{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1997:GATWJ2NQLU4EBJFCCTRA4QJMUM","short_pith_number":"pith:GATWJ2NQ","canonical_record":{"source":{"id":"alg-geom/9708014","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1997-08-18T07:52:26Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"a3794bcaecd194a29cc836b352ff6eb12e930b5ee8bf7465a986f1dd4b99a879","abstract_canon_sha256":"b2cf8b6c29230a37ccb941351da377e443c982cac4606b522938507f8cd42951"},"schema_version":"1.0"},"canonical_sha256":"302764e9b05d3840a4a214e20e412ca33c081648ea537f3d4729c8be134add70","source":{"kind":"arxiv","id":"alg-geom/9708014","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9708014","created_at":"2026-05-18T01:07:47Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9708014v1","created_at":"2026-05-18T01:07:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9708014","created_at":"2026-05-18T01:07:47Z"},{"alias_kind":"pith_short_12","alias_value":"GATWJ2NQLU4E","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"GATWJ2NQLU4EBJFC","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"GATWJ2NQ","created_at":"2026-05-18T12:25:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1997:GATWJ2NQLU4EBJFCCTRA4QJMUM","target":"record","payload":{"canonical_record":{"source":{"id":"alg-geom/9708014","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1997-08-18T07:52:26Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"a3794bcaecd194a29cc836b352ff6eb12e930b5ee8bf7465a986f1dd4b99a879","abstract_canon_sha256":"b2cf8b6c29230a37ccb941351da377e443c982cac4606b522938507f8cd42951"},"schema_version":"1.0"},"canonical_sha256":"302764e9b05d3840a4a214e20e412ca33c081648ea537f3d4729c8be134add70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:47.039885Z","signature_b64":"MC1xshTb6Mauk3MznCashTRZ5cinN101NmX5ltYgLl82ntfBMk/ce+2s5XWacBdu4KAfFX3O/5fSGfhyP7ZDDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"302764e9b05d3840a4a214e20e412ca33c081648ea537f3d4729c8be134add70","last_reissued_at":"2026-05-18T01:07:47.039459Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:47.039459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"alg-geom/9708014","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":"2026-05-18T01:07:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MHeVLXtJ1Ig5kj6SUI/YVgDkMVYYWuoiOoiF3y7NtcgF9g6eLjaKCMNKCYVurr3dhQcGFwainyAdZ0tAuNsaAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T15:04:36.055370Z"},"content_sha256":"5c6e24fedf10f01a109a30944c06ec811d8426938b7568d6bc42195262033178","schema_version":"1.0","event_id":"sha256:5c6e24fedf10f01a109a30944c06ec811d8426938b7568d6bc42195262033178"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1997:GATWJ2NQLU4EBJFCCTRA4QJMUM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A stratification of the moduli space of vector bundles on curves","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"H. Lange, L. Brambila-Paz","submitted_at":"1997-08-18T07:52:26Z","abstract_excerpt":"Let $E$ be a vector bundle of rank $r\\geq 2$ on a smooth projective curve $C$ of genus $g \\geq 2$ over an algebraically closed field $K$ of arbitrary characteristic. For any integer with $1\\le k\\le r-1$ we define $${\\se}_k(E):=k\\deg E-r\\max\\deg F.$$ where the maximum is taken over all subbundles $F$ of rank $k$ of $E$. The ${s}_k$ gives a stratification of the moduli space ${\\cal M}(r,d)$ of stable vector bundles of rank $r$ and degree on $d$ on $C$ into locally closed subsets ${\\calM}(r,d,k,s)$ according to the value of $s$ and $k$. There is a component ${\\cal M}^0(r,d,k,s)$ of ${\\cal M}(r,d,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9708014","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":"2026-05-18T01:07:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s2vM1vnSzrv7lR1mTJer31s4zbHV3JJTCfsxV0aAJbecNEZOuL0hFBFrp2HmJEy1+VaECZc3todUBGH1RukeAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T15:04:36.056089Z"},"content_sha256":"4489eb89d55487923099fb0d7463df7264b0d7564669724a702720349f298316","schema_version":"1.0","event_id":"sha256:4489eb89d55487923099fb0d7463df7264b0d7564669724a702720349f298316"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GATWJ2NQLU4EBJFCCTRA4QJMUM/bundle.json","state_url":"https://pith.science/pith/GATWJ2NQLU4EBJFCCTRA4QJMUM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GATWJ2NQLU4EBJFCCTRA4QJMUM/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":"2026-06-08T15:04:36Z","links":{"resolver":"https://pith.science/pith/GATWJ2NQLU4EBJFCCTRA4QJMUM","bundle":"https://pith.science/pith/GATWJ2NQLU4EBJFCCTRA4QJMUM/bundle.json","state":"https://pith.science/pith/GATWJ2NQLU4EBJFCCTRA4QJMUM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GATWJ2NQLU4EBJFCCTRA4QJMUM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:GATWJ2NQLU4EBJFCCTRA4QJMUM","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":"b2cf8b6c29230a37ccb941351da377e443c982cac4606b522938507f8cd42951","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1997-08-18T07:52:26Z","title_canon_sha256":"a3794bcaecd194a29cc836b352ff6eb12e930b5ee8bf7465a986f1dd4b99a879"},"schema_version":"1.0","source":{"id":"alg-geom/9708014","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9708014","created_at":"2026-05-18T01:07:47Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9708014v1","created_at":"2026-05-18T01:07:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9708014","created_at":"2026-05-18T01:07:47Z"},{"alias_kind":"pith_short_12","alias_value":"GATWJ2NQLU4E","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"GATWJ2NQLU4EBJFC","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"GATWJ2NQ","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:4489eb89d55487923099fb0d7463df7264b0d7564669724a702720349f298316","target":"graph","created_at":"2026-05-18T01:07:47Z","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":"Let $E$ be a vector bundle of rank $r\\geq 2$ on a smooth projective curve $C$ of genus $g \\geq 2$ over an algebraically closed field $K$ of arbitrary characteristic. For any integer with $1\\le k\\le r-1$ we define $${\\se}_k(E):=k\\deg E-r\\max\\deg F.$$ where the maximum is taken over all subbundles $F$ of rank $k$ of $E$. The ${s}_k$ gives a stratification of the moduli space ${\\cal M}(r,d)$ of stable vector bundles of rank $r$ and degree on $d$ on $C$ into locally closed subsets ${\\calM}(r,d,k,s)$ according to the value of $s$ and $k$. There is a component ${\\cal M}^0(r,d,k,s)$ of ${\\cal M}(r,d,","authors_text":"H. Lange, L. Brambila-Paz","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"alg-geom","submitted_at":"1997-08-18T07:52:26Z","title":"A stratification of the moduli space of vector bundles on curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9708014","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":"sha256:5c6e24fedf10f01a109a30944c06ec811d8426938b7568d6bc42195262033178","target":"record","created_at":"2026-05-18T01:07:47Z","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":"b2cf8b6c29230a37ccb941351da377e443c982cac4606b522938507f8cd42951","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1997-08-18T07:52:26Z","title_canon_sha256":"a3794bcaecd194a29cc836b352ff6eb12e930b5ee8bf7465a986f1dd4b99a879"},"schema_version":"1.0","source":{"id":"alg-geom/9708014","kind":"arxiv","version":1}},"canonical_sha256":"302764e9b05d3840a4a214e20e412ca33c081648ea537f3d4729c8be134add70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"302764e9b05d3840a4a214e20e412ca33c081648ea537f3d4729c8be134add70","first_computed_at":"2026-05-18T01:07:47.039459Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:47.039459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MC1xshTb6Mauk3MznCashTRZ5cinN101NmX5ltYgLl82ntfBMk/ce+2s5XWacBdu4KAfFX3O/5fSGfhyP7ZDDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:47.039885Z","signed_message":"canonical_sha256_bytes"},"source_id":"alg-geom/9708014","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c6e24fedf10f01a109a30944c06ec811d8426938b7568d6bc42195262033178","sha256:4489eb89d55487923099fb0d7463df7264b0d7564669724a702720349f298316"],"state_sha256":"c561053bdac83fdd80dfe8a210da1f5a3d31f66cd63c3395acd4d71dc2cf0a44"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T6ARcGkuVnc02aOZB1YxCbqS+LxFmoxzQN17mwEyxjuBh5m+VZFXc7WkRWZH8dWHe2YOE84TtGJV5lC2Bco1Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T15:04:36.060264Z","bundle_sha256":"99f0aa873e25d9629eb4347ebe362b63b40f8e555dfd5a4c744f0eb5a5c2b187"}}