{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:WVRRD3U5BKXDVDYQPDV7JXTYEL","short_pith_number":"pith:WVRRD3U5","canonical_record":{"source":{"id":"1209.4430","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-09-20T05:31:08Z","cross_cats_sorted":[],"title_canon_sha256":"f32fb37de297e853630ef0c6382930fdeb1b6a11c7687485afd890b1a7a61f0f","abstract_canon_sha256":"686d39b3e7dc5abecc50c3c34082c469334482e3e69e65f61d6f7fb8e4e71163"},"schema_version":"1.0"},"canonical_sha256":"b56311ee9d0aae3a8f1078ebf4de7822c3a46327fcba31cfbf2cd70a78ffe215","source":{"kind":"arxiv","id":"1209.4430","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4430","created_at":"2026-05-18T03:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4430v2","created_at":"2026-05-18T03:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4430","created_at":"2026-05-18T03:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"WVRRD3U5BKXD","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"WVRRD3U5BKXDVDYQ","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"WVRRD3U5","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:WVRRD3U5BKXDVDYQPDV7JXTYEL","target":"record","payload":{"canonical_record":{"source":{"id":"1209.4430","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-09-20T05:31:08Z","cross_cats_sorted":[],"title_canon_sha256":"f32fb37de297e853630ef0c6382930fdeb1b6a11c7687485afd890b1a7a61f0f","abstract_canon_sha256":"686d39b3e7dc5abecc50c3c34082c469334482e3e69e65f61d6f7fb8e4e71163"},"schema_version":"1.0"},"canonical_sha256":"b56311ee9d0aae3a8f1078ebf4de7822c3a46327fcba31cfbf2cd70a78ffe215","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:23.576762Z","signature_b64":"VZvoN4Q5uxtlmTGYQ03iCj5EYkb2R1Fgkm4VOnqbCzF9OCuYeaQKiXxRvwr0stExYluemPEMxX1/FAbWWixsCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b56311ee9d0aae3a8f1078ebf4de7822c3a46327fcba31cfbf2cd70a78ffe215","last_reissued_at":"2026-05-18T03:42:23.576051Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:23.576051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.4430","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:42:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J2D90q/LcSt8HQclF1U3hnACd6CKBdf4pXWiy1l2E4sspYCeqsR2Lb4S2E9xBAwebFpeXWxTRzeKhKyPxoFjCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T07:30:45.589909Z"},"content_sha256":"9d88c598411b498613e119417191af4394271feb815b49bd20efb3250dcfac0a","schema_version":"1.0","event_id":"sha256:9d88c598411b498613e119417191af4394271feb815b49bd20efb3250dcfac0a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:WVRRD3U5BKXDVDYQPDV7JXTYEL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Proper holomorphic immersions in homotopy classes of maps from finitely connected planar domains into CxC*","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Finnur Larusson, Tyson Ritter","submitted_at":"2012-09-20T05:31:08Z","abstract_excerpt":"Gromov, in his seminal 1989 paper on the Oka principle, proved that every continuous map from a Stein manifold into an elliptic manifold is homotopic to a holomorphic map. Previously we have shown that, given a continuous map $X \\to \\C\\times\\C^*$ from a finitely connected planar domain $X$ without isolated boundary points, a stronger Oka property holds, namely that the map is homotopic to a proper holomorphic embedding. Here we show that every continuous map from a finitely connected planar domain, possibly with punctures, into $\\C\\times\\C^*$ is homotopic to a proper immersion that identifies "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4430","kind":"arxiv","version":2},"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":"2026-05-18T03:42:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"km3ntd7K3lnjeEYF6u+VJGGKErcOlFieQkBD8orZz03AQeuste3bEBQMUQZ9w0qPIITHLzN5Sc12gYAsIp3fAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T07:30:45.590549Z"},"content_sha256":"8e9fa3e4375bb81fbef67e968daed18ad3071b4ad64dc817ba97b3294a9cb48b","schema_version":"1.0","event_id":"sha256:8e9fa3e4375bb81fbef67e968daed18ad3071b4ad64dc817ba97b3294a9cb48b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WVRRD3U5BKXDVDYQPDV7JXTYEL/bundle.json","state_url":"https://pith.science/pith/WVRRD3U5BKXDVDYQPDV7JXTYEL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WVRRD3U5BKXDVDYQPDV7JXTYEL/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":"2026-06-11T07:30:45Z","links":{"resolver":"https://pith.science/pith/WVRRD3U5BKXDVDYQPDV7JXTYEL","bundle":"https://pith.science/pith/WVRRD3U5BKXDVDYQPDV7JXTYEL/bundle.json","state":"https://pith.science/pith/WVRRD3U5BKXDVDYQPDV7JXTYEL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WVRRD3U5BKXDVDYQPDV7JXTYEL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WVRRD3U5BKXDVDYQPDV7JXTYEL","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":"686d39b3e7dc5abecc50c3c34082c469334482e3e69e65f61d6f7fb8e4e71163","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-09-20T05:31:08Z","title_canon_sha256":"f32fb37de297e853630ef0c6382930fdeb1b6a11c7687485afd890b1a7a61f0f"},"schema_version":"1.0","source":{"id":"1209.4430","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4430","created_at":"2026-05-18T03:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4430v2","created_at":"2026-05-18T03:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4430","created_at":"2026-05-18T03:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"WVRRD3U5BKXD","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"WVRRD3U5BKXDVDYQ","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"WVRRD3U5","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:8e9fa3e4375bb81fbef67e968daed18ad3071b4ad64dc817ba97b3294a9cb48b","target":"graph","created_at":"2026-05-18T03:42:23Z","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":"Gromov, in his seminal 1989 paper on the Oka principle, proved that every continuous map from a Stein manifold into an elliptic manifold is homotopic to a holomorphic map. Previously we have shown that, given a continuous map $X \\to \\C\\times\\C^*$ from a finitely connected planar domain $X$ without isolated boundary points, a stronger Oka property holds, namely that the map is homotopic to a proper holomorphic embedding. Here we show that every continuous map from a finitely connected planar domain, possibly with punctures, into $\\C\\times\\C^*$ is homotopic to a proper immersion that identifies ","authors_text":"Finnur Larusson, Tyson Ritter","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-09-20T05:31:08Z","title":"Proper holomorphic immersions in homotopy classes of maps from finitely connected planar domains into CxC*"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4430","kind":"arxiv","version":2},"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":"sha256:9d88c598411b498613e119417191af4394271feb815b49bd20efb3250dcfac0a","target":"record","created_at":"2026-05-18T03:42:23Z","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":"686d39b3e7dc5abecc50c3c34082c469334482e3e69e65f61d6f7fb8e4e71163","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-09-20T05:31:08Z","title_canon_sha256":"f32fb37de297e853630ef0c6382930fdeb1b6a11c7687485afd890b1a7a61f0f"},"schema_version":"1.0","source":{"id":"1209.4430","kind":"arxiv","version":2}},"canonical_sha256":"b56311ee9d0aae3a8f1078ebf4de7822c3a46327fcba31cfbf2cd70a78ffe215","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b56311ee9d0aae3a8f1078ebf4de7822c3a46327fcba31cfbf2cd70a78ffe215","first_computed_at":"2026-05-18T03:42:23.576051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:23.576051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VZvoN4Q5uxtlmTGYQ03iCj5EYkb2R1Fgkm4VOnqbCzF9OCuYeaQKiXxRvwr0stExYluemPEMxX1/FAbWWixsCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:23.576762Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.4430","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d88c598411b498613e119417191af4394271feb815b49bd20efb3250dcfac0a","sha256:8e9fa3e4375bb81fbef67e968daed18ad3071b4ad64dc817ba97b3294a9cb48b"],"state_sha256":"e470db7f0184d57efc4eb89394c07357bbe8c6699800cffe72b653d09ab88b5d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cCEk5xPcX1paFQRNb9svgGx43tkIumI0oTDNcJTMrODU1Ao8bcFsJEXycqUbpQax/LSzFmHC6gp9bmjf55H9DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T07:30:45.594180Z","bundle_sha256":"d02859fa0a7b5a1bfe6b8882eebda17b9fef921c3a28926ace622f1d3dd972a6"}}