{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:M52PEYAAWEMCTPR2FHWKCO5GQT","short_pith_number":"pith:M52PEYAA","schema_version":"1.0","canonical_sha256":"6774f26000b11829be3a29eca13ba684f0809451109c04d272ade13d4f75434f","source":{"kind":"arxiv","id":"1610.07998","version":3},"attestation_state":"computed","paper":{"title":"Stability and coercivity for toric polarizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Tomoyuki Hisamoto","submitted_at":"2016-10-25T18:15:25Z","abstract_excerpt":"We introduce uniform K-stability and its relationship with the coercivity property of the K-energy functional, for general polarized manifolds. Since the automorphism groups are not necessarily finite, size of the norm measuring uniformity should be reduced with respect to the group action. About this point we explain that it is enough to take the reduced norm for a single sub-torus, actually the center, in the cscK problem. Our main theorem then describes the slope of the reduced J-functional along any torus-equivariant test configuration. In the toric case it is shown that the uniform stabil"},"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":"1610.07998","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-25T18:15:25Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"2589f9ea508c08a6e759bfa33b20644d9175ac1bedf61b0d653658b938cfb2d0","abstract_canon_sha256":"540c863ea86bb9bd05e11e3554003478ac6d82b57f10a66dbf826d439e5fb4ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:17:14.974705Z","signature_b64":"giDRdn+DTh8hz7xkNSxV0kF0wzv0o7TJinlkFO2EASGbrDJ01vwxTwEq+Fh7+4W9ik4XzAHrinKjiqTG+GITCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6774f26000b11829be3a29eca13ba684f0809451109c04d272ade13d4f75434f","last_reissued_at":"2026-07-05T01:17:14.974323Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:17:14.974323Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability and coercivity for toric polarizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Tomoyuki Hisamoto","submitted_at":"2016-10-25T18:15:25Z","abstract_excerpt":"We introduce uniform K-stability and its relationship with the coercivity property of the K-energy functional, for general polarized manifolds. Since the automorphism groups are not necessarily finite, size of the norm measuring uniformity should be reduced with respect to the group action. About this point we explain that it is enough to take the reduced norm for a single sub-torus, actually the center, in the cscK problem. Our main theorem then describes the slope of the reduced J-functional along any torus-equivariant test configuration. In the toric case it is shown that the uniform stabil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07998","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1610.07998/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":"1610.07998","created_at":"2026-07-05T01:17:14.974389+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.07998v3","created_at":"2026-07-05T01:17:14.974389+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07998","created_at":"2026-07-05T01:17:14.974389+00:00"},{"alias_kind":"pith_short_12","alias_value":"M52PEYAAWEMC","created_at":"2026-07-05T01:17:14.974389+00:00"},{"alias_kind":"pith_short_16","alias_value":"M52PEYAAWEMCTPR2","created_at":"2026-07-05T01:17:14.974389+00:00"},{"alias_kind":"pith_short_8","alias_value":"M52PEYAA","created_at":"2026-07-05T01:17:14.974389+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.06688","citing_title":"Poisson K-stability and the semiclassical Yau--Tian--Donaldson correspondence","ref_index":59,"is_internal_anchor":true},{"citing_arxiv_id":"2506.02360","citing_title":"Relative uniform $K$-stability over models implies existence of extremal metrics","ref_index":24,"is_internal_anchor":false},{"citing_arxiv_id":"2605.08789","citing_title":"On coupled K\\\"ahler-Einstein metrics and weighted solitons on Fano manifolds","ref_index":42,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/M52PEYAAWEMCTPR2FHWKCO5GQT","json":"https://pith.science/pith/M52PEYAAWEMCTPR2FHWKCO5GQT.json","graph_json":"https://pith.science/api/pith-number/M52PEYAAWEMCTPR2FHWKCO5GQT/graph.json","events_json":"https://pith.science/api/pith-number/M52PEYAAWEMCTPR2FHWKCO5GQT/events.json","paper":"https://pith.science/paper/M52PEYAA"},"agent_actions":{"view_html":"https://pith.science/pith/M52PEYAAWEMCTPR2FHWKCO5GQT","download_json":"https://pith.science/pith/M52PEYAAWEMCTPR2FHWKCO5GQT.json","view_paper":"https://pith.science/paper/M52PEYAA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.07998&json=true","fetch_graph":"https://pith.science/api/pith-number/M52PEYAAWEMCTPR2FHWKCO5GQT/graph.json","fetch_events":"https://pith.science/api/pith-number/M52PEYAAWEMCTPR2FHWKCO5GQT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M52PEYAAWEMCTPR2FHWKCO5GQT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M52PEYAAWEMCTPR2FHWKCO5GQT/action/storage_attestation","attest_author":"https://pith.science/pith/M52PEYAAWEMCTPR2FHWKCO5GQT/action/author_attestation","sign_citation":"https://pith.science/pith/M52PEYAAWEMCTPR2FHWKCO5GQT/action/citation_signature","submit_replication":"https://pith.science/pith/M52PEYAAWEMCTPR2FHWKCO5GQT/action/replication_record"}},"created_at":"2026-07-05T01:17:14.974389+00:00","updated_at":"2026-07-05T01:17:14.974389+00:00"}