{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:S6PXRXH5C3TOBLEGKYBTF7EPQI","short_pith_number":"pith:S6PXRXH5","canonical_record":{"source":{"id":"1212.6558","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-12-28T19:45:19Z","cross_cats_sorted":[],"title_canon_sha256":"d52e34630553abbb756a070b0ae56c54b710a1163b1ebfcb9e1c368e44106119","abstract_canon_sha256":"fd50c970a2ad960ae7d2dda4cba5ab7df1da84702c8b4460c22f20d1cb745727"},"schema_version":"1.0"},"canonical_sha256":"979f78dcfd16e6e0ac86560332fc8f822067abe4753892194102fef727d031d1","source":{"kind":"arxiv","id":"1212.6558","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6558","created_at":"2026-05-18T03:37:31Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6558v1","created_at":"2026-05-18T03:37:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6558","created_at":"2026-05-18T03:37:31Z"},{"alias_kind":"pith_short_12","alias_value":"S6PXRXH5C3TO","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"S6PXRXH5C3TOBLEG","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"S6PXRXH5","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:S6PXRXH5C3TOBLEGKYBTF7EPQI","target":"record","payload":{"canonical_record":{"source":{"id":"1212.6558","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-12-28T19:45:19Z","cross_cats_sorted":[],"title_canon_sha256":"d52e34630553abbb756a070b0ae56c54b710a1163b1ebfcb9e1c368e44106119","abstract_canon_sha256":"fd50c970a2ad960ae7d2dda4cba5ab7df1da84702c8b4460c22f20d1cb745727"},"schema_version":"1.0"},"canonical_sha256":"979f78dcfd16e6e0ac86560332fc8f822067abe4753892194102fef727d031d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:31.564334Z","signature_b64":"OF6aeJ0G2ACgUhU79/lDhN6346zrmbKf10sP27d17gr9Q8207Dilbi0DSsNaD2chUtvgfTPVFQMKDwOjJ2Q+DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"979f78dcfd16e6e0ac86560332fc8f822067abe4753892194102fef727d031d1","last_reissued_at":"2026-05-18T03:37:31.563547Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:31.563547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.6558","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":"2026-05-18T03:37:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mWXKq4FtF8DtvN8JwCv5ewpIJg+LdTqK9NX0RB/gELbJbSzetVii9JmKaUHy+pgwGWhG4gPxmtsRral0NLk6CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:44:21.809898Z"},"content_sha256":"8f2ebd916edee2e8d00f8ca468931391d66a4aec19d2ef1b5a0f740acaf5dae7","schema_version":"1.0","event_id":"sha256:8f2ebd916edee2e8d00f8ca468931391d66a4aec19d2ef1b5a0f740acaf5dae7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:S6PXRXH5C3TOBLEGKYBTF7EPQI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scalar curvature behavior of homogeneous Ricci flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ramiro A. Lafuente","submitted_at":"2012-12-28T19:45:19Z","abstract_excerpt":"We prove that the scalar curvature of a homogeneous Ricci flow solution blows up at a forward or backward finite-time singularity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6558","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":"2026-05-18T03:37:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sbWb+lNlLTqZqrhhLozexpRaAjekvDDSnch0qJazz4YO/hRgDiI+KEtKT4L5Y6554j5JmF1/Oizm3KlbX1peDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:44:21.810244Z"},"content_sha256":"5ddecfeda84ae7a52f0ca50c3613b15dcaababeb5038f65d9e6ffc94c5ddf572","schema_version":"1.0","event_id":"sha256:5ddecfeda84ae7a52f0ca50c3613b15dcaababeb5038f65d9e6ffc94c5ddf572"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S6PXRXH5C3TOBLEGKYBTF7EPQI/bundle.json","state_url":"https://pith.science/pith/S6PXRXH5C3TOBLEGKYBTF7EPQI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S6PXRXH5C3TOBLEGKYBTF7EPQI/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":"2026-06-01T12:44:21Z","links":{"resolver":"https://pith.science/pith/S6PXRXH5C3TOBLEGKYBTF7EPQI","bundle":"https://pith.science/pith/S6PXRXH5C3TOBLEGKYBTF7EPQI/bundle.json","state":"https://pith.science/pith/S6PXRXH5C3TOBLEGKYBTF7EPQI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S6PXRXH5C3TOBLEGKYBTF7EPQI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:S6PXRXH5C3TOBLEGKYBTF7EPQI","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":"fd50c970a2ad960ae7d2dda4cba5ab7df1da84702c8b4460c22f20d1cb745727","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-12-28T19:45:19Z","title_canon_sha256":"d52e34630553abbb756a070b0ae56c54b710a1163b1ebfcb9e1c368e44106119"},"schema_version":"1.0","source":{"id":"1212.6558","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6558","created_at":"2026-05-18T03:37:31Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6558v1","created_at":"2026-05-18T03:37:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6558","created_at":"2026-05-18T03:37:31Z"},{"alias_kind":"pith_short_12","alias_value":"S6PXRXH5C3TO","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"S6PXRXH5C3TOBLEG","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"S6PXRXH5","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:5ddecfeda84ae7a52f0ca50c3613b15dcaababeb5038f65d9e6ffc94c5ddf572","target":"graph","created_at":"2026-05-18T03:37:31Z","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 prove that the scalar curvature of a homogeneous Ricci flow solution blows up at a forward or backward finite-time singularity.","authors_text":"Ramiro A. Lafuente","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-12-28T19:45:19Z","title":"Scalar curvature behavior of homogeneous Ricci flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6558","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":"sha256:8f2ebd916edee2e8d00f8ca468931391d66a4aec19d2ef1b5a0f740acaf5dae7","target":"record","created_at":"2026-05-18T03:37:31Z","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":"fd50c970a2ad960ae7d2dda4cba5ab7df1da84702c8b4460c22f20d1cb745727","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-12-28T19:45:19Z","title_canon_sha256":"d52e34630553abbb756a070b0ae56c54b710a1163b1ebfcb9e1c368e44106119"},"schema_version":"1.0","source":{"id":"1212.6558","kind":"arxiv","version":1}},"canonical_sha256":"979f78dcfd16e6e0ac86560332fc8f822067abe4753892194102fef727d031d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"979f78dcfd16e6e0ac86560332fc8f822067abe4753892194102fef727d031d1","first_computed_at":"2026-05-18T03:37:31.563547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:31.563547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OF6aeJ0G2ACgUhU79/lDhN6346zrmbKf10sP27d17gr9Q8207Dilbi0DSsNaD2chUtvgfTPVFQMKDwOjJ2Q+DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:31.564334Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.6558","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f2ebd916edee2e8d00f8ca468931391d66a4aec19d2ef1b5a0f740acaf5dae7","sha256:5ddecfeda84ae7a52f0ca50c3613b15dcaababeb5038f65d9e6ffc94c5ddf572"],"state_sha256":"ca55825add438875e5c2416a092228317ad704f7b4e3c462d3f2a01a1be6d072"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dV3LzhI+QAIOyRgw685ZUDLmp3Ju6pPL0ol3hUCzsYSY3A7dXoSB5pkfx2suh1NwWWPWH+xITrBvQA0moyo7Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:44:21.812146Z","bundle_sha256":"89cae3ebe392642dd1a9c5e57ee4cbc5b39f1e49147db6495b32923c54da3487"}}