{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FG2KH7UAHOFBTBBUI3FW3JXAZP","short_pith_number":"pith:FG2KH7UA","schema_version":"1.0","canonical_sha256":"29b4a3fe803b8a19843446cb6da6e0cbeca8c123becca5423c1e3305d3bb2657","source":{"kind":"arxiv","id":"1606.03019","version":5},"attestation_state":"computed","paper":{"title":"Bergman iteration and $C^{\\infty}$-convergence towards K\\\"ahler-Ricci flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ryosuke Takahashi","submitted_at":"2016-06-09T16:32:02Z","abstract_excerpt":"On a polarized manifold $(X,L)$, the Bergman iteration $\\phi_k^{(m)}$ is defined as a sequence of Bergman metrics on $L$ with two integer parameters $k, m$. We study the relation between the K\\\"ahler-Ricci flow $\\phi_t$ at any time $t \\geq 0$ and the limiting behavior of metrics $\\phi_k^{(m)}$ when $m=m(k)$ and the ratio $m/k$ approaches to $t$ as $k \\to \\infty$. Mainly, three settings are investigated: the case when $L$ is a general polarization on a Calabi-Yau manifold $X$ and the case when $L=\\pm K_X$ is the (anti-) canonical bundle. Recently, Berman showed that the convergence $\\phi_k^{(m)"},"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":"1606.03019","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-09T16:32:02Z","cross_cats_sorted":[],"title_canon_sha256":"2d7bcc50ac931263c16a698e71edc729853d375a8823bbd15f0af736dea2806b","abstract_canon_sha256":"f9be8e7c47c608dc1601332f1c749fc7a570e4b8599f46f3c4f2a2777a5cf802"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:26.303731Z","signature_b64":"8avBf6A5ebJo3fKnzo8PBdoPNLOuONjeG0Cw/znsiGIt5nOay7Mq6kNM/lPR573wVmRWI/FrgosqCd9G7asDAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29b4a3fe803b8a19843446cb6da6e0cbeca8c123becca5423c1e3305d3bb2657","last_reissued_at":"2026-05-17T23:51:26.303232Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:26.303232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bergman iteration and $C^{\\infty}$-convergence towards K\\\"ahler-Ricci flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ryosuke Takahashi","submitted_at":"2016-06-09T16:32:02Z","abstract_excerpt":"On a polarized manifold $(X,L)$, the Bergman iteration $\\phi_k^{(m)}$ is defined as a sequence of Bergman metrics on $L$ with two integer parameters $k, m$. We study the relation between the K\\\"ahler-Ricci flow $\\phi_t$ at any time $t \\geq 0$ and the limiting behavior of metrics $\\phi_k^{(m)}$ when $m=m(k)$ and the ratio $m/k$ approaches to $t$ as $k \\to \\infty$. Mainly, three settings are investigated: the case when $L$ is a general polarization on a Calabi-Yau manifold $X$ and the case when $L=\\pm K_X$ is the (anti-) canonical bundle. Recently, Berman showed that the convergence $\\phi_k^{(m)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03019","kind":"arxiv","version":5},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1606.03019","created_at":"2026-05-17T23:51:26.303311+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.03019v5","created_at":"2026-05-17T23:51:26.303311+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03019","created_at":"2026-05-17T23:51:26.303311+00:00"},{"alias_kind":"pith_short_12","alias_value":"FG2KH7UAHOFB","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FG2KH7UAHOFBTBBU","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FG2KH7UA","created_at":"2026-05-18T12:30:15.759754+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FG2KH7UAHOFBTBBUI3FW3JXAZP","json":"https://pith.science/pith/FG2KH7UAHOFBTBBUI3FW3JXAZP.json","graph_json":"https://pith.science/api/pith-number/FG2KH7UAHOFBTBBUI3FW3JXAZP/graph.json","events_json":"https://pith.science/api/pith-number/FG2KH7UAHOFBTBBUI3FW3JXAZP/events.json","paper":"https://pith.science/paper/FG2KH7UA"},"agent_actions":{"view_html":"https://pith.science/pith/FG2KH7UAHOFBTBBUI3FW3JXAZP","download_json":"https://pith.science/pith/FG2KH7UAHOFBTBBUI3FW3JXAZP.json","view_paper":"https://pith.science/paper/FG2KH7UA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.03019&json=true","fetch_graph":"https://pith.science/api/pith-number/FG2KH7UAHOFBTBBUI3FW3JXAZP/graph.json","fetch_events":"https://pith.science/api/pith-number/FG2KH7UAHOFBTBBUI3FW3JXAZP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FG2KH7UAHOFBTBBUI3FW3JXAZP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FG2KH7UAHOFBTBBUI3FW3JXAZP/action/storage_attestation","attest_author":"https://pith.science/pith/FG2KH7UAHOFBTBBUI3FW3JXAZP/action/author_attestation","sign_citation":"https://pith.science/pith/FG2KH7UAHOFBTBBUI3FW3JXAZP/action/citation_signature","submit_replication":"https://pith.science/pith/FG2KH7UAHOFBTBBUI3FW3JXAZP/action/replication_record"}},"created_at":"2026-05-17T23:51:26.303311+00:00","updated_at":"2026-05-17T23:51:26.303311+00:00"}