{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:C4ORPSXOXUBS7A7DPSM6BS2D6I","short_pith_number":"pith:C4ORPSXO","canonical_record":{"source":{"id":"1009.6231","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-30T19:49:16Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"1df56408812a1d9e5c9104aba3e5ec0e60bbf46b9141930bb45027df4058adaa","abstract_canon_sha256":"363bf2f8b250cecdcab2c08d76ad0b4aedbdbdeb9fa6990f0529cf33981a19f2"},"schema_version":"1.0"},"canonical_sha256":"171d17caeebd032f83e37c99e0cb43f2013709eca7964717161fadcda8f35d32","source":{"kind":"arxiv","id":"1009.6231","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.6231","created_at":"2026-05-18T04:34:19Z"},{"alias_kind":"arxiv_version","alias_value":"1009.6231v2","created_at":"2026-05-18T04:34:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.6231","created_at":"2026-05-18T04:34:19Z"},{"alias_kind":"pith_short_12","alias_value":"C4ORPSXOXUBS","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"C4ORPSXOXUBS7A7D","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"C4ORPSXO","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:C4ORPSXOXUBS7A7DPSM6BS2D6I","target":"record","payload":{"canonical_record":{"source":{"id":"1009.6231","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-30T19:49:16Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"1df56408812a1d9e5c9104aba3e5ec0e60bbf46b9141930bb45027df4058adaa","abstract_canon_sha256":"363bf2f8b250cecdcab2c08d76ad0b4aedbdbdeb9fa6990f0529cf33981a19f2"},"schema_version":"1.0"},"canonical_sha256":"171d17caeebd032f83e37c99e0cb43f2013709eca7964717161fadcda8f35d32","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:19.169400Z","signature_b64":"9pMeZ8zn8pWyKXWBHyXqIlSGWDqKV4vE0Ev73ZM+Zm6rNg4//EY63aDWabj1HTPweqtwj9lC9iBSIwMUe+DBCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"171d17caeebd032f83e37c99e0cb43f2013709eca7964717161fadcda8f35d32","last_reissued_at":"2026-05-18T04:34:19.168792Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:19.168792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.6231","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:34:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+tKK9H0I8eJzh3NRd5YyDf7lk14BWaW1hR77aZdE2AMONTv2J5K4HwPPtfz6yV7wnn0NL9+qIdSAE/Tg6N2wBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:07:45.245174Z"},"content_sha256":"63086a9d99aeed866e37c2f2c31056fd23e5e6b6ba5ea2858af5328b5a8b4a83","schema_version":"1.0","event_id":"sha256:63086a9d99aeed866e37c2f2c31056fd23e5e6b6ba5ea2858af5328b5a8b4a83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:C4ORPSXOXUBS7A7DPSM6BS2D6I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Balanced metrics and chow stability of projective bundles over Riemann surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Reza Seyyedali","submitted_at":"2010-09-30T19:49:16Z","abstract_excerpt":"In 1980, I. Morrison proved that slope stability of a vector bundle of rank 2 over a compact Riemann surface implies Chow stability of the projectivization of the bundle with respect to certain polarizations. We generalized Morrison's result to higher rank vector bundles over compact algebraic manifolds of arbitrary dimension that admit constant scalar curvature metric and have discrete automorphism group. In this article, we give a simple proof for polarizations $\\mathcal{O}_{\\mathbb{P}E^*}(d)\\otimes \\pi^* L^k$, where $d$ is a positive integer, $k \\gg 0$ and the base manifold is a compact Rie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.6231","kind":"arxiv","version":2},"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":"2026-05-18T04:34:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hk/P2D5i5gzBkLdovV72WbFA9HmlArCBcmK/etDF30w7ptG0m08SVJPhN5A9u/APhxykfuKK3p4dQceYul9SBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:07:45.245540Z"},"content_sha256":"69b4f964064eb9af5bbc16b0b3af0fbd5f2598ca1d803f65db2b34c19c103fdd","schema_version":"1.0","event_id":"sha256:69b4f964064eb9af5bbc16b0b3af0fbd5f2598ca1d803f65db2b34c19c103fdd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C4ORPSXOXUBS7A7DPSM6BS2D6I/bundle.json","state_url":"https://pith.science/pith/C4ORPSXOXUBS7A7DPSM6BS2D6I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C4ORPSXOXUBS7A7DPSM6BS2D6I/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":"2026-06-23T14:07:45Z","links":{"resolver":"https://pith.science/pith/C4ORPSXOXUBS7A7DPSM6BS2D6I","bundle":"https://pith.science/pith/C4ORPSXOXUBS7A7DPSM6BS2D6I/bundle.json","state":"https://pith.science/pith/C4ORPSXOXUBS7A7DPSM6BS2D6I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C4ORPSXOXUBS7A7DPSM6BS2D6I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:C4ORPSXOXUBS7A7DPSM6BS2D6I","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":"363bf2f8b250cecdcab2c08d76ad0b4aedbdbdeb9fa6990f0529cf33981a19f2","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-30T19:49:16Z","title_canon_sha256":"1df56408812a1d9e5c9104aba3e5ec0e60bbf46b9141930bb45027df4058adaa"},"schema_version":"1.0","source":{"id":"1009.6231","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.6231","created_at":"2026-05-18T04:34:19Z"},{"alias_kind":"arxiv_version","alias_value":"1009.6231v2","created_at":"2026-05-18T04:34:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.6231","created_at":"2026-05-18T04:34:19Z"},{"alias_kind":"pith_short_12","alias_value":"C4ORPSXOXUBS","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"C4ORPSXOXUBS7A7D","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"C4ORPSXO","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:69b4f964064eb9af5bbc16b0b3af0fbd5f2598ca1d803f65db2b34c19c103fdd","target":"graph","created_at":"2026-05-18T04:34:19Z","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":"In 1980, I. Morrison proved that slope stability of a vector bundle of rank 2 over a compact Riemann surface implies Chow stability of the projectivization of the bundle with respect to certain polarizations. We generalized Morrison's result to higher rank vector bundles over compact algebraic manifolds of arbitrary dimension that admit constant scalar curvature metric and have discrete automorphism group. In this article, we give a simple proof for polarizations $\\mathcal{O}_{\\mathbb{P}E^*}(d)\\otimes \\pi^* L^k$, where $d$ is a positive integer, $k \\gg 0$ and the base manifold is a compact Rie","authors_text":"Reza Seyyedali","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-30T19:49:16Z","title":"Balanced metrics and chow stability of projective bundles over Riemann surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.6231","kind":"arxiv","version":2},"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":"sha256:63086a9d99aeed866e37c2f2c31056fd23e5e6b6ba5ea2858af5328b5a8b4a83","target":"record","created_at":"2026-05-18T04:34:19Z","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":"363bf2f8b250cecdcab2c08d76ad0b4aedbdbdeb9fa6990f0529cf33981a19f2","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-30T19:49:16Z","title_canon_sha256":"1df56408812a1d9e5c9104aba3e5ec0e60bbf46b9141930bb45027df4058adaa"},"schema_version":"1.0","source":{"id":"1009.6231","kind":"arxiv","version":2}},"canonical_sha256":"171d17caeebd032f83e37c99e0cb43f2013709eca7964717161fadcda8f35d32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"171d17caeebd032f83e37c99e0cb43f2013709eca7964717161fadcda8f35d32","first_computed_at":"2026-05-18T04:34:19.168792Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:19.168792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9pMeZ8zn8pWyKXWBHyXqIlSGWDqKV4vE0Ev73ZM+Zm6rNg4//EY63aDWabj1HTPweqtwj9lC9iBSIwMUe+DBCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:19.169400Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.6231","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63086a9d99aeed866e37c2f2c31056fd23e5e6b6ba5ea2858af5328b5a8b4a83","sha256:69b4f964064eb9af5bbc16b0b3af0fbd5f2598ca1d803f65db2b34c19c103fdd"],"state_sha256":"6658e3f9624fc4bfdd789dc3ae3642fbe338172113aab5dae869c656ff203bf0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cVyW5BqV4/nTZ+ImBhEhFjllQqOKouaWRXotJoWbZsQsGTN9NS9RO9XzW8ujiXB0ri5EuuOpxjb/r4whaWOvBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:07:45.247525Z","bundle_sha256":"667989379747577883b1ade0abfb19ec9041dc5481cba7124caef8fc7f771a8e"}}