{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:V2D4NWMYABVSBKB5XGRTFKHITU","short_pith_number":"pith:V2D4NWMY","canonical_record":{"source":{"id":"1409.6899","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-24T11:06:28Z","cross_cats_sorted":[],"title_canon_sha256":"acb532d43ddce79a82a4db3ed93d588511ffe7c8b3839dad8320426e51131d08","abstract_canon_sha256":"13ac8884aa6d4632876c53063f224967fe527358c658bd34178929db259a32f8"},"schema_version":"1.0"},"canonical_sha256":"ae87c6d998006b20a83db9a332a8e89d0f00ee42753fbd4654bbae5995db18ae","source":{"kind":"arxiv","id":"1409.6899","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.6899","created_at":"2026-05-18T00:55:25Z"},{"alias_kind":"arxiv_version","alias_value":"1409.6899v3","created_at":"2026-05-18T00:55:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6899","created_at":"2026-05-18T00:55:25Z"},{"alias_kind":"pith_short_12","alias_value":"V2D4NWMYABVS","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"V2D4NWMYABVSBKB5","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"V2D4NWMY","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:V2D4NWMYABVSBKB5XGRTFKHITU","target":"record","payload":{"canonical_record":{"source":{"id":"1409.6899","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-24T11:06:28Z","cross_cats_sorted":[],"title_canon_sha256":"acb532d43ddce79a82a4db3ed93d588511ffe7c8b3839dad8320426e51131d08","abstract_canon_sha256":"13ac8884aa6d4632876c53063f224967fe527358c658bd34178929db259a32f8"},"schema_version":"1.0"},"canonical_sha256":"ae87c6d998006b20a83db9a332a8e89d0f00ee42753fbd4654bbae5995db18ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:25.878288Z","signature_b64":"/O5CsLhAehrlj5FnUOTfWCX596LJiY/z00FQ3FjJcvuk9m62x0f8zlIfWAleubHA2KAuMrXpnsdRoxlo+NIlCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae87c6d998006b20a83db9a332a8e89d0f00ee42753fbd4654bbae5995db18ae","last_reissued_at":"2026-05-18T00:55:25.877625Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:25.877625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.6899","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:55:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xr03NZgiUoeE3KH9ssXydYCTylcTQeRTmWSQluF/ozJXEy5+aPipnTHlUhPdxpnehcTzatwVvi+n75E4DwVSAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T04:36:23.132914Z"},"content_sha256":"478e06a5965f999a5b53a2f36e1707b028e87887fbdb6133cfc0c0aabb239274","schema_version":"1.0","event_id":"sha256:478e06a5965f999a5b53a2f36e1707b028e87887fbdb6133cfc0c0aabb239274"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:V2D4NWMYABVSBKB5XGRTFKHITU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Introductory course on $\\ell$-adic sheaves and their ramification theory on curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Kay R\\\"ulling, Lars Kindler","submitted_at":"2014-09-24T11:06:28Z","abstract_excerpt":"These are the notes accompanying 13 lectures given by the authors at the Clay Mathematics Institute Summer School 2014 in Madrid. The notes give an introduction into the theory of $\\ell$-adic sheaves with emphasis on their ramification theory on curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6899","kind":"arxiv","version":3},"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":"2026-05-18T00:55:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BFALEjWgu7umJ4ivFjngCIrWLUYDp3WcNAx/LLwOdRcRVzk9X1exl/3ZMMacUV7zq2BANsAIobXYPCst3rsECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T04:36:23.133239Z"},"content_sha256":"5ef9556eb298771d5f7d0e92e27bb9b14d2432b73991c061f3f4abc90c2f4dd4","schema_version":"1.0","event_id":"sha256:5ef9556eb298771d5f7d0e92e27bb9b14d2432b73991c061f3f4abc90c2f4dd4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V2D4NWMYABVSBKB5XGRTFKHITU/bundle.json","state_url":"https://pith.science/pith/V2D4NWMYABVSBKB5XGRTFKHITU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V2D4NWMYABVSBKB5XGRTFKHITU/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":"2026-06-25T04:36:23Z","links":{"resolver":"https://pith.science/pith/V2D4NWMYABVSBKB5XGRTFKHITU","bundle":"https://pith.science/pith/V2D4NWMYABVSBKB5XGRTFKHITU/bundle.json","state":"https://pith.science/pith/V2D4NWMYABVSBKB5XGRTFKHITU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V2D4NWMYABVSBKB5XGRTFKHITU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:V2D4NWMYABVSBKB5XGRTFKHITU","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":"13ac8884aa6d4632876c53063f224967fe527358c658bd34178929db259a32f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-24T11:06:28Z","title_canon_sha256":"acb532d43ddce79a82a4db3ed93d588511ffe7c8b3839dad8320426e51131d08"},"schema_version":"1.0","source":{"id":"1409.6899","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.6899","created_at":"2026-05-18T00:55:25Z"},{"alias_kind":"arxiv_version","alias_value":"1409.6899v3","created_at":"2026-05-18T00:55:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6899","created_at":"2026-05-18T00:55:25Z"},{"alias_kind":"pith_short_12","alias_value":"V2D4NWMYABVS","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"V2D4NWMYABVSBKB5","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"V2D4NWMY","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:5ef9556eb298771d5f7d0e92e27bb9b14d2432b73991c061f3f4abc90c2f4dd4","target":"graph","created_at":"2026-05-18T00:55:25Z","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 are the notes accompanying 13 lectures given by the authors at the Clay Mathematics Institute Summer School 2014 in Madrid. The notes give an introduction into the theory of $\\ell$-adic sheaves with emphasis on their ramification theory on curves.","authors_text":"Kay R\\\"ulling, Lars Kindler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-24T11:06:28Z","title":"Introductory course on $\\ell$-adic sheaves and their ramification theory on curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6899","kind":"arxiv","version":3},"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":"sha256:478e06a5965f999a5b53a2f36e1707b028e87887fbdb6133cfc0c0aabb239274","target":"record","created_at":"2026-05-18T00:55:25Z","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":"13ac8884aa6d4632876c53063f224967fe527358c658bd34178929db259a32f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-24T11:06:28Z","title_canon_sha256":"acb532d43ddce79a82a4db3ed93d588511ffe7c8b3839dad8320426e51131d08"},"schema_version":"1.0","source":{"id":"1409.6899","kind":"arxiv","version":3}},"canonical_sha256":"ae87c6d998006b20a83db9a332a8e89d0f00ee42753fbd4654bbae5995db18ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae87c6d998006b20a83db9a332a8e89d0f00ee42753fbd4654bbae5995db18ae","first_computed_at":"2026-05-18T00:55:25.877625Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:25.877625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/O5CsLhAehrlj5FnUOTfWCX596LJiY/z00FQ3FjJcvuk9m62x0f8zlIfWAleubHA2KAuMrXpnsdRoxlo+NIlCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:25.878288Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.6899","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:478e06a5965f999a5b53a2f36e1707b028e87887fbdb6133cfc0c0aabb239274","sha256:5ef9556eb298771d5f7d0e92e27bb9b14d2432b73991c061f3f4abc90c2f4dd4"],"state_sha256":"abe0faec6f574b98548e787ccddda27eff65c970b55589358425daac3cabe520"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1LzkSv0FpIDMW1XYU4V7cyDArxShEyvojuixiE/Fcv6Akh1WROJ0ydsfnmY2rdd2DRAARWyFv6b7/IsmnejwCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T04:36:23.135091Z","bundle_sha256":"68e4619dc3dd4d7926430fba956087e5792aa97842fb49d172504bc6a2d276f8"}}