{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:IJGAZ4LGIERK4AVBYNWZIYZAK5","short_pith_number":"pith:IJGAZ4LG","canonical_record":{"source":{"id":"1012.1497","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-07T13:12:01Z","cross_cats_sorted":[],"title_canon_sha256":"2412c6e9c04a9d28329f7b1a0f0c3d10cdd29385a08a78cbf75be03e14f60c2e","abstract_canon_sha256":"83075aa933f60c8f31614b5b1ae27e4b12cdc4933b13029e2df6930afa76c2c6"},"schema_version":"1.0"},"canonical_sha256":"424c0cf1664122ae02a1c36d946320576ebb9c44e1c41a489c3d7be370b56fa6","source":{"kind":"arxiv","id":"1012.1497","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.1497","created_at":"2026-05-18T04:10:48Z"},{"alias_kind":"arxiv_version","alias_value":"1012.1497v2","created_at":"2026-05-18T04:10:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1497","created_at":"2026-05-18T04:10:48Z"},{"alias_kind":"pith_short_12","alias_value":"IJGAZ4LGIERK","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IJGAZ4LGIERK4AVB","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IJGAZ4LG","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:IJGAZ4LGIERK4AVBYNWZIYZAK5","target":"record","payload":{"canonical_record":{"source":{"id":"1012.1497","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-07T13:12:01Z","cross_cats_sorted":[],"title_canon_sha256":"2412c6e9c04a9d28329f7b1a0f0c3d10cdd29385a08a78cbf75be03e14f60c2e","abstract_canon_sha256":"83075aa933f60c8f31614b5b1ae27e4b12cdc4933b13029e2df6930afa76c2c6"},"schema_version":"1.0"},"canonical_sha256":"424c0cf1664122ae02a1c36d946320576ebb9c44e1c41a489c3d7be370b56fa6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:48.277728Z","signature_b64":"GsaAGEXiYcnFst5grmWkJgr+cWDRtG6VI8KJRrQkhpYdDzEYxBhtIzhVMa2y5BdtPyXBypMH1XuGhRhTOlErCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"424c0cf1664122ae02a1c36d946320576ebb9c44e1c41a489c3d7be370b56fa6","last_reissued_at":"2026-05-18T04:10:48.277216Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:48.277216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.1497","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":"2026-05-18T04:10:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uj7hsvKIxlaPIcmERUOvfWuq0nb8A3UQ5U3Dw4CoHykquLKED2u2cTvAY2m1T19wJV5pRnS75CvdIjB/xMViCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:03:24.759971Z"},"content_sha256":"8793ad702e6bec3b9cf3acaefe004f24a2ac570ab33b047cd7e70f8b804e5a4b","schema_version":"1.0","event_id":"sha256:8793ad702e6bec3b9cf3acaefe004f24a2ac570ab33b047cd7e70f8b804e5a4b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:IJGAZ4LGIERK4AVBYNWZIYZAK5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On bifurcation of solutions of the Yamabe problem in product manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"L. L. de Lima, M. Zedda, P. Piccione","submitted_at":"2010-12-07T13:12:01Z","abstract_excerpt":"We study local rigidity and multiplicity of constant scalar curvature metrics in arbitrary products of compact manifolds. Using (equivariant) bifurcation theory we determine the existence of infinitely many metrics that are accumulation points of pairwise non homothetic solutions of the Yamabe problem. Using local rigidity and some compactness results for solutions of the Yamabe problem, we also exhibit new examples of conformal classes (with positive Yamabe constant) for which uniqueness holds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1497","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":"2026-05-18T04:10:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oww11FdrMlZJNkFGQuK7wUEkTXkQSRt72zHWhTiTv+epAmRPLW43nOKc2pSoMqcGSNyGGZHf34WzW5cQlDfvAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:03:24.760460Z"},"content_sha256":"7cf462edf9a784673751e28215afc0cebb7d1dad712a831de4eb24d0760e5d8d","schema_version":"1.0","event_id":"sha256:7cf462edf9a784673751e28215afc0cebb7d1dad712a831de4eb24d0760e5d8d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IJGAZ4LGIERK4AVBYNWZIYZAK5/bundle.json","state_url":"https://pith.science/pith/IJGAZ4LGIERK4AVBYNWZIYZAK5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IJGAZ4LGIERK4AVBYNWZIYZAK5/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":"2026-06-24T23:03:24Z","links":{"resolver":"https://pith.science/pith/IJGAZ4LGIERK4AVBYNWZIYZAK5","bundle":"https://pith.science/pith/IJGAZ4LGIERK4AVBYNWZIYZAK5/bundle.json","state":"https://pith.science/pith/IJGAZ4LGIERK4AVBYNWZIYZAK5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IJGAZ4LGIERK4AVBYNWZIYZAK5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IJGAZ4LGIERK4AVBYNWZIYZAK5","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":"83075aa933f60c8f31614b5b1ae27e4b12cdc4933b13029e2df6930afa76c2c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-07T13:12:01Z","title_canon_sha256":"2412c6e9c04a9d28329f7b1a0f0c3d10cdd29385a08a78cbf75be03e14f60c2e"},"schema_version":"1.0","source":{"id":"1012.1497","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.1497","created_at":"2026-05-18T04:10:48Z"},{"alias_kind":"arxiv_version","alias_value":"1012.1497v2","created_at":"2026-05-18T04:10:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1497","created_at":"2026-05-18T04:10:48Z"},{"alias_kind":"pith_short_12","alias_value":"IJGAZ4LGIERK","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IJGAZ4LGIERK4AVB","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IJGAZ4LG","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:7cf462edf9a784673751e28215afc0cebb7d1dad712a831de4eb24d0760e5d8d","target":"graph","created_at":"2026-05-18T04:10:48Z","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":"We study local rigidity and multiplicity of constant scalar curvature metrics in arbitrary products of compact manifolds. Using (equivariant) bifurcation theory we determine the existence of infinitely many metrics that are accumulation points of pairwise non homothetic solutions of the Yamabe problem. Using local rigidity and some compactness results for solutions of the Yamabe problem, we also exhibit new examples of conformal classes (with positive Yamabe constant) for which uniqueness holds.","authors_text":"L. L. de Lima, M. Zedda, P. Piccione","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-07T13:12:01Z","title":"On bifurcation of solutions of the Yamabe problem in product manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1497","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":"sha256:8793ad702e6bec3b9cf3acaefe004f24a2ac570ab33b047cd7e70f8b804e5a4b","target":"record","created_at":"2026-05-18T04:10:48Z","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":"83075aa933f60c8f31614b5b1ae27e4b12cdc4933b13029e2df6930afa76c2c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-07T13:12:01Z","title_canon_sha256":"2412c6e9c04a9d28329f7b1a0f0c3d10cdd29385a08a78cbf75be03e14f60c2e"},"schema_version":"1.0","source":{"id":"1012.1497","kind":"arxiv","version":2}},"canonical_sha256":"424c0cf1664122ae02a1c36d946320576ebb9c44e1c41a489c3d7be370b56fa6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"424c0cf1664122ae02a1c36d946320576ebb9c44e1c41a489c3d7be370b56fa6","first_computed_at":"2026-05-18T04:10:48.277216Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:48.277216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GsaAGEXiYcnFst5grmWkJgr+cWDRtG6VI8KJRrQkhpYdDzEYxBhtIzhVMa2y5BdtPyXBypMH1XuGhRhTOlErCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:48.277728Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.1497","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8793ad702e6bec3b9cf3acaefe004f24a2ac570ab33b047cd7e70f8b804e5a4b","sha256:7cf462edf9a784673751e28215afc0cebb7d1dad712a831de4eb24d0760e5d8d"],"state_sha256":"a4a51805e1110695a51571fa7e3c778435b0308873d4cf071e51d8747da1388e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EdIU9CPqdS4mHJbOYFJ/SnWuSGIgSoxND2oA2pnVNAxfgmZjWNNhsowdIw8ZJdWgwSbNpxi9Bb+DUonzjcbtDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T23:03:24.763002Z","bundle_sha256":"50fb902827f08f3d4b4777ef28194fb0e961b8c81a4fcaf48a542394976e1384"}}