{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1993:XAWJTFKBE6LWRKX5TIPDRTQJHE","short_pith_number":"pith:XAWJTFKB","canonical_record":{"source":{"id":"math/9307230","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"1993-07-01T00:00:00Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"7d7746c2be6d77201b57aee765dfb8ff84b135daafc6055b294aa95cc5d7c855","abstract_canon_sha256":"3805ba9cb68f8628734a277eee1969b85f476ded7b87d860b224a85f741b8085"},"schema_version":"1.0"},"canonical_sha256":"b82c999541279768aafd9a1e38ce093919d669bafa2a45255ca18b671b8341d3","source":{"kind":"arxiv","id":"math/9307230","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9307230","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"arxiv_version","alias_value":"math/9307230v1","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9307230","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"pith_short_12","alias_value":"XAWJTFKBE6LW","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"XAWJTFKBE6LWRKX5","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"XAWJTFKB","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1993:XAWJTFKBE6LWRKX5TIPDRTQJHE","target":"record","payload":{"canonical_record":{"source":{"id":"math/9307230","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"1993-07-01T00:00:00Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"7d7746c2be6d77201b57aee765dfb8ff84b135daafc6055b294aa95cc5d7c855","abstract_canon_sha256":"3805ba9cb68f8628734a277eee1969b85f476ded7b87d860b224a85f741b8085"},"schema_version":"1.0"},"canonical_sha256":"b82c999541279768aafd9a1e38ce093919d669bafa2a45255ca18b671b8341d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:52.024888Z","signature_b64":"9hqxF19wOUNIFZj163fgjaegd4zSUkJgYAq5pboLUiBZ8dItt8/jvlyz7LtvOtTKpdxnjnE94uOcGjwodxn5AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b82c999541279768aafd9a1e38ce093919d669bafa2a45255ca18b671b8341d3","last_reissued_at":"2026-05-18T01:05:52.024346Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:52.024346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9307230","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":"2026-05-18T01:05:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mT2fKLN2F1OMS2flVaQ0S2MXDVBakXn7svJUOj3XcBFgZ6BC+JET1T3U12r5CPlvqb0rCy6iPap6WXIiwYVeAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:37:52.443943Z"},"content_sha256":"ce988e9337e7dfd59205f81e391c564a80dde3969ac4769f7c9fca1ff7c370c9","schema_version":"1.0","event_id":"sha256:ce988e9337e7dfd59205f81e391c564a80dde3969ac4769f7c9fca1ff7c370c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1993:XAWJTFKBE6LWRKX5TIPDRTQJHE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The genus-minimizing property of algebraic curves","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Peter B. Kronheimer","submitted_at":"1993-07-01T00:00:00Z","abstract_excerpt":"A viable and still unproved conjecture states that, if $X$ is a smooth algebraic surface and $C$ is a smooth algebraic curve in $X$, then $C$ realizes the smallest possible genus amongst all smoothly embedded $2$-manifolds in its homology class. A proof is announced here for this conjecture, for a large class of surfaces $X$, under the assumption that the normal bundle of $C$ has positive degree."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9307230","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":"2026-05-18T01:05:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BMd/kZ5MFOzl7MWQ2WGCuUSSgwYTEdgn7mfH6eQlEWqTFSI1tbWpx6Dl7NEK4vxtbesGDE/XSgu0553vdWPZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:37:52.444415Z"},"content_sha256":"177cd2079860e78bb5766d4a575c08c0cb780fa31bcfd027664cf8cd88cd56ad","schema_version":"1.0","event_id":"sha256:177cd2079860e78bb5766d4a575c08c0cb780fa31bcfd027664cf8cd88cd56ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XAWJTFKBE6LWRKX5TIPDRTQJHE/bundle.json","state_url":"https://pith.science/pith/XAWJTFKBE6LWRKX5TIPDRTQJHE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XAWJTFKBE6LWRKX5TIPDRTQJHE/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":"2026-06-23T17:37:52Z","links":{"resolver":"https://pith.science/pith/XAWJTFKBE6LWRKX5TIPDRTQJHE","bundle":"https://pith.science/pith/XAWJTFKBE6LWRKX5TIPDRTQJHE/bundle.json","state":"https://pith.science/pith/XAWJTFKBE6LWRKX5TIPDRTQJHE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XAWJTFKBE6LWRKX5TIPDRTQJHE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:XAWJTFKBE6LWRKX5TIPDRTQJHE","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":"3805ba9cb68f8628734a277eee1969b85f476ded7b87d860b224a85f741b8085","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.GT","submitted_at":"1993-07-01T00:00:00Z","title_canon_sha256":"7d7746c2be6d77201b57aee765dfb8ff84b135daafc6055b294aa95cc5d7c855"},"schema_version":"1.0","source":{"id":"math/9307230","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9307230","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"arxiv_version","alias_value":"math/9307230v1","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9307230","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"pith_short_12","alias_value":"XAWJTFKBE6LW","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"XAWJTFKBE6LWRKX5","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"XAWJTFKB","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:177cd2079860e78bb5766d4a575c08c0cb780fa31bcfd027664cf8cd88cd56ad","target":"graph","created_at":"2026-05-18T01:05:52Z","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":"A viable and still unproved conjecture states that, if $X$ is a smooth algebraic surface and $C$ is a smooth algebraic curve in $X$, then $C$ realizes the smallest possible genus amongst all smoothly embedded $2$-manifolds in its homology class. A proof is announced here for this conjecture, for a large class of surfaces $X$, under the assumption that the normal bundle of $C$ has positive degree.","authors_text":"Peter B. Kronheimer","cross_cats":["math.DG"],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"1993-07-01T00:00:00Z","title":"The genus-minimizing property of algebraic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9307230","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:ce988e9337e7dfd59205f81e391c564a80dde3969ac4769f7c9fca1ff7c370c9","target":"record","created_at":"2026-05-18T01:05:52Z","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":"3805ba9cb68f8628734a277eee1969b85f476ded7b87d860b224a85f741b8085","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.GT","submitted_at":"1993-07-01T00:00:00Z","title_canon_sha256":"7d7746c2be6d77201b57aee765dfb8ff84b135daafc6055b294aa95cc5d7c855"},"schema_version":"1.0","source":{"id":"math/9307230","kind":"arxiv","version":1}},"canonical_sha256":"b82c999541279768aafd9a1e38ce093919d669bafa2a45255ca18b671b8341d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b82c999541279768aafd9a1e38ce093919d669bafa2a45255ca18b671b8341d3","first_computed_at":"2026-05-18T01:05:52.024346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:52.024346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9hqxF19wOUNIFZj163fgjaegd4zSUkJgYAq5pboLUiBZ8dItt8/jvlyz7LtvOtTKpdxnjnE94uOcGjwodxn5AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:52.024888Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9307230","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce988e9337e7dfd59205f81e391c564a80dde3969ac4769f7c9fca1ff7c370c9","sha256:177cd2079860e78bb5766d4a575c08c0cb780fa31bcfd027664cf8cd88cd56ad"],"state_sha256":"4fc0c736aeb62d10606af136743640bbf756e986cc1302831fb47a8f23ae379b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lZ8f4938tDRSkuX/joABsYt3SZ9drTu5s22vA54lB2WmRRUhAEdrMdcGxjsktJUmeSxcbbXf4RzfjnG+2FofDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T17:37:52.446467Z","bundle_sha256":"4ffec4ab03967b125b24b75dcc37203c13c83e4fb7e0cd1e11fbffd726527198"}}