{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:RBJ2HEON66HPZV5M766H5YZ5LP","short_pith_number":"pith:RBJ2HEON","canonical_record":{"source":{"id":"1511.00178","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-31T21:30:48Z","cross_cats_sorted":[],"title_canon_sha256":"c9176c1c6e277ed50c7cf5f1cf62dbcbbbeccde1afb9272c5dc36662fdc980e3","abstract_canon_sha256":"ee08a7a68f16e19034a20f3b750bcf84a28d465b0d88d1dd08cf99ff924dca78"},"schema_version":"1.0"},"canonical_sha256":"8853a391cdf78efcd7acffbc7ee33d5be7dfd3afeafd0285473ab4230e8f6c5a","source":{"kind":"arxiv","id":"1511.00178","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.00178","created_at":"2026-05-18T01:19:49Z"},{"alias_kind":"arxiv_version","alias_value":"1511.00178v2","created_at":"2026-05-18T01:19:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00178","created_at":"2026-05-18T01:19:49Z"},{"alias_kind":"pith_short_12","alias_value":"RBJ2HEON66HP","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RBJ2HEON66HPZV5M","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RBJ2HEON","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:RBJ2HEON66HPZV5M766H5YZ5LP","target":"record","payload":{"canonical_record":{"source":{"id":"1511.00178","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-31T21:30:48Z","cross_cats_sorted":[],"title_canon_sha256":"c9176c1c6e277ed50c7cf5f1cf62dbcbbbeccde1afb9272c5dc36662fdc980e3","abstract_canon_sha256":"ee08a7a68f16e19034a20f3b750bcf84a28d465b0d88d1dd08cf99ff924dca78"},"schema_version":"1.0"},"canonical_sha256":"8853a391cdf78efcd7acffbc7ee33d5be7dfd3afeafd0285473ab4230e8f6c5a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:49.482213Z","signature_b64":"+7sZGE3BD0O6TQZ6f9OqrlXCQ7iarrjCdTqdEUhAiIHRi1dU0DXG9bV8QttFfSSimC4eD88pNvMg8ts9Rsb/Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8853a391cdf78efcd7acffbc7ee33d5be7dfd3afeafd0285473ab4230e8f6c5a","last_reissued_at":"2026-05-18T01:19:49.481773Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:49.481773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.00178","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kX4XA7G9bwRGP4kvut5YVOjT5Quh0GbTdQ+EUHMx83CnoBTJesp427VyXGLTmQrZkiOe5PXpPMQajp3sprElBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T12:39:35.969538Z"},"content_sha256":"b1992d7b982c1683b60473619662221aeb27b8e5650da5ccf378513a2f657575","schema_version":"1.0","event_id":"sha256:b1992d7b982c1683b60473619662221aeb27b8e5650da5ccf378513a2f657575"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:RBJ2HEON66HPZV5M766H5YZ5LP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subharmonicity of conic Mabuchi's functional, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Long Li","submitted_at":"2015-10-31T21:30:48Z","abstract_excerpt":"The purpose of this paper is to generalize the convexity of Mabuchi's functional to the conic setting. We first established a frame to study conic cscK metrics, and then the conic Mabuchi functional was introduced in such a way that conic cscK metrics are its critical points. Finally we proved the convexity of the conic Mabuchi functional along any conic geodesics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00178","kind":"arxiv","version":2},"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":"2026-05-18T01:19:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RaegxqQs99hwjNx0r0HqUz3GTATCFvqLGqFewjT+mB1O5CKed8U+a5TbzCf5Eu/VzExFC+WPV9l17jcGDMMeCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T12:39:35.969884Z"},"content_sha256":"8cca44a4dc48e28ea81dfc968ee3ab1122536893ce13305c56a14fa1a6e0af04","schema_version":"1.0","event_id":"sha256:8cca44a4dc48e28ea81dfc968ee3ab1122536893ce13305c56a14fa1a6e0af04"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RBJ2HEON66HPZV5M766H5YZ5LP/bundle.json","state_url":"https://pith.science/pith/RBJ2HEON66HPZV5M766H5YZ5LP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RBJ2HEON66HPZV5M766H5YZ5LP/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":"2026-06-03T12:39:35Z","links":{"resolver":"https://pith.science/pith/RBJ2HEON66HPZV5M766H5YZ5LP","bundle":"https://pith.science/pith/RBJ2HEON66HPZV5M766H5YZ5LP/bundle.json","state":"https://pith.science/pith/RBJ2HEON66HPZV5M766H5YZ5LP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RBJ2HEON66HPZV5M766H5YZ5LP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RBJ2HEON66HPZV5M766H5YZ5LP","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":"ee08a7a68f16e19034a20f3b750bcf84a28d465b0d88d1dd08cf99ff924dca78","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-31T21:30:48Z","title_canon_sha256":"c9176c1c6e277ed50c7cf5f1cf62dbcbbbeccde1afb9272c5dc36662fdc980e3"},"schema_version":"1.0","source":{"id":"1511.00178","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.00178","created_at":"2026-05-18T01:19:49Z"},{"alias_kind":"arxiv_version","alias_value":"1511.00178v2","created_at":"2026-05-18T01:19:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00178","created_at":"2026-05-18T01:19:49Z"},{"alias_kind":"pith_short_12","alias_value":"RBJ2HEON66HP","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RBJ2HEON66HPZV5M","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RBJ2HEON","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:8cca44a4dc48e28ea81dfc968ee3ab1122536893ce13305c56a14fa1a6e0af04","target":"graph","created_at":"2026-05-18T01:19:49Z","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":"The purpose of this paper is to generalize the convexity of Mabuchi's functional to the conic setting. We first established a frame to study conic cscK metrics, and then the conic Mabuchi functional was introduced in such a way that conic cscK metrics are its critical points. Finally we proved the convexity of the conic Mabuchi functional along any conic geodesics.","authors_text":"Long Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-31T21:30:48Z","title":"Subharmonicity of conic Mabuchi's functional, I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00178","kind":"arxiv","version":2},"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:b1992d7b982c1683b60473619662221aeb27b8e5650da5ccf378513a2f657575","target":"record","created_at":"2026-05-18T01:19:49Z","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":"ee08a7a68f16e19034a20f3b750bcf84a28d465b0d88d1dd08cf99ff924dca78","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-31T21:30:48Z","title_canon_sha256":"c9176c1c6e277ed50c7cf5f1cf62dbcbbbeccde1afb9272c5dc36662fdc980e3"},"schema_version":"1.0","source":{"id":"1511.00178","kind":"arxiv","version":2}},"canonical_sha256":"8853a391cdf78efcd7acffbc7ee33d5be7dfd3afeafd0285473ab4230e8f6c5a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8853a391cdf78efcd7acffbc7ee33d5be7dfd3afeafd0285473ab4230e8f6c5a","first_computed_at":"2026-05-18T01:19:49.481773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:49.481773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+7sZGE3BD0O6TQZ6f9OqrlXCQ7iarrjCdTqdEUhAiIHRi1dU0DXG9bV8QttFfSSimC4eD88pNvMg8ts9Rsb/Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:49.482213Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.00178","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1992d7b982c1683b60473619662221aeb27b8e5650da5ccf378513a2f657575","sha256:8cca44a4dc48e28ea81dfc968ee3ab1122536893ce13305c56a14fa1a6e0af04"],"state_sha256":"be9e392936c167ee7131be26651510742b0363b84ad582aab958be348f56896a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q29dKedg+ngCk9FGz6aS91Di3F4O+k1Sxl6Klq1FBYhP9ZpYkk+ALwSWnSUGh+63nsNSGf9ZCv2CgQLPfhiGCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T12:39:35.971995Z","bundle_sha256":"34ac8cfdca40d761883bce69bdb3ed6da1571f14ef72963b3367165c9bcf340a"}}