfmwawmvjGsMbUJ8+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2def29524b9bb3e64ce536246b43f1387134072a0ecde90d73c8f3394143a868","last_reissued_at":"2026-05-18T01:29:14.048385Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:14.048385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.07449","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":"2026-05-18T01:29:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/lV2/HpS/JLpEslCUZcnE9EZibLILcZe0DfKns/TrbjAdnCV5MnG31fMBo/OmWVqKfZjd68N594woJgJaj7ADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:13:55.863368Z"},"content_sha256":"384884caca9353dabe1cce3df363726b17a700656af27520d1a9950e8cd191f8","schema_version":"1.0","event_id":"sha256:384884caca9353dabe1cce3df363726b17a700656af27520d1a9950e8cd191f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FXXSSUSLTOZ6MTHFGYSGWQ7RHB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fatou's web","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Vasiliki Evdoridou","submitted_at":"2015-10-26T11:59:36Z","abstract_excerpt":"Let $f$ be Fatou's function, that is, $f(z)= z+1+e^{-z}$. We prove that the escaping set of $f$ has the structure of a `spider's web' and we show that this result implies that the non-escaping endpoints of the Julia set of $f$ together with infinity form a totally disconnected set. We also give a well-known transcendental entire function, due to Bergweiler, for which the escaping set is a spider's web and we point out that the same property holds for families of functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07449","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":"2026-05-18T01:29:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c2EWWMhX97N3E3L3xfWufKB19wSFMcCacsSc4lb7+z9Mf0gPeVYjbXIB1XGCTVwCsTCH4jx1opmWXKMBzKQgDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:13:55.864006Z"},"content_sha256":"042c948c428ea4984a8fd93aee6f633105b5290c516632e2e58472e0ad58097e","schema_version":"1.0","event_id":"sha256:042c948c428ea4984a8fd93aee6f633105b5290c516632e2e58472e0ad58097e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FXXSSUSLTOZ6MTHFGYSGWQ7RHB/bundle.json","state_url":"https://pith.science/pith/FXXSSUSLTOZ6MTHFGYSGWQ7RHB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FXXSSUSLTOZ6MTHFGYSGWQ7RHB/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":"2026-05-31T18:13:55Z","links":{"resolver":"https://pith.science/pith/FXXSSUSLTOZ6MTHFGYSGWQ7RHB","bundle":"https://pith.science/pith/FXXSSUSLTOZ6MTHFGYSGWQ7RHB/bundle.json","state":"https://pith.science/pith/FXXSSUSLTOZ6MTHFGYSGWQ7RHB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FXXSSUSLTOZ6MTHFGYSGWQ7RHB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FXXSSUSLTOZ6MTHFGYSGWQ7RHB","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":"35c09c8e2845e961efe303f7fa9c38491f72149794d6e3c85da8e9fb15b1cb9d","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-26T11:59:36Z","title_canon_sha256":"58ed67079c62a7dc197631d33eccf32e2d028012db957e9f1cb47dadfaef0ac8"},"schema_version":"1.0","source":{"id":"1510.07449","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07449","created_at":"2026-05-18T01:29:14Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07449v1","created_at":"2026-05-18T01:29:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07449","created_at":"2026-05-18T01:29:14Z"},{"alias_kind":"pith_short_12","alias_value":"FXXSSUSLTOZ6","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FXXSSUSLTOZ6MTHF","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FXXSSUSL","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:042c948c428ea4984a8fd93aee6f633105b5290c516632e2e58472e0ad58097e","target":"graph","created_at":"2026-05-18T01:29:14Z","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":"Let $f$ be Fatou's function, that is, $f(z)= z+1+e^{-z}$. We prove that the escaping set of $f$ has the structure of a `spider's web' and we show that this result implies that the non-escaping endpoints of the Julia set of $f$ together with infinity form a totally disconnected set. We also give a well-known transcendental entire function, due to Bergweiler, for which the escaping set is a spider's web and we point out that the same property holds for families of functions.","authors_text":"Vasiliki Evdoridou","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-26T11:59:36Z","title":"Fatou's web"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07449","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":"sha256:384884caca9353dabe1cce3df363726b17a700656af27520d1a9950e8cd191f8","target":"record","created_at":"2026-05-18T01:29:14Z","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":"35c09c8e2845e961efe303f7fa9c38491f72149794d6e3c85da8e9fb15b1cb9d","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-26T11:59:36Z","title_canon_sha256":"58ed67079c62a7dc197631d33eccf32e2d028012db957e9f1cb47dadfaef0ac8"},"schema_version":"1.0","source":{"id":"1510.07449","kind":"arxiv","version":1}},"canonical_sha256":"2def29524b9bb3e64ce536246b43f1387134072a0ecde90d73c8f3394143a868","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2def29524b9bb3e64ce536246b43f1387134072a0ecde90d73c8f3394143a868","first_computed_at":"2026-05-18T01:29:14.048385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:14.048385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6VlDrFx6WyZLHACPhmsef9b50HmVkA354XdBC80/Ed42Htt8prlu6tTZSe2bO4haBp0xfmwawmvjGsMbUJ8+AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:14.049014Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.07449","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:384884caca9353dabe1cce3df363726b17a700656af27520d1a9950e8cd191f8","sha256:042c948c428ea4984a8fd93aee6f633105b5290c516632e2e58472e0ad58097e"],"state_sha256":"039ba1de9413334fd6e8c648ccb89dd9e39e9afa74c5300ce40b3f9144c64ead"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7yYfyxnEDiNmnHDz8s9Zf/2nBHsus+30iZpS7K9KkVu1Hn0VPIOJpZQerTyebUXk6o1pfzvU9N2ikKG7nTd0Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T18:13:55.867479Z","bundle_sha256":"fb2a5736721744990e9a945d22c427a257e174f968ae60d2a4189c57e43a8368"}}