{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZADTDHCKWQDHX5TDZ6U7RKJ5B3","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":"d0d830710dfe93b81b789545ab87a67287c41c0c798380bba9ed9633a0e21a76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-09-26T18:27:11Z","title_canon_sha256":"7678cd5657906377a823fa0469f14510123040e17cec94b5e0bd39068c7f259d"},"schema_version":"1.0","source":{"id":"1709.09211","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.09211","created_at":"2026-05-18T00:34:12Z"},{"alias_kind":"arxiv_version","alias_value":"1709.09211v1","created_at":"2026-05-18T00:34:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09211","created_at":"2026-05-18T00:34:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZADTDHCKWQDH","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZADTDHCKWQDHX5TD","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZADTDHCK","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:9c4070c9d328e89208bb9240c80cc3933538726cde7c7f2ab37fb1a55116c25c","target":"graph","created_at":"2026-05-18T00:34:12Z","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 prove that the homotopy type of a map from a Peano continuum into a planar or one-dimensional space is determined by the induced homomorphism of fundamental groups. This provides a new proof that planar sets are aspherical and is used to prove that two planar or one-dimensional Peano continua are homotopy equivalent if and only if they have isomorphic fundamental groups.","authors_text":"Curtis Kent","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-09-26T18:27:11Z","title":"Homotopy type of planar continua"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09211","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:ac7edf39f66b548a9b6cefcc505a4855cdc1d33d0fab40cb0c544b236d76be13","target":"record","created_at":"2026-05-18T00:34:12Z","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":"d0d830710dfe93b81b789545ab87a67287c41c0c798380bba9ed9633a0e21a76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-09-26T18:27:11Z","title_canon_sha256":"7678cd5657906377a823fa0469f14510123040e17cec94b5e0bd39068c7f259d"},"schema_version":"1.0","source":{"id":"1709.09211","kind":"arxiv","version":1}},"canonical_sha256":"c807319c4ab4067bf663cfa9f8a93d0ec67680bb6e843d08ac47e6957af57dc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c807319c4ab4067bf663cfa9f8a93d0ec67680bb6e843d08ac47e6957af57dc0","first_computed_at":"2026-05-18T00:34:12.509364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:12.509364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wea7EDT8ymLuXXjBioEI4b97MedeG1V0a8ZStfyIuWq9jWscIznuXa9buKoJyD92lPNqfTticNoP3J9YkDuMDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:12.509813Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.09211","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac7edf39f66b548a9b6cefcc505a4855cdc1d33d0fab40cb0c544b236d76be13","sha256:9c4070c9d328e89208bb9240c80cc3933538726cde7c7f2ab37fb1a55116c25c"],"state_sha256":"213944dcb8eb87e36be4d2118249798cae544e3b9f57655f5171088c9e6226aa"}