{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Y6OCVWDA5I2UGWWDHBHE5MQ33M","short_pith_number":"pith:Y6OCVWDA","canonical_record":{"source":{"id":"1509.01734","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-05T20:44:01Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"2c271d36410a73698e122b8114edc58e2212397a096cfab081c8927f5bd32f3c","abstract_canon_sha256":"c344b44f6cafefd214e7d966fbd74f3d71ca4c782e83fa5e3056a21add240fa9"},"schema_version":"1.0"},"canonical_sha256":"c79c2ad860ea35435ac3384e4eb21bdb1492843b113d9a74c7f0e9c152dad767","source":{"kind":"arxiv","id":"1509.01734","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01734","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01734v1","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01734","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"pith_short_12","alias_value":"Y6OCVWDA5I2U","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"Y6OCVWDA5I2UGWWD","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"Y6OCVWDA","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Y6OCVWDA5I2UGWWDHBHE5MQ33M","target":"record","payload":{"canonical_record":{"source":{"id":"1509.01734","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-05T20:44:01Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"2c271d36410a73698e122b8114edc58e2212397a096cfab081c8927f5bd32f3c","abstract_canon_sha256":"c344b44f6cafefd214e7d966fbd74f3d71ca4c782e83fa5e3056a21add240fa9"},"schema_version":"1.0"},"canonical_sha256":"c79c2ad860ea35435ac3384e4eb21bdb1492843b113d9a74c7f0e9c152dad767","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:50.742627Z","signature_b64":"b90QZgryZzD9ODZ60xvVvP7UJY8vxMM/HuyOrtnOhjMfBcEXTNuA1343aBDMK79th1is9vyTixSwPVjvrwSQAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c79c2ad860ea35435ac3384e4eb21bdb1492843b113d9a74c7f0e9c152dad767","last_reissued_at":"2026-05-18T01:33:50.742044Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:50.742044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.01734","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":"2026-05-18T01:33:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mIftOkCb5zoYb5G3tjj6AnVcZ1jWtuNSd8sTEmzFb9KEJevQPtmxnYHhogkQ6ZfzPRWjuo95CtGPXsLlvxVSAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:19:31.008436Z"},"content_sha256":"3bd2a4739508a266c3767fa974110c32f461db8e48ac5bba3569eb914804a486","schema_version":"1.0","event_id":"sha256:3bd2a4739508a266c3767fa974110c32f461db8e48ac5bba3569eb914804a486"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Y6OCVWDA5I2UGWWDHBHE5MQ33M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Differential geometry of holomorphic vector bundles on a curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Florent Schaffhauser","submitted_at":"2015-09-05T20:44:01Z","abstract_excerpt":"These notes are based on a series of five lectures given at the 2009 Villa de Leyva Summer School on Geometric and Topological Methods for Quantum Field Theory. The purpose of the lectures was to give an introduction to differential-geometric methods in the study of holomorphic vector bundles on a compact connected Riemann surface."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01734","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":"2026-05-18T01:33:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GSkufurzWHMSjVfzRc5S5qNfaKLPeJM+FyMoz+J2Xp6T4wsdHTtdzeJUlE1RIpxZmLpvnoCtS/avJcPpPHg4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:19:31.009159Z"},"content_sha256":"6894b29bc49bdf4ac6d892a042cf0ab3c0fc86184aaf2ad4c50073c8e0e19225","schema_version":"1.0","event_id":"sha256:6894b29bc49bdf4ac6d892a042cf0ab3c0fc86184aaf2ad4c50073c8e0e19225"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y6OCVWDA5I2UGWWDHBHE5MQ33M/bundle.json","state_url":"https://pith.science/pith/Y6OCVWDA5I2UGWWDHBHE5MQ33M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y6OCVWDA5I2UGWWDHBHE5MQ33M/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":"2026-06-06T15:19:31Z","links":{"resolver":"https://pith.science/pith/Y6OCVWDA5I2UGWWDHBHE5MQ33M","bundle":"https://pith.science/pith/Y6OCVWDA5I2UGWWDHBHE5MQ33M/bundle.json","state":"https://pith.science/pith/Y6OCVWDA5I2UGWWDHBHE5MQ33M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y6OCVWDA5I2UGWWDHBHE5MQ33M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Y6OCVWDA5I2UGWWDHBHE5MQ33M","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":"c344b44f6cafefd214e7d966fbd74f3d71ca4c782e83fa5e3056a21add240fa9","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-05T20:44:01Z","title_canon_sha256":"2c271d36410a73698e122b8114edc58e2212397a096cfab081c8927f5bd32f3c"},"schema_version":"1.0","source":{"id":"1509.01734","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01734","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01734v1","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01734","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"pith_short_12","alias_value":"Y6OCVWDA5I2U","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"Y6OCVWDA5I2UGWWD","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"Y6OCVWDA","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:6894b29bc49bdf4ac6d892a042cf0ab3c0fc86184aaf2ad4c50073c8e0e19225","target":"graph","created_at":"2026-05-18T01:33:50Z","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":"These notes are based on a series of five lectures given at the 2009 Villa de Leyva Summer School on Geometric and Topological Methods for Quantum Field Theory. The purpose of the lectures was to give an introduction to differential-geometric methods in the study of holomorphic vector bundles on a compact connected Riemann surface.","authors_text":"Florent Schaffhauser","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-05T20:44:01Z","title":"Differential geometry of holomorphic vector bundles on a curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01734","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":"sha256:3bd2a4739508a266c3767fa974110c32f461db8e48ac5bba3569eb914804a486","target":"record","created_at":"2026-05-18T01:33:50Z","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":"c344b44f6cafefd214e7d966fbd74f3d71ca4c782e83fa5e3056a21add240fa9","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-05T20:44:01Z","title_canon_sha256":"2c271d36410a73698e122b8114edc58e2212397a096cfab081c8927f5bd32f3c"},"schema_version":"1.0","source":{"id":"1509.01734","kind":"arxiv","version":1}},"canonical_sha256":"c79c2ad860ea35435ac3384e4eb21bdb1492843b113d9a74c7f0e9c152dad767","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c79c2ad860ea35435ac3384e4eb21bdb1492843b113d9a74c7f0e9c152dad767","first_computed_at":"2026-05-18T01:33:50.742044Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:50.742044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b90QZgryZzD9ODZ60xvVvP7UJY8vxMM/HuyOrtnOhjMfBcEXTNuA1343aBDMK79th1is9vyTixSwPVjvrwSQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:50.742627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.01734","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3bd2a4739508a266c3767fa974110c32f461db8e48ac5bba3569eb914804a486","sha256:6894b29bc49bdf4ac6d892a042cf0ab3c0fc86184aaf2ad4c50073c8e0e19225"],"state_sha256":"3939f392ab4960bca827c5472045c61236119cb3416cc569137e0d66674f1c8d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t8NUDndatehSdb2fe+Nmsmw7yRWUNJzMTB2I1j5k9M25UJxkDRQuJ8qWKis26+KW/oP6EkUUfI7gDpTn6mDfAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T15:19:31.013903Z","bundle_sha256":"5a6cbb02308917ba9324f66d3dcd297e1ecb61f8ceca54f1af4002b3070c2583"}}