{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:PBSJDD6EKEHAEACDPUSPKGCNMG","short_pith_number":"pith:PBSJDD6E","schema_version":"1.0","canonical_sha256":"7864918fc4510e0200437d24f5184d619d86dc404a3fe037fdbaafa65239f40b","source":{"kind":"arxiv","id":"math/0611002","version":1},"attestation_state":"computed","paper":{"title":"Extremal metrics and K-stability (PhD thesis)","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"G\\'abor Sz\\'ekelyhidi","submitted_at":"2006-10-31T22:14:05Z","abstract_excerpt":"In this thesis we study the relationship between the existence of canonical metrics on a complex manifold and stability in the sense of geometric invariant theory. We introduce a modification of K-stability of a polarised variety which we conjecture to be equivalent to the existence of an extremal metric in the polarisation class. A variant for a complete extremal metric on the complement of a smooth divisor is also given. On toric surfaces we prove a Jordan-Holder type theorem for decomposing semistable surfaces into stable pieces. On a ruled surface we compute the infimum of the Calabi funct"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0611002","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2006-10-31T22:14:05Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"9a29bb219e35555f58e33aaedd492495484322cef74b5ec3ad5012efa3204a8e","abstract_canon_sha256":"b30cb1de564ba6be9c5cf2d7c38e0f1723df2653a03bc2dc1704c4ea804b0491"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:57:37.219378Z","signature_b64":"DaM+vf7/WUR4J2LQpk76siw4QVoXjk2cSq8JPQFq+r2vNZ/Ui42GPGIaGLomPeEAis2ckS/NRjAx4RGteQkhDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7864918fc4510e0200437d24f5184d619d86dc404a3fe037fdbaafa65239f40b","last_reissued_at":"2026-07-04T14:57:37.218993Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:57:37.218993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extremal metrics and K-stability (PhD thesis)","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"G\\'abor Sz\\'ekelyhidi","submitted_at":"2006-10-31T22:14:05Z","abstract_excerpt":"In this thesis we study the relationship between the existence of canonical metrics on a complex manifold and stability in the sense of geometric invariant theory. We introduce a modification of K-stability of a polarised variety which we conjecture to be equivalent to the existence of an extremal metric in the polarisation class. A variant for a complete extremal metric on the complement of a smooth divisor is also given. On toric surfaces we prove a Jordan-Holder type theorem for decomposing semistable surfaces into stable pieces. On a ruled surface we compute the infimum of the Calabi funct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611002","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0611002/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0611002","created_at":"2026-07-04T14:57:37.219057+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0611002v1","created_at":"2026-07-04T14:57:37.219057+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611002","created_at":"2026-07-04T14:57:37.219057+00:00"},{"alias_kind":"pith_short_12","alias_value":"PBSJDD6EKEHA","created_at":"2026-07-04T14:57:37.219057+00:00"},{"alias_kind":"pith_short_16","alias_value":"PBSJDD6EKEHAEACD","created_at":"2026-07-04T14:57:37.219057+00:00"},{"alias_kind":"pith_short_8","alias_value":"PBSJDD6E","created_at":"2026-07-04T14:57:37.219057+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2607.06688","citing_title":"Poisson K-stability and the semiclassical Yau--Tian--Donaldson correspondence","ref_index":88,"is_internal_anchor":true},{"citing_arxiv_id":"2505.19257","citing_title":"Existence of Conical Higher cscK Metrics on a Minimal Ruled Surface","ref_index":38,"is_internal_anchor":true},{"citing_arxiv_id":"2605.01179","citing_title":"Poincar\\'e type J-equation","ref_index":31,"is_internal_anchor":false},{"citing_arxiv_id":"2604.14040","citing_title":"A lower bound on the Calabi functional for a degeneration of polarized varieties","ref_index":15,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PBSJDD6EKEHAEACDPUSPKGCNMG","json":"https://pith.science/pith/PBSJDD6EKEHAEACDPUSPKGCNMG.json","graph_json":"https://pith.science/api/pith-number/PBSJDD6EKEHAEACDPUSPKGCNMG/graph.json","events_json":"https://pith.science/api/pith-number/PBSJDD6EKEHAEACDPUSPKGCNMG/events.json","paper":"https://pith.science/paper/PBSJDD6E"},"agent_actions":{"view_html":"https://pith.science/pith/PBSJDD6EKEHAEACDPUSPKGCNMG","download_json":"https://pith.science/pith/PBSJDD6EKEHAEACDPUSPKGCNMG.json","view_paper":"https://pith.science/paper/PBSJDD6E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0611002&json=true","fetch_graph":"https://pith.science/api/pith-number/PBSJDD6EKEHAEACDPUSPKGCNMG/graph.json","fetch_events":"https://pith.science/api/pith-number/PBSJDD6EKEHAEACDPUSPKGCNMG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PBSJDD6EKEHAEACDPUSPKGCNMG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PBSJDD6EKEHAEACDPUSPKGCNMG/action/storage_attestation","attest_author":"https://pith.science/pith/PBSJDD6EKEHAEACDPUSPKGCNMG/action/author_attestation","sign_citation":"https://pith.science/pith/PBSJDD6EKEHAEACDPUSPKGCNMG/action/citation_signature","submit_replication":"https://pith.science/pith/PBSJDD6EKEHAEACDPUSPKGCNMG/action/replication_record"}},"created_at":"2026-07-04T14:57:37.219057+00:00","updated_at":"2026-07-04T14:57:37.219057+00:00"}