{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UNB3O56DYEM66C4ERPR3QSYXLK","short_pith_number":"pith:UNB3O56D","canonical_record":{"source":{"id":"1206.1285","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-06T17:42:57Z","cross_cats_sorted":[],"title_canon_sha256":"82f0912e94904de10dc3e2180a6b16564627615bc9506103aaf4bb56f1e74cd9","abstract_canon_sha256":"a56dd04d0bdfd851e1f75c120e7c665427a175e3a0739069e4b5f9123520bc74"},"schema_version":"1.0"},"canonical_sha256":"a343b777c3c119ef0b848be3b84b175a877b8c3392f15b48ffed6304d0fd1b41","source":{"kind":"arxiv","id":"1206.1285","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.1285","created_at":"2026-05-18T03:27:34Z"},{"alias_kind":"arxiv_version","alias_value":"1206.1285v2","created_at":"2026-05-18T03:27:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1285","created_at":"2026-05-18T03:27:34Z"},{"alias_kind":"pith_short_12","alias_value":"UNB3O56DYEM6","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UNB3O56DYEM66C4E","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UNB3O56D","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UNB3O56DYEM66C4ERPR3QSYXLK","target":"record","payload":{"canonical_record":{"source":{"id":"1206.1285","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-06T17:42:57Z","cross_cats_sorted":[],"title_canon_sha256":"82f0912e94904de10dc3e2180a6b16564627615bc9506103aaf4bb56f1e74cd9","abstract_canon_sha256":"a56dd04d0bdfd851e1f75c120e7c665427a175e3a0739069e4b5f9123520bc74"},"schema_version":"1.0"},"canonical_sha256":"a343b777c3c119ef0b848be3b84b175a877b8c3392f15b48ffed6304d0fd1b41","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:34.461368Z","signature_b64":"BHqTIxGPXhop/Hlydi2Z9feg2qBHvcXEPrjWcWf2dSbggeOrYFuRiFgDatrq6CfT5DehMmuZ7DjMbpLKtLTpBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a343b777c3c119ef0b848be3b84b175a877b8c3392f15b48ffed6304d0fd1b41","last_reissued_at":"2026-05-18T03:27:34.460873Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:34.460873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.1285","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":"2026-05-18T03:27:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HlSyUqktnEr5HOs7uO3dhQFcy7YNUdb1FJgE/iwkX0NjTqFx37lwTVcWXNgseGzfdIuG0nP36Ff+CToYoJC8CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:37:41.053104Z"},"content_sha256":"bf0c8bc9bbbc4d038592a9101990320233577b4d74050e76d352b84776877880","schema_version":"1.0","event_id":"sha256:bf0c8bc9bbbc4d038592a9101990320233577b4d74050e76d352b84776877880"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UNB3O56DYEM66C4ERPR3QSYXLK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Einstein metrics and Yamabe invariants of weighted projective spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jeff A. Viaclovsky","submitted_at":"2012-06-06T17:42:57Z","abstract_excerpt":"An orbifold version of the Hitchin-Thorpe inequality is used to prove that certain weighted projective spaces do not admit orbifold Einstein metrics. Also, several estimates for the orbifold Yamabe invariants of weighted projective spaces are proved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1285","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":"2026-05-18T03:27:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z7QXDnJY2s+7XI+righIhS9bucwP3qzE86yTD0KyIv6IHUwscAlFB2fL11ah6i3dypzGPBuiLXVIdtqoMqYdAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:37:41.053466Z"},"content_sha256":"fb5314fef0639c18886ff5ce4c78f3040d9fb4f7bc075576d917889eeafdd02b","schema_version":"1.0","event_id":"sha256:fb5314fef0639c18886ff5ce4c78f3040d9fb4f7bc075576d917889eeafdd02b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UNB3O56DYEM66C4ERPR3QSYXLK/bundle.json","state_url":"https://pith.science/pith/UNB3O56DYEM66C4ERPR3QSYXLK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UNB3O56DYEM66C4ERPR3QSYXLK/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":"2026-06-27T12:37:41Z","links":{"resolver":"https://pith.science/pith/UNB3O56DYEM66C4ERPR3QSYXLK","bundle":"https://pith.science/pith/UNB3O56DYEM66C4ERPR3QSYXLK/bundle.json","state":"https://pith.science/pith/UNB3O56DYEM66C4ERPR3QSYXLK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UNB3O56DYEM66C4ERPR3QSYXLK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UNB3O56DYEM66C4ERPR3QSYXLK","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":"a56dd04d0bdfd851e1f75c120e7c665427a175e3a0739069e4b5f9123520bc74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-06T17:42:57Z","title_canon_sha256":"82f0912e94904de10dc3e2180a6b16564627615bc9506103aaf4bb56f1e74cd9"},"schema_version":"1.0","source":{"id":"1206.1285","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.1285","created_at":"2026-05-18T03:27:34Z"},{"alias_kind":"arxiv_version","alias_value":"1206.1285v2","created_at":"2026-05-18T03:27:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1285","created_at":"2026-05-18T03:27:34Z"},{"alias_kind":"pith_short_12","alias_value":"UNB3O56DYEM6","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UNB3O56DYEM66C4E","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UNB3O56D","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:fb5314fef0639c18886ff5ce4c78f3040d9fb4f7bc075576d917889eeafdd02b","target":"graph","created_at":"2026-05-18T03:27:34Z","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":"An orbifold version of the Hitchin-Thorpe inequality is used to prove that certain weighted projective spaces do not admit orbifold Einstein metrics. Also, several estimates for the orbifold Yamabe invariants of weighted projective spaces are proved.","authors_text":"Jeff A. Viaclovsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-06T17:42:57Z","title":"Einstein metrics and Yamabe invariants of weighted projective spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1285","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:bf0c8bc9bbbc4d038592a9101990320233577b4d74050e76d352b84776877880","target":"record","created_at":"2026-05-18T03:27:34Z","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":"a56dd04d0bdfd851e1f75c120e7c665427a175e3a0739069e4b5f9123520bc74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-06T17:42:57Z","title_canon_sha256":"82f0912e94904de10dc3e2180a6b16564627615bc9506103aaf4bb56f1e74cd9"},"schema_version":"1.0","source":{"id":"1206.1285","kind":"arxiv","version":2}},"canonical_sha256":"a343b777c3c119ef0b848be3b84b175a877b8c3392f15b48ffed6304d0fd1b41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a343b777c3c119ef0b848be3b84b175a877b8c3392f15b48ffed6304d0fd1b41","first_computed_at":"2026-05-18T03:27:34.460873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:34.460873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BHqTIxGPXhop/Hlydi2Z9feg2qBHvcXEPrjWcWf2dSbggeOrYFuRiFgDatrq6CfT5DehMmuZ7DjMbpLKtLTpBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:34.461368Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.1285","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf0c8bc9bbbc4d038592a9101990320233577b4d74050e76d352b84776877880","sha256:fb5314fef0639c18886ff5ce4c78f3040d9fb4f7bc075576d917889eeafdd02b"],"state_sha256":"a8247590ecfdb2ecc9a743779ac3bbaf44eb128c41eaf28ebe29f61706943543"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wfnwflK7HQiqNgmkVLi7eRXVOMlzrLMP7cl6y1zKgm2eJFDH6a0m6URmVwGcQrd9bEqKSBXKd48gSMr9xJVqCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T12:37:41.055830Z","bundle_sha256":"f17418cfc36ee993028635a5f1d923961d3b99bed357b8729fcac04f7d849c7b"}}