{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QSGM6KDIJZXG7VT6HMYMB5Z5H3","short_pith_number":"pith:QSGM6KDI","canonical_record":{"source":{"id":"1203.5411","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-24T13:31:45Z","cross_cats_sorted":[],"title_canon_sha256":"a4ccd84ef4fb9d016fe1c19eaad1f015662522efafa216a81d1417f4c610e10a","abstract_canon_sha256":"78c30256ccc91819ddc5b06435fd7c859e9392c4ab6356f1ec47252b538467a7"},"schema_version":"1.0"},"canonical_sha256":"848ccf28684e6e6fd67e3b30c0f73d3ec7777d0d4a7bb4468dc4afe3ee839d76","source":{"kind":"arxiv","id":"1203.5411","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.5411","created_at":"2026-05-18T03:59:15Z"},{"alias_kind":"arxiv_version","alias_value":"1203.5411v1","created_at":"2026-05-18T03:59:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.5411","created_at":"2026-05-18T03:59:15Z"},{"alias_kind":"pith_short_12","alias_value":"QSGM6KDIJZXG","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QSGM6KDIJZXG7VT6","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QSGM6KDI","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QSGM6KDIJZXG7VT6HMYMB5Z5H3","target":"record","payload":{"canonical_record":{"source":{"id":"1203.5411","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-24T13:31:45Z","cross_cats_sorted":[],"title_canon_sha256":"a4ccd84ef4fb9d016fe1c19eaad1f015662522efafa216a81d1417f4c610e10a","abstract_canon_sha256":"78c30256ccc91819ddc5b06435fd7c859e9392c4ab6356f1ec47252b538467a7"},"schema_version":"1.0"},"canonical_sha256":"848ccf28684e6e6fd67e3b30c0f73d3ec7777d0d4a7bb4468dc4afe3ee839d76","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:15.164173Z","signature_b64":"8cFtxA/iR4hHxD/s6gt+P2ZY07+Lff9ta5qwoPWup4NE+qpuwfdZAOfBbatYAaORfqIi5hGRP663Cu0z2LQ0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"848ccf28684e6e6fd67e3b30c0f73d3ec7777d0d4a7bb4468dc4afe3ee839d76","last_reissued_at":"2026-05-18T03:59:15.163641Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:15.163641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.5411","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":"2026-05-18T03:59:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0yKFgTMkptapSrCp0vvsFWNlPvtqJ0wVbCHQJuH7+h+Vo5w6dH6GjEu6umTKjO8T+9iVUd0NBnfzG4J1Q1frAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T11:01:58.129403Z"},"content_sha256":"a9aca4f1253fd7e63c1786096b0b7d1e99696dad1997b9d4139ec304ebb4101c","schema_version":"1.0","event_id":"sha256:a9aca4f1253fd7e63c1786096b0b7d1e99696dad1997b9d4139ec304ebb4101c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QSGM6KDIJZXG7VT6HMYMB5Z5H3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monotonicity formulae, vanishing theorems and some geometric applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hezi Lin, Yuxin Dong","submitted_at":"2012-03-24T13:31:45Z","abstract_excerpt":"Using the stress energy tensor, we establish some monotonicity formulae for vector bundle-valued p-forms satisfying the conservation law, provided that the base Riemannian (resp. K\\\"ahler) manifolds poss some real (resp. complex) p-exhaustion functions. Vanishing theorems follow immediately from the monotonicity formulae under suitable growth conditions on the energy of the p-forms. As an application, we establish a monotonicity formula for the Ricci form of a K\\\"ahler manifold of constant scalar curvature and then get a growth condition to derive the Ricci flatness of the K\\\"ahler manifold. I"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5411","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":"2026-05-18T03:59:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bcFUwV689W0FIa0hWT1lwnfUiBgycdtOxcv8BFWdxST4lHoI5vdDhptBnPAGfUX4/7kHhydJmLtOIAWugkYUAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T11:01:58.130022Z"},"content_sha256":"def454b0d2d18fce38b919b197c26a57976ced129b73d8c33250e15211566a2d","schema_version":"1.0","event_id":"sha256:def454b0d2d18fce38b919b197c26a57976ced129b73d8c33250e15211566a2d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QSGM6KDIJZXG7VT6HMYMB5Z5H3/bundle.json","state_url":"https://pith.science/pith/QSGM6KDIJZXG7VT6HMYMB5Z5H3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QSGM6KDIJZXG7VT6HMYMB5Z5H3/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":"2026-06-07T11:01:58Z","links":{"resolver":"https://pith.science/pith/QSGM6KDIJZXG7VT6HMYMB5Z5H3","bundle":"https://pith.science/pith/QSGM6KDIJZXG7VT6HMYMB5Z5H3/bundle.json","state":"https://pith.science/pith/QSGM6KDIJZXG7VT6HMYMB5Z5H3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QSGM6KDIJZXG7VT6HMYMB5Z5H3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QSGM6KDIJZXG7VT6HMYMB5Z5H3","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":"78c30256ccc91819ddc5b06435fd7c859e9392c4ab6356f1ec47252b538467a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-24T13:31:45Z","title_canon_sha256":"a4ccd84ef4fb9d016fe1c19eaad1f015662522efafa216a81d1417f4c610e10a"},"schema_version":"1.0","source":{"id":"1203.5411","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.5411","created_at":"2026-05-18T03:59:15Z"},{"alias_kind":"arxiv_version","alias_value":"1203.5411v1","created_at":"2026-05-18T03:59:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.5411","created_at":"2026-05-18T03:59:15Z"},{"alias_kind":"pith_short_12","alias_value":"QSGM6KDIJZXG","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QSGM6KDIJZXG7VT6","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QSGM6KDI","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:def454b0d2d18fce38b919b197c26a57976ced129b73d8c33250e15211566a2d","target":"graph","created_at":"2026-05-18T03:59:15Z","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":"Using the stress energy tensor, we establish some monotonicity formulae for vector bundle-valued p-forms satisfying the conservation law, provided that the base Riemannian (resp. K\\\"ahler) manifolds poss some real (resp. complex) p-exhaustion functions. Vanishing theorems follow immediately from the monotonicity formulae under suitable growth conditions on the energy of the p-forms. As an application, we establish a monotonicity formula for the Ricci form of a K\\\"ahler manifold of constant scalar curvature and then get a growth condition to derive the Ricci flatness of the K\\\"ahler manifold. I","authors_text":"Hezi Lin, Yuxin Dong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-24T13:31:45Z","title":"Monotonicity formulae, vanishing theorems and some geometric applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5411","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:a9aca4f1253fd7e63c1786096b0b7d1e99696dad1997b9d4139ec304ebb4101c","target":"record","created_at":"2026-05-18T03:59:15Z","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":"78c30256ccc91819ddc5b06435fd7c859e9392c4ab6356f1ec47252b538467a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-24T13:31:45Z","title_canon_sha256":"a4ccd84ef4fb9d016fe1c19eaad1f015662522efafa216a81d1417f4c610e10a"},"schema_version":"1.0","source":{"id":"1203.5411","kind":"arxiv","version":1}},"canonical_sha256":"848ccf28684e6e6fd67e3b30c0f73d3ec7777d0d4a7bb4468dc4afe3ee839d76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"848ccf28684e6e6fd67e3b30c0f73d3ec7777d0d4a7bb4468dc4afe3ee839d76","first_computed_at":"2026-05-18T03:59:15.163641Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:15.163641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8cFtxA/iR4hHxD/s6gt+P2ZY07+Lff9ta5qwoPWup4NE+qpuwfdZAOfBbatYAaORfqIi5hGRP663Cu0z2LQ0BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:15.164173Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.5411","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9aca4f1253fd7e63c1786096b0b7d1e99696dad1997b9d4139ec304ebb4101c","sha256:def454b0d2d18fce38b919b197c26a57976ced129b73d8c33250e15211566a2d"],"state_sha256":"55e90b7e670c31946a28e51ea90188b111ca0cc772e157e86606e8ce1becd832"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9XQPoNuT2TYNgJ+oUzZaUtKojNgs4S/bCJf34zBC19FWit5YSpgyY0Kb9yKIXNoL/R4/sdETtPv0hyLuQFCtBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T11:01:58.133301Z","bundle_sha256":"c41be1ca921a4abed6ea134932b00a11186f4b059ce11684c82dae8b80a22569"}}