{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JMQXBTUETHQPZ4UJH64YMUNQT6","short_pith_number":"pith:JMQXBTUE","canonical_record":{"source":{"id":"1308.0710","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-03T15:53:31Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"144f0589b2776d53e57cfb2368efb784449242a026bd9cf352c203af48c33f4b","abstract_canon_sha256":"d7cd854af0ecfe7c223a1ada967276e5a3959594a859725f49ea590f686c2952"},"schema_version":"1.0"},"canonical_sha256":"4b2170ce8499e0fcf2893fb98651b09fa668b6b1e41bb563750498513b18557a","source":{"kind":"arxiv","id":"1308.0710","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0710","created_at":"2026-05-18T02:43:24Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0710v3","created_at":"2026-05-18T02:43:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0710","created_at":"2026-05-18T02:43:24Z"},{"alias_kind":"pith_short_12","alias_value":"JMQXBTUETHQP","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JMQXBTUETHQPZ4UJ","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JMQXBTUE","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JMQXBTUETHQPZ4UJH64YMUNQT6","target":"record","payload":{"canonical_record":{"source":{"id":"1308.0710","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-03T15:53:31Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"144f0589b2776d53e57cfb2368efb784449242a026bd9cf352c203af48c33f4b","abstract_canon_sha256":"d7cd854af0ecfe7c223a1ada967276e5a3959594a859725f49ea590f686c2952"},"schema_version":"1.0"},"canonical_sha256":"4b2170ce8499e0fcf2893fb98651b09fa668b6b1e41bb563750498513b18557a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:24.346890Z","signature_b64":"aSk7tL6uy0wiO4lGvg/nyx7bRbRQrLbvSmmHaUa8Le2vIC+cRG563DGxzAMv647BCjkXQIB/9+EvjhUX9FQeDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b2170ce8499e0fcf2893fb98651b09fa668b6b1e41bb563750498513b18557a","last_reissued_at":"2026-05-18T02:43:24.346258Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:24.346258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.0710","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:43:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"em9j8uISE278M3t6a/2qLoKyN3tOV8vGKzIJ0UeCapYEaKP2mcc7foGntHRvkRk0FOuAWb+r6P6WgjMjI2HtCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T05:33:48.967351Z"},"content_sha256":"a46b70b2dc24bcf80f2b7256d745af4015956807f92d8d18954a85fb22ce7766","schema_version":"1.0","event_id":"sha256:a46b70b2dc24bcf80f2b7256d745af4015956807f92d8d18954a85fb22ce7766"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JMQXBTUETHQPZ4UJH64YMUNQT6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Three Circle Theorems on K\\\"ahler manifolds and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Gang Liu","submitted_at":"2013-08-03T15:53:31Z","abstract_excerpt":"The classical Hadamard three circle theorem is generalized to complete K\\\"ahler manifolds. More precisely, we show that the nonnegativity of the holomorphic sectional curvature is a necessary and sufficient condition for the three circle theorem. As corollaries, two sharp monotonicity formulae for holomorphic functions are derived. Among applications, we derive sharp dimension estimates (with rigidity) of holomorphic functions with polynomial growth when the holomorphic sectional curvature is nonnegative. When the bisectional curvature is nonnegative, this was due to Ni. Also we study holomorp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0710","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":""},"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":"2026-05-18T02:43:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wo5o9uB23F1W7PIVYANH/wwXEVspsCXOyzJxqaTwGKV3WaIKQeN2FLnbiDddUs9bxwovRloHWyKfWgvDGa6GCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T05:33:48.967700Z"},"content_sha256":"69577752a5ba4fc9c32bc845032de798ed3481ef7aa07686001845b7954dc9f8","schema_version":"1.0","event_id":"sha256:69577752a5ba4fc9c32bc845032de798ed3481ef7aa07686001845b7954dc9f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JMQXBTUETHQPZ4UJH64YMUNQT6/bundle.json","state_url":"https://pith.science/pith/JMQXBTUETHQPZ4UJH64YMUNQT6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JMQXBTUETHQPZ4UJH64YMUNQT6/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":"2026-06-04T05:33:48Z","links":{"resolver":"https://pith.science/pith/JMQXBTUETHQPZ4UJH64YMUNQT6","bundle":"https://pith.science/pith/JMQXBTUETHQPZ4UJH64YMUNQT6/bundle.json","state":"https://pith.science/pith/JMQXBTUETHQPZ4UJH64YMUNQT6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JMQXBTUETHQPZ4UJH64YMUNQT6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JMQXBTUETHQPZ4UJH64YMUNQT6","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":"d7cd854af0ecfe7c223a1ada967276e5a3959594a859725f49ea590f686c2952","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-03T15:53:31Z","title_canon_sha256":"144f0589b2776d53e57cfb2368efb784449242a026bd9cf352c203af48c33f4b"},"schema_version":"1.0","source":{"id":"1308.0710","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0710","created_at":"2026-05-18T02:43:24Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0710v3","created_at":"2026-05-18T02:43:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0710","created_at":"2026-05-18T02:43:24Z"},{"alias_kind":"pith_short_12","alias_value":"JMQXBTUETHQP","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JMQXBTUETHQPZ4UJ","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JMQXBTUE","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:69577752a5ba4fc9c32bc845032de798ed3481ef7aa07686001845b7954dc9f8","target":"graph","created_at":"2026-05-18T02:43:24Z","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 classical Hadamard three circle theorem is generalized to complete K\\\"ahler manifolds. More precisely, we show that the nonnegativity of the holomorphic sectional curvature is a necessary and sufficient condition for the three circle theorem. As corollaries, two sharp monotonicity formulae for holomorphic functions are derived. Among applications, we derive sharp dimension estimates (with rigidity) of holomorphic functions with polynomial growth when the holomorphic sectional curvature is nonnegative. When the bisectional curvature is nonnegative, this was due to Ni. Also we study holomorp","authors_text":"Gang Liu","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-03T15:53:31Z","title":"Three Circle Theorems on K\\\"ahler manifolds and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0710","kind":"arxiv","version":3},"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:a46b70b2dc24bcf80f2b7256d745af4015956807f92d8d18954a85fb22ce7766","target":"record","created_at":"2026-05-18T02:43:24Z","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":"d7cd854af0ecfe7c223a1ada967276e5a3959594a859725f49ea590f686c2952","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-03T15:53:31Z","title_canon_sha256":"144f0589b2776d53e57cfb2368efb784449242a026bd9cf352c203af48c33f4b"},"schema_version":"1.0","source":{"id":"1308.0710","kind":"arxiv","version":3}},"canonical_sha256":"4b2170ce8499e0fcf2893fb98651b09fa668b6b1e41bb563750498513b18557a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b2170ce8499e0fcf2893fb98651b09fa668b6b1e41bb563750498513b18557a","first_computed_at":"2026-05-18T02:43:24.346258Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:24.346258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aSk7tL6uy0wiO4lGvg/nyx7bRbRQrLbvSmmHaUa8Le2vIC+cRG563DGxzAMv647BCjkXQIB/9+EvjhUX9FQeDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:24.346890Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.0710","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a46b70b2dc24bcf80f2b7256d745af4015956807f92d8d18954a85fb22ce7766","sha256:69577752a5ba4fc9c32bc845032de798ed3481ef7aa07686001845b7954dc9f8"],"state_sha256":"21140b2acb280133653aef8f938cca892caa2cdf751ec39b477a4503c21986aa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y0dB8KD6Rs1XzANqytIE+bHwqXbrExvozmBjwls6DWzMxi3dIG+bv3Oo/s7qNMaPg/dC90nfuAASGkrxeGLOAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T05:33:48.969789Z","bundle_sha256":"b37f2eecd62c085f7404fa692c639bc3663c4646fef409dff1d109a39d700525"}}