{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:O7ZKH2BZHS7MPYF5RTBVGORTFB","short_pith_number":"pith:O7ZKH2BZ","canonical_record":{"source":{"id":"1302.4315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-18T15:35:31Z","cross_cats_sorted":[],"title_canon_sha256":"683a1eabad2f177add55a8281396ce591c97535c759a0d074efe73ded5921f65","abstract_canon_sha256":"0fb019084443547f41519036f65a277e33695bfcb18d81b254f3395598ad8dbb"},"schema_version":"1.0"},"canonical_sha256":"77f2a3e8393cbec7e0bd8cc3533a3328422bcfbf0ebedd417069269d1be489e6","source":{"kind":"arxiv","id":"1302.4315","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4315","created_at":"2026-05-18T03:33:23Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4315v1","created_at":"2026-05-18T03:33:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4315","created_at":"2026-05-18T03:33:23Z"},{"alias_kind":"pith_short_12","alias_value":"O7ZKH2BZHS7M","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O7ZKH2BZHS7MPYF5","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O7ZKH2BZ","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:O7ZKH2BZHS7MPYF5RTBVGORTFB","target":"record","payload":{"canonical_record":{"source":{"id":"1302.4315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-18T15:35:31Z","cross_cats_sorted":[],"title_canon_sha256":"683a1eabad2f177add55a8281396ce591c97535c759a0d074efe73ded5921f65","abstract_canon_sha256":"0fb019084443547f41519036f65a277e33695bfcb18d81b254f3395598ad8dbb"},"schema_version":"1.0"},"canonical_sha256":"77f2a3e8393cbec7e0bd8cc3533a3328422bcfbf0ebedd417069269d1be489e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:23.427342Z","signature_b64":"DrcjTxF52oXupQWZy7MIpom9uJqwb0G8MRSW4sZGURRFXobWKialr7nyBG95hzcLw9JsOvK69RcQ1RqcyKbNAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77f2a3e8393cbec7e0bd8cc3533a3328422bcfbf0ebedd417069269d1be489e6","last_reissued_at":"2026-05-18T03:33:23.426547Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:23.426547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.4315","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":"2026-05-18T03:33:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/q9xMLdyqsxdLJDGTafLIAd9Uyib1/rCdYBUKjEqDb5QFD+eW+tUH1uG/VB+rHab8sW9sZEL3GaFuA3mEGmXDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T11:58:27.537107Z"},"content_sha256":"e83d14d97438f80f93bedac5efbcb883f27ccb4f27b200e6e7db53bd717c7ed9","schema_version":"1.0","event_id":"sha256:e83d14d97438f80f93bedac5efbcb883f27ccb4f27b200e6e7db53bd717c7ed9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:O7ZKH2BZHS7MPYF5RTBVGORTFB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Embedded triply periodic zero mean curvature surfaces of mixed type in Lorentz-Minkowski 3-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Kotaro Yamada, Masaaki Umehara, Seong-Deog Yang, Shoichi Fujimori, Wayne Rossman","submitted_at":"2013-02-18T15:35:31Z","abstract_excerpt":"We construct embedded triply periodic zero mean curvature surfaces of mixed type in the Lorentz-Minkowski 3-space with the same topology as the Schwarz D surface in the Euclidean 3-space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4315","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":"2026-05-18T03:33:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RzY5fgt9UTuDAcrVqqpF4RJx0rcnAaQ6MyHN9z0c7M/Lukq1m2o4fnec/zdEGCqpgwADsBpmWFAHzHX7Hw2iAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T11:58:27.537707Z"},"content_sha256":"d524afb41e3919c556bab08de35276e95b704f6af6c5148c99e6d85889a3d7af","schema_version":"1.0","event_id":"sha256:d524afb41e3919c556bab08de35276e95b704f6af6c5148c99e6d85889a3d7af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O7ZKH2BZHS7MPYF5RTBVGORTFB/bundle.json","state_url":"https://pith.science/pith/O7ZKH2BZHS7MPYF5RTBVGORTFB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O7ZKH2BZHS7MPYF5RTBVGORTFB/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":"2026-05-25T11:58:27Z","links":{"resolver":"https://pith.science/pith/O7ZKH2BZHS7MPYF5RTBVGORTFB","bundle":"https://pith.science/pith/O7ZKH2BZHS7MPYF5RTBVGORTFB/bundle.json","state":"https://pith.science/pith/O7ZKH2BZHS7MPYF5RTBVGORTFB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O7ZKH2BZHS7MPYF5RTBVGORTFB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:O7ZKH2BZHS7MPYF5RTBVGORTFB","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":"0fb019084443547f41519036f65a277e33695bfcb18d81b254f3395598ad8dbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-18T15:35:31Z","title_canon_sha256":"683a1eabad2f177add55a8281396ce591c97535c759a0d074efe73ded5921f65"},"schema_version":"1.0","source":{"id":"1302.4315","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4315","created_at":"2026-05-18T03:33:23Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4315v1","created_at":"2026-05-18T03:33:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4315","created_at":"2026-05-18T03:33:23Z"},{"alias_kind":"pith_short_12","alias_value":"O7ZKH2BZHS7M","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O7ZKH2BZHS7MPYF5","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O7ZKH2BZ","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:d524afb41e3919c556bab08de35276e95b704f6af6c5148c99e6d85889a3d7af","target":"graph","created_at":"2026-05-18T03:33:23Z","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":"We construct embedded triply periodic zero mean curvature surfaces of mixed type in the Lorentz-Minkowski 3-space with the same topology as the Schwarz D surface in the Euclidean 3-space.","authors_text":"Kotaro Yamada, Masaaki Umehara, Seong-Deog Yang, Shoichi Fujimori, Wayne Rossman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-18T15:35:31Z","title":"Embedded triply periodic zero mean curvature surfaces of mixed type in Lorentz-Minkowski 3-space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4315","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:e83d14d97438f80f93bedac5efbcb883f27ccb4f27b200e6e7db53bd717c7ed9","target":"record","created_at":"2026-05-18T03:33:23Z","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":"0fb019084443547f41519036f65a277e33695bfcb18d81b254f3395598ad8dbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-18T15:35:31Z","title_canon_sha256":"683a1eabad2f177add55a8281396ce591c97535c759a0d074efe73ded5921f65"},"schema_version":"1.0","source":{"id":"1302.4315","kind":"arxiv","version":1}},"canonical_sha256":"77f2a3e8393cbec7e0bd8cc3533a3328422bcfbf0ebedd417069269d1be489e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77f2a3e8393cbec7e0bd8cc3533a3328422bcfbf0ebedd417069269d1be489e6","first_computed_at":"2026-05-18T03:33:23.426547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:23.426547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DrcjTxF52oXupQWZy7MIpom9uJqwb0G8MRSW4sZGURRFXobWKialr7nyBG95hzcLw9JsOvK69RcQ1RqcyKbNAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:23.427342Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.4315","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e83d14d97438f80f93bedac5efbcb883f27ccb4f27b200e6e7db53bd717c7ed9","sha256:d524afb41e3919c556bab08de35276e95b704f6af6c5148c99e6d85889a3d7af"],"state_sha256":"7a08e5e5a5957b4310d06c460db5689c4b774585193dae5e639a7a9d319c6181"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V/qz5oTnI5u+KLOSVPSGStTjL25ITmGmwrUMisjFSSuU0dEE5aBPSQowY8TRTg1tjyHCppgo5Mz8AqiBJl8XAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T11:58:27.540854Z","bundle_sha256":"695e5e4c3aa41b6a4c13e549924851e2462da27650e62ef0d4179b149870fc71"}}