{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4WEZXAZGOBQTH662MQHA7QKINH","short_pith_number":"pith:4WEZXAZG","canonical_record":{"source":{"id":"1609.01834","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-09-07T04:37:15Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"8c1c219307ff335074645b4d6fbbd980d925a1061dc8a800e22cae77fff23031","abstract_canon_sha256":"7f64b2b8208b22c848bdea365e8c2b217ca7a3ddee9f4771f7c148e47cbd0bd5"},"schema_version":"1.0"},"canonical_sha256":"e5899b8326706133fbda640e0fc14869ebc6d950364ebdbb9ce05284b6a5a7c0","source":{"kind":"arxiv","id":"1609.01834","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01834","created_at":"2026-05-18T01:05:09Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01834v1","created_at":"2026-05-18T01:05:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01834","created_at":"2026-05-18T01:05:09Z"},{"alias_kind":"pith_short_12","alias_value":"4WEZXAZGOBQT","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4WEZXAZGOBQTH662","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4WEZXAZG","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4WEZXAZGOBQTH662MQHA7QKINH","target":"record","payload":{"canonical_record":{"source":{"id":"1609.01834","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-09-07T04:37:15Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"8c1c219307ff335074645b4d6fbbd980d925a1061dc8a800e22cae77fff23031","abstract_canon_sha256":"7f64b2b8208b22c848bdea365e8c2b217ca7a3ddee9f4771f7c148e47cbd0bd5"},"schema_version":"1.0"},"canonical_sha256":"e5899b8326706133fbda640e0fc14869ebc6d950364ebdbb9ce05284b6a5a7c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:09.928847Z","signature_b64":"PNXbi0BzSv6IiAyXl//mHjW/VUnAA5Q9Z8Cl+VQ92nHtTNbjhsiMpAUAlAFU9xazCZB5talv/6dQOHUAZPktDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5899b8326706133fbda640e0fc14869ebc6d950364ebdbb9ce05284b6a5a7c0","last_reissued_at":"2026-05-18T01:05:09.928233Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:09.928233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.01834","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zj1YJtEENq2Eq5Ys9GiUZXWBw22+ZCZnnFQbfXC03mbBjDkbfnlAWZm+plF5onsC6RSzcDJ+uwlqrPmB42uXAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:14:04.995589Z"},"content_sha256":"7ad339b67c0ed42148405857179a02ff934ed2569a1dcfe5b4b0f41e17035fe5","schema_version":"1.0","event_id":"sha256:7ad339b67c0ed42148405857179a02ff934ed2569a1dcfe5b4b0f41e17035fe5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4WEZXAZGOBQTH662MQHA7QKINH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the extension and smoothing of the Calabi flow on complex tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Hongnian Huang","submitted_at":"2016-09-07T04:37:15Z","abstract_excerpt":"In this paper, we continue to study the Calabi flow on complex tori. We develop a new method to obtain an explicit bound of the curvature of the Calabi flow. As an application, we show that when $n=2$, the Calabi flow starting from a weak K\\\"ahler metric will become smooth immediately. It implies that in our settings, the weak minimizer of the Mabuchi energy is a smooth one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01834","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":""},"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":"2026-05-18T01:05:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kpu5lZze1urJSBsQ2bOknRE7LiGrGcdIXISZI90HcCp5u/DekZydaCptpmw69UbpAoZ0yR4coSdJSix2NoFdDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:14:04.995937Z"},"content_sha256":"d40ca203b8fd792b3e0ffff2e3da06f22566c6f1d680d4ddb69e8169d5cfbdc0","schema_version":"1.0","event_id":"sha256:d40ca203b8fd792b3e0ffff2e3da06f22566c6f1d680d4ddb69e8169d5cfbdc0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4WEZXAZGOBQTH662MQHA7QKINH/bundle.json","state_url":"https://pith.science/pith/4WEZXAZGOBQTH662MQHA7QKINH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4WEZXAZGOBQTH662MQHA7QKINH/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":"2026-06-11T12:14:04Z","links":{"resolver":"https://pith.science/pith/4WEZXAZGOBQTH662MQHA7QKINH","bundle":"https://pith.science/pith/4WEZXAZGOBQTH662MQHA7QKINH/bundle.json","state":"https://pith.science/pith/4WEZXAZGOBQTH662MQHA7QKINH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4WEZXAZGOBQTH662MQHA7QKINH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4WEZXAZGOBQTH662MQHA7QKINH","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":"7f64b2b8208b22c848bdea365e8c2b217ca7a3ddee9f4771f7c148e47cbd0bd5","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-09-07T04:37:15Z","title_canon_sha256":"8c1c219307ff335074645b4d6fbbd980d925a1061dc8a800e22cae77fff23031"},"schema_version":"1.0","source":{"id":"1609.01834","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01834","created_at":"2026-05-18T01:05:09Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01834v1","created_at":"2026-05-18T01:05:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01834","created_at":"2026-05-18T01:05:09Z"},{"alias_kind":"pith_short_12","alias_value":"4WEZXAZGOBQT","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4WEZXAZGOBQTH662","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4WEZXAZG","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:d40ca203b8fd792b3e0ffff2e3da06f22566c6f1d680d4ddb69e8169d5cfbdc0","target":"graph","created_at":"2026-05-18T01:05:09Z","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 this paper, we continue to study the Calabi flow on complex tori. We develop a new method to obtain an explicit bound of the curvature of the Calabi flow. As an application, we show that when $n=2$, the Calabi flow starting from a weak K\\\"ahler metric will become smooth immediately. It implies that in our settings, the weak minimizer of the Mabuchi energy is a smooth one.","authors_text":"Hongnian Huang","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-09-07T04:37:15Z","title":"On the extension and smoothing of the Calabi flow on complex tori"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01834","kind":"arxiv","version":1},"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":"sha256:7ad339b67c0ed42148405857179a02ff934ed2569a1dcfe5b4b0f41e17035fe5","target":"record","created_at":"2026-05-18T01:05:09Z","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":"7f64b2b8208b22c848bdea365e8c2b217ca7a3ddee9f4771f7c148e47cbd0bd5","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-09-07T04:37:15Z","title_canon_sha256":"8c1c219307ff335074645b4d6fbbd980d925a1061dc8a800e22cae77fff23031"},"schema_version":"1.0","source":{"id":"1609.01834","kind":"arxiv","version":1}},"canonical_sha256":"e5899b8326706133fbda640e0fc14869ebc6d950364ebdbb9ce05284b6a5a7c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5899b8326706133fbda640e0fc14869ebc6d950364ebdbb9ce05284b6a5a7c0","first_computed_at":"2026-05-18T01:05:09.928233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:09.928233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PNXbi0BzSv6IiAyXl//mHjW/VUnAA5Q9Z8Cl+VQ92nHtTNbjhsiMpAUAlAFU9xazCZB5talv/6dQOHUAZPktDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:09.928847Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.01834","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ad339b67c0ed42148405857179a02ff934ed2569a1dcfe5b4b0f41e17035fe5","sha256:d40ca203b8fd792b3e0ffff2e3da06f22566c6f1d680d4ddb69e8169d5cfbdc0"],"state_sha256":"15c1b83d15137918ae2d1f4631b5f781c42179c4fbee93af0a3f98862a1135a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1QnzADUuZsyU1pe00SvHjoMr/ADgK3+uvll7yTKz7moCe2a7IIe6LmYumHp9msw4920HB+kx0eVBMf8U8XL7DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T12:14:04.997848Z","bundle_sha256":"a490e5e49a66d4f81c9bc14aff643ad95007af0d46c859ad3b9101b5394122f4"}}