{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:3YLW26ZIHH5HVXMF2C25F7E7BZ","short_pith_number":"pith:3YLW26ZI","canonical_record":{"source":{"id":"1112.1886","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-08T17:19:02Z","cross_cats_sorted":[],"title_canon_sha256":"2980b08e756687e4fc3748558c0181937c5f639ebf9ae2828c583dcf3b5facca","abstract_canon_sha256":"44a47c4ee0120af5478df9643c537e08269483f1fed0580bf80a7d20b417dc79"},"schema_version":"1.0"},"canonical_sha256":"de176d7b2839fa7add85d0b5d2fc9f0e73db498a84580871593ec40bc9425947","source":{"kind":"arxiv","id":"1112.1886","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1886","created_at":"2026-05-18T01:37:29Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1886v4","created_at":"2026-05-18T01:37:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1886","created_at":"2026-05-18T01:37:29Z"},{"alias_kind":"pith_short_12","alias_value":"3YLW26ZIHH5H","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"3YLW26ZIHH5HVXMF","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"3YLW26ZI","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:3YLW26ZIHH5HVXMF2C25F7E7BZ","target":"record","payload":{"canonical_record":{"source":{"id":"1112.1886","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-08T17:19:02Z","cross_cats_sorted":[],"title_canon_sha256":"2980b08e756687e4fc3748558c0181937c5f639ebf9ae2828c583dcf3b5facca","abstract_canon_sha256":"44a47c4ee0120af5478df9643c537e08269483f1fed0580bf80a7d20b417dc79"},"schema_version":"1.0"},"canonical_sha256":"de176d7b2839fa7add85d0b5d2fc9f0e73db498a84580871593ec40bc9425947","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:29.083895Z","signature_b64":"mPDq+CMxkY9hjkshPIGjQ3+RTCn9VqT2INFj7UklRBTHMROnkbMDWLrgruRx3WOos3k9bTISVlCxzip98wsYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de176d7b2839fa7add85d0b5d2fc9f0e73db498a84580871593ec40bc9425947","last_reissued_at":"2026-05-18T01:37:29.083260Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:29.083260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.1886","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ubqDabKTgUxxc+KTMHPdMPaNVih/0Xx8Iyic5Rd41Y4JVKLdEi+GjAkJ42np5mffWSPK9vuPrdDk2IifXRRBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T22:23:03.816097Z"},"content_sha256":"c5738282684dc2443da4f0f774cafe8baa521ea654e0da430a80f56387cbb3ce","schema_version":"1.0","event_id":"sha256:c5738282684dc2443da4f0f774cafe8baa521ea654e0da430a80f56387cbb3ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:3YLW26ZIHH5HVXMF2C25F7E7BZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A GIT interpretration of the Harder-Narasimhan filtration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alfonso Zamora, Ignacio Sols, Tomas L. Gomez","submitted_at":"2011-12-08T17:19:02Z","abstract_excerpt":"An unstable torsion free sheaf on a smooth projective variety gives a GIT unstable point in certain Quot scheme. To a GIT unstable point, Kempf associates a \"maximally destabilizing\" 1-parameter subgroup, and this induces a filtration of the torsion free sheaf. We show that this filtration coincides with the Harder-Narasimhan filtration."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1886","kind":"arxiv","version":4},"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":"2026-05-18T01:37:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5OuJuboIPl40Ol3d1gfVwnjLkiZznLoJbyPskC/XgNyisHAoKqMVzZTxbzV/R8s9NGU2/JhIM32DYqcYFAmTAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T22:23:03.816450Z"},"content_sha256":"b805cc6d3e5d8cb07b134004edf22f2cee4fce3ac79bc43455edcdb4133fad89","schema_version":"1.0","event_id":"sha256:b805cc6d3e5d8cb07b134004edf22f2cee4fce3ac79bc43455edcdb4133fad89"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3YLW26ZIHH5HVXMF2C25F7E7BZ/bundle.json","state_url":"https://pith.science/pith/3YLW26ZIHH5HVXMF2C25F7E7BZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3YLW26ZIHH5HVXMF2C25F7E7BZ/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":"2026-06-27T22:23:03Z","links":{"resolver":"https://pith.science/pith/3YLW26ZIHH5HVXMF2C25F7E7BZ","bundle":"https://pith.science/pith/3YLW26ZIHH5HVXMF2C25F7E7BZ/bundle.json","state":"https://pith.science/pith/3YLW26ZIHH5HVXMF2C25F7E7BZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3YLW26ZIHH5HVXMF2C25F7E7BZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3YLW26ZIHH5HVXMF2C25F7E7BZ","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":"44a47c4ee0120af5478df9643c537e08269483f1fed0580bf80a7d20b417dc79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-08T17:19:02Z","title_canon_sha256":"2980b08e756687e4fc3748558c0181937c5f639ebf9ae2828c583dcf3b5facca"},"schema_version":"1.0","source":{"id":"1112.1886","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1886","created_at":"2026-05-18T01:37:29Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1886v4","created_at":"2026-05-18T01:37:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1886","created_at":"2026-05-18T01:37:29Z"},{"alias_kind":"pith_short_12","alias_value":"3YLW26ZIHH5H","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"3YLW26ZIHH5HVXMF","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"3YLW26ZI","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:b805cc6d3e5d8cb07b134004edf22f2cee4fce3ac79bc43455edcdb4133fad89","target":"graph","created_at":"2026-05-18T01:37:29Z","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":"An unstable torsion free sheaf on a smooth projective variety gives a GIT unstable point in certain Quot scheme. To a GIT unstable point, Kempf associates a \"maximally destabilizing\" 1-parameter subgroup, and this induces a filtration of the torsion free sheaf. We show that this filtration coincides with the Harder-Narasimhan filtration.","authors_text":"Alfonso Zamora, Ignacio Sols, Tomas L. Gomez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-08T17:19:02Z","title":"A GIT interpretration of the Harder-Narasimhan filtration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1886","kind":"arxiv","version":4},"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:c5738282684dc2443da4f0f774cafe8baa521ea654e0da430a80f56387cbb3ce","target":"record","created_at":"2026-05-18T01:37:29Z","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":"44a47c4ee0120af5478df9643c537e08269483f1fed0580bf80a7d20b417dc79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-08T17:19:02Z","title_canon_sha256":"2980b08e756687e4fc3748558c0181937c5f639ebf9ae2828c583dcf3b5facca"},"schema_version":"1.0","source":{"id":"1112.1886","kind":"arxiv","version":4}},"canonical_sha256":"de176d7b2839fa7add85d0b5d2fc9f0e73db498a84580871593ec40bc9425947","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de176d7b2839fa7add85d0b5d2fc9f0e73db498a84580871593ec40bc9425947","first_computed_at":"2026-05-18T01:37:29.083260Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:29.083260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mPDq+CMxkY9hjkshPIGjQ3+RTCn9VqT2INFj7UklRBTHMROnkbMDWLrgruRx3WOos3k9bTISVlCxzip98wsYCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:29.083895Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1886","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5738282684dc2443da4f0f774cafe8baa521ea654e0da430a80f56387cbb3ce","sha256:b805cc6d3e5d8cb07b134004edf22f2cee4fce3ac79bc43455edcdb4133fad89"],"state_sha256":"99e77fb291a9e44a3c39bef3422a5780183bc57439830f3ce11c49206889faab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Q8y4NDpS+TBu2GSQH46Ocz3Hs+dGI92GmNwlhTSVvD3ClsdPURpztF36yvWoczesyIBLSp5je0tmTYMH56gDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T22:23:03.818253Z","bundle_sha256":"12a38ac9f2240be3fc0f9e0e2379c74e958b88dcffca94397b4f5131ef961849"}}