{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:D3O7EDUZEGTAVTB22WT4X6P7ZS","short_pith_number":"pith:D3O7EDUZ","canonical_record":{"source":{"id":"1712.04727","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-13T12:14:13Z","cross_cats_sorted":[],"title_canon_sha256":"a8011b63aa7e6c15ff90c9f3feb037ca652083ff3c98dd26b094c279ad856091","abstract_canon_sha256":"fab10c12b9ba761d50b35aa0cb6211bd299e87c1880990ad112112b469c63936"},"schema_version":"1.0"},"canonical_sha256":"1eddf20e9921a60acc3ad5a7cbf9ffcc8f48ef1a688f4ade3cd6fec82f845335","source":{"kind":"arxiv","id":"1712.04727","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04727","created_at":"2026-05-17T23:58:48Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04727v2","created_at":"2026-05-17T23:58:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04727","created_at":"2026-05-17T23:58:48Z"},{"alias_kind":"pith_short_12","alias_value":"D3O7EDUZEGTA","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"D3O7EDUZEGTAVTB2","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"D3O7EDUZ","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:D3O7EDUZEGTAVTB22WT4X6P7ZS","target":"record","payload":{"canonical_record":{"source":{"id":"1712.04727","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-13T12:14:13Z","cross_cats_sorted":[],"title_canon_sha256":"a8011b63aa7e6c15ff90c9f3feb037ca652083ff3c98dd26b094c279ad856091","abstract_canon_sha256":"fab10c12b9ba761d50b35aa0cb6211bd299e87c1880990ad112112b469c63936"},"schema_version":"1.0"},"canonical_sha256":"1eddf20e9921a60acc3ad5a7cbf9ffcc8f48ef1a688f4ade3cd6fec82f845335","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:48.446823Z","signature_b64":"GQC5MOw8IMZoDa4HFob/OqyvUP178WlK9krmcuV/JBP3NwnKyWPehDWZZes03RDObBDGu+aeJSwEo/oRZMrhBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1eddf20e9921a60acc3ad5a7cbf9ffcc8f48ef1a688f4ade3cd6fec82f845335","last_reissued_at":"2026-05-17T23:58:48.446372Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:48.446372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.04727","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":"2026-05-17T23:58:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KSu8xKDM0Mv+ph1ADq/JVSbZh3KVtFkfoLsRhpmNjybb7QY1xlDEc/zoGDuR0fAmSe8+sZ/tsdvBN61iz/FMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:57:20.375654Z"},"content_sha256":"fc02bb650a4b13b2aa6ebd57b64babb9e464f4cb32dfea051bdf5931c3aa965e","schema_version":"1.0","event_id":"sha256:fc02bb650a4b13b2aa6ebd57b64babb9e464f4cb32dfea051bdf5931c3aa965e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:D3O7EDUZEGTAVTB22WT4X6P7ZS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interpolation and optimal hitting for complete minimal surfaces with finite total curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Antonio Alarcon, Francisco J. Lopez, Ildefonso Castro-Infantes","submitted_at":"2017-12-13T12:14:13Z","abstract_excerpt":"We prove that, given a compact Riemann surface $\\Sigma$ and disjoint finite sets $\\varnothing\\neq E\\subset\\Sigma$ and $\\Lambda\\subset\\Sigma$, every map $\\Lambda \\to \\mathbb{R}^3$ extends to a complete conformal minimal immersion $\\Sigma\\setminus E\\to \\mathbb{R}^3$ with finite total curvature.\n  This result opens the door to study optimal hitting problems in the framework of complete minimal surfaces in $\\mathbb{R}^3$ with finite total curvature. To this respect we provide, for each integer $r\\ge 1$, a set $A\\subset\\mathbb{R}^3$ consisting of $12r+3$ points in an affine plane such that if $A$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04727","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":"2026-05-17T23:58:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5punGF0BAZnYohuYt296REjCSKfdQsHWGzhxUcBXVquhR8pi6S4LtgxozZzNXeoZblDSo66sugchaGLNEZnqAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:57:20.376545Z"},"content_sha256":"9e2028c0483436d0a7334606b040b59b51631359b108c621ce5ce00c1c605ac4","schema_version":"1.0","event_id":"sha256:9e2028c0483436d0a7334606b040b59b51631359b108c621ce5ce00c1c605ac4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D3O7EDUZEGTAVTB22WT4X6P7ZS/bundle.json","state_url":"https://pith.science/pith/D3O7EDUZEGTAVTB22WT4X6P7ZS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D3O7EDUZEGTAVTB22WT4X6P7ZS/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":"2026-05-31T05:57:20Z","links":{"resolver":"https://pith.science/pith/D3O7EDUZEGTAVTB22WT4X6P7ZS","bundle":"https://pith.science/pith/D3O7EDUZEGTAVTB22WT4X6P7ZS/bundle.json","state":"https://pith.science/pith/D3O7EDUZEGTAVTB22WT4X6P7ZS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D3O7EDUZEGTAVTB22WT4X6P7ZS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:D3O7EDUZEGTAVTB22WT4X6P7ZS","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":"fab10c12b9ba761d50b35aa0cb6211bd299e87c1880990ad112112b469c63936","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-13T12:14:13Z","title_canon_sha256":"a8011b63aa7e6c15ff90c9f3feb037ca652083ff3c98dd26b094c279ad856091"},"schema_version":"1.0","source":{"id":"1712.04727","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04727","created_at":"2026-05-17T23:58:48Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04727v2","created_at":"2026-05-17T23:58:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04727","created_at":"2026-05-17T23:58:48Z"},{"alias_kind":"pith_short_12","alias_value":"D3O7EDUZEGTA","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"D3O7EDUZEGTAVTB2","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"D3O7EDUZ","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:9e2028c0483436d0a7334606b040b59b51631359b108c621ce5ce00c1c605ac4","target":"graph","created_at":"2026-05-17T23:58:48Z","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, given a compact Riemann surface $\\Sigma$ and disjoint finite sets $\\varnothing\\neq E\\subset\\Sigma$ and $\\Lambda\\subset\\Sigma$, every map $\\Lambda \\to \\mathbb{R}^3$ extends to a complete conformal minimal immersion $\\Sigma\\setminus E\\to \\mathbb{R}^3$ with finite total curvature.\n  This result opens the door to study optimal hitting problems in the framework of complete minimal surfaces in $\\mathbb{R}^3$ with finite total curvature. To this respect we provide, for each integer $r\\ge 1$, a set $A\\subset\\mathbb{R}^3$ consisting of $12r+3$ points in an affine plane such that if $A$ i","authors_text":"Antonio Alarcon, Francisco J. Lopez, Ildefonso Castro-Infantes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-13T12:14:13Z","title":"Interpolation and optimal hitting for complete minimal surfaces with finite total curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04727","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:fc02bb650a4b13b2aa6ebd57b64babb9e464f4cb32dfea051bdf5931c3aa965e","target":"record","created_at":"2026-05-17T23:58:48Z","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":"fab10c12b9ba761d50b35aa0cb6211bd299e87c1880990ad112112b469c63936","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-13T12:14:13Z","title_canon_sha256":"a8011b63aa7e6c15ff90c9f3feb037ca652083ff3c98dd26b094c279ad856091"},"schema_version":"1.0","source":{"id":"1712.04727","kind":"arxiv","version":2}},"canonical_sha256":"1eddf20e9921a60acc3ad5a7cbf9ffcc8f48ef1a688f4ade3cd6fec82f845335","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1eddf20e9921a60acc3ad5a7cbf9ffcc8f48ef1a688f4ade3cd6fec82f845335","first_computed_at":"2026-05-17T23:58:48.446372Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:48.446372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GQC5MOw8IMZoDa4HFob/OqyvUP178WlK9krmcuV/JBP3NwnKyWPehDWZZes03RDObBDGu+aeJSwEo/oRZMrhBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:48.446823Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.04727","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc02bb650a4b13b2aa6ebd57b64babb9e464f4cb32dfea051bdf5931c3aa965e","sha256:9e2028c0483436d0a7334606b040b59b51631359b108c621ce5ce00c1c605ac4"],"state_sha256":"5c5fb27d5d8f96a2c0a2f2b1bdc35e744fd385a067638e4072878b0ce3caa4ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5IhVfiA1bwLXje3Ow5YQ3Z2eOrQc95Z7yq2GVJudkJCEbVdkcS95qUBYE9NGh3Fe/YdWDcPugaWJZfK7hJhCDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:57:20.379718Z","bundle_sha256":"b4ad7af7d60f6b15a6416a736325b449f5f27dae7c5e017dc9255056efac5a80"}}