{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XI6G7UBYBUMHCBGV564O4U22AY","short_pith_number":"pith:XI6G7UBY","canonical_record":{"source":{"id":"1504.02910","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-11T19:29:07Z","cross_cats_sorted":[],"title_canon_sha256":"ded4602d0b54099e0b285fb5e9bd9687d6e5e48d2cb6b37031d1f857fdb3b394","abstract_canon_sha256":"20b5747c4462d4060d8455723dbc400b0feb6beafe250d7954fe762d2cfa59c9"},"schema_version":"1.0"},"canonical_sha256":"ba3c6fd0380d187104d5efb8ee535a063b4c83f49b8c23b746857ec5468209fb","source":{"kind":"arxiv","id":"1504.02910","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02910","created_at":"2026-05-18T02:18:59Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02910v1","created_at":"2026-05-18T02:18:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02910","created_at":"2026-05-18T02:18:59Z"},{"alias_kind":"pith_short_12","alias_value":"XI6G7UBYBUMH","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XI6G7UBYBUMHCBGV","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XI6G7UBY","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XI6G7UBYBUMHCBGV564O4U22AY","target":"record","payload":{"canonical_record":{"source":{"id":"1504.02910","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-11T19:29:07Z","cross_cats_sorted":[],"title_canon_sha256":"ded4602d0b54099e0b285fb5e9bd9687d6e5e48d2cb6b37031d1f857fdb3b394","abstract_canon_sha256":"20b5747c4462d4060d8455723dbc400b0feb6beafe250d7954fe762d2cfa59c9"},"schema_version":"1.0"},"canonical_sha256":"ba3c6fd0380d187104d5efb8ee535a063b4c83f49b8c23b746857ec5468209fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:59.685722Z","signature_b64":"Vm2AiZjRpRfqqOxIsihEKSamlQNemFjBlTZRDqjzbSxz1lspAFRxX+YH/QIyQaoQZw9Nkou/vKikzyQRE/I+Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba3c6fd0380d187104d5efb8ee535a063b4c83f49b8c23b746857ec5468209fb","last_reissued_at":"2026-05-18T02:18:59.685178Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:59.685178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.02910","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":"2026-05-18T02:18:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PS5HLDVfCJvkiIzupR/P/utZkBUCEP565Cy8qH+pVWR59ZaDPybiezTKKk+Fz+hgESM00erGy9vdomjisGI6Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T09:13:25.984851Z"},"content_sha256":"bd6c5a6a3ed188e5c956941d242ad5ca60dcc5b83ec6cff2fcc806ccbbc0c01a","schema_version":"1.0","event_id":"sha256:bd6c5a6a3ed188e5c956941d242ad5ca60dcc5b83ec6cff2fcc806ccbbc0c01a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XI6G7UBYBUMHCBGV564O4U22AY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extending four dimensional Ricci flows with bounded scalar curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Miles Simon","submitted_at":"2015-04-11T19:29:07Z","abstract_excerpt":"We consider smooth solutions (M,g(t)), 0 <= t <T, to Ricci flow on compact, connected, four dimensional manifolds without boundary. We assume that the scalar curvature is bounded uniformly, and that T is finite. In this case, we show that the metric space (M,d(t)) associated to (M,g(t)) converges uniformly in the C^0 sense to (X,d), as t approaches T, where (X,d) is a C^0 Riemannian orbifold with at most finitely many orbifold points. Estimates on the rate of convergence near and away from the orbifold points are given. We also show that it is possible to continue the flow past (X,d) using the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02910","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":"2026-05-18T02:18:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rlc4lueffYAdf8hZ7VZ9Lzr/nvNcArZmHWpV0cFis5fxMey+mRXaIu/QNlTxFQbWn9Y+ZpJbhefa0PtUVWfLBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T09:13:25.985187Z"},"content_sha256":"ff8c445e55c998056236b61f2a2cbf3c3a03fac881be236778c488990dff1644","schema_version":"1.0","event_id":"sha256:ff8c445e55c998056236b61f2a2cbf3c3a03fac881be236778c488990dff1644"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XI6G7UBYBUMHCBGV564O4U22AY/bundle.json","state_url":"https://pith.science/pith/XI6G7UBYBUMHCBGV564O4U22AY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XI6G7UBYBUMHCBGV564O4U22AY/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":"2026-06-29T09:13:25Z","links":{"resolver":"https://pith.science/pith/XI6G7UBYBUMHCBGV564O4U22AY","bundle":"https://pith.science/pith/XI6G7UBYBUMHCBGV564O4U22AY/bundle.json","state":"https://pith.science/pith/XI6G7UBYBUMHCBGV564O4U22AY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XI6G7UBYBUMHCBGV564O4U22AY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XI6G7UBYBUMHCBGV564O4U22AY","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":"20b5747c4462d4060d8455723dbc400b0feb6beafe250d7954fe762d2cfa59c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-11T19:29:07Z","title_canon_sha256":"ded4602d0b54099e0b285fb5e9bd9687d6e5e48d2cb6b37031d1f857fdb3b394"},"schema_version":"1.0","source":{"id":"1504.02910","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02910","created_at":"2026-05-18T02:18:59Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02910v1","created_at":"2026-05-18T02:18:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02910","created_at":"2026-05-18T02:18:59Z"},{"alias_kind":"pith_short_12","alias_value":"XI6G7UBYBUMH","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XI6G7UBYBUMHCBGV","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XI6G7UBY","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:ff8c445e55c998056236b61f2a2cbf3c3a03fac881be236778c488990dff1644","target":"graph","created_at":"2026-05-18T02:18:59Z","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 consider smooth solutions (M,g(t)), 0 <= t <T, to Ricci flow on compact, connected, four dimensional manifolds without boundary. We assume that the scalar curvature is bounded uniformly, and that T is finite. In this case, we show that the metric space (M,d(t)) associated to (M,g(t)) converges uniformly in the C^0 sense to (X,d), as t approaches T, where (X,d) is a C^0 Riemannian orbifold with at most finitely many orbifold points. Estimates on the rate of convergence near and away from the orbifold points are given. We also show that it is possible to continue the flow past (X,d) using the","authors_text":"Miles Simon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-11T19:29:07Z","title":"Extending four dimensional Ricci flows with bounded scalar curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02910","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:bd6c5a6a3ed188e5c956941d242ad5ca60dcc5b83ec6cff2fcc806ccbbc0c01a","target":"record","created_at":"2026-05-18T02:18:59Z","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":"20b5747c4462d4060d8455723dbc400b0feb6beafe250d7954fe762d2cfa59c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-11T19:29:07Z","title_canon_sha256":"ded4602d0b54099e0b285fb5e9bd9687d6e5e48d2cb6b37031d1f857fdb3b394"},"schema_version":"1.0","source":{"id":"1504.02910","kind":"arxiv","version":1}},"canonical_sha256":"ba3c6fd0380d187104d5efb8ee535a063b4c83f49b8c23b746857ec5468209fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba3c6fd0380d187104d5efb8ee535a063b4c83f49b8c23b746857ec5468209fb","first_computed_at":"2026-05-18T02:18:59.685178Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:59.685178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vm2AiZjRpRfqqOxIsihEKSamlQNemFjBlTZRDqjzbSxz1lspAFRxX+YH/QIyQaoQZw9Nkou/vKikzyQRE/I+Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:59.685722Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.02910","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd6c5a6a3ed188e5c956941d242ad5ca60dcc5b83ec6cff2fcc806ccbbc0c01a","sha256:ff8c445e55c998056236b61f2a2cbf3c3a03fac881be236778c488990dff1644"],"state_sha256":"d83a38b89db546a968e4640e4f85c911ab61cde49c8df7e4af74b6772b9a5eec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PuR8oLX7MYmbJvpeZnBFnfPwxFDpx00bWbQrM74ONL1eyiU0tEq3Jnz7OLiNjTTxaTJ0QRRD+9+5uzeTV0CBDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T09:13:25.987274Z","bundle_sha256":"76dedde94ff14c25cbb617dfb06b84e7dccdd1888327a80a7fdb28ed8f78ab7c"}}