{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:XNYEN5376ZWNYOWKVVC5EPLYOY","short_pith_number":"pith:XNYEN537","canonical_record":{"source":{"id":"2009.11854","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-09-24T17:57:09Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"9c244a61933aa0947dbcb9bab881d357c90e4fd8cbd2e0f2d57a61897981a4f6","abstract_canon_sha256":"fdbb720e1e51009f4e4bc65a189c22aef718abe185820187ddfb25f4096f2a24"},"schema_version":"1.0"},"canonical_sha256":"bb7046f77ff66cdc3acaad45d23d78761cb8aea993402968145daa923a370f04","source":{"kind":"arxiv","id":"2009.11854","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.11854","created_at":"2026-07-05T01:37:50Z"},{"alias_kind":"arxiv_version","alias_value":"2009.11854v1","created_at":"2026-07-05T01:37:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.11854","created_at":"2026-07-05T01:37:50Z"},{"alias_kind":"pith_short_12","alias_value":"XNYEN5376ZWN","created_at":"2026-07-05T01:37:50Z"},{"alias_kind":"pith_short_16","alias_value":"XNYEN5376ZWNYOWK","created_at":"2026-07-05T01:37:50Z"},{"alias_kind":"pith_short_8","alias_value":"XNYEN537","created_at":"2026-07-05T01:37:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:XNYEN5376ZWNYOWKVVC5EPLYOY","target":"record","payload":{"canonical_record":{"source":{"id":"2009.11854","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-09-24T17:57:09Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"9c244a61933aa0947dbcb9bab881d357c90e4fd8cbd2e0f2d57a61897981a4f6","abstract_canon_sha256":"fdbb720e1e51009f4e4bc65a189c22aef718abe185820187ddfb25f4096f2a24"},"schema_version":"1.0"},"canonical_sha256":"bb7046f77ff66cdc3acaad45d23d78761cb8aea993402968145daa923a370f04","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:37:50.257664Z","signature_b64":"2ugBPdQ2GCTeTMPHOAPW3B+BjABHfk71iPoIyh+YqvqBn36sNOy3APvhPbdpvgqBqlyATo252TI5YShUCT8eBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb7046f77ff66cdc3acaad45d23d78761cb8aea993402968145daa923a370f04","last_reissued_at":"2026-07-05T01:37:50.257148Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:37:50.257148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2009.11854","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":"2026-07-05T01:37:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WMqV+GUfYGjgtBwMmtqUUJdqrloOOz8yphPRH19RcucuIEXHNqODo8mi0HQMqhzyqT7yDcAQTNVvzlaRRfjrDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T12:23:09.422653Z"},"content_sha256":"ae5d4eda28e4582644d125511fb2ba422bf9f2b69eb471fa25ebc50c807e2753","schema_version":"1.0","event_id":"sha256:ae5d4eda28e4582644d125511fb2ba422bf9f2b69eb471fa25ebc50c807e2753"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:XNYEN5376ZWNYOWKVVC5EPLYOY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$L^p$-stability and positive scalar curvature rigidity of Ricci-flat ALE manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Klaus Kroencke, Oliver Lindblad Petersen","submitted_at":"2020-09-24T17:57:09Z","abstract_excerpt":"We prove stability of integrable ALE manifolds with a parallel spinor under Ricci flow, given an initial metric which is close in $L^p \\cap L^\\infty$, for any $p \\in (1, n)$, where $n$ is the dimension of the manifold. In particular, our result applies to all known examples of $4$-dimensional gravitational instantons. Our decay rates are strong enough to prove positive scalar curvature rigidity in $L^p$, for each $p \\in \\left[1, \\frac{n}{n-2}\\right)$, generalizing a result by Appleton."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.11854","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2009.11854/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:37:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tF31PpCzv+CPvoQyasuQEKfal8hhz56jx1L0ejKpX2NLq73qkqEoOBMUtlb+GGmjPrEyh3HOuL7Z42Kjn88UDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T12:23:09.423018Z"},"content_sha256":"a883e02d391969dab7ab18037d6be1787fbba11fa7ec2e6ea0560fd2058696ce","schema_version":"1.0","event_id":"sha256:a883e02d391969dab7ab18037d6be1787fbba11fa7ec2e6ea0560fd2058696ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XNYEN5376ZWNYOWKVVC5EPLYOY/bundle.json","state_url":"https://pith.science/pith/XNYEN5376ZWNYOWKVVC5EPLYOY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XNYEN5376ZWNYOWKVVC5EPLYOY/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":"2026-07-07T12:23:09Z","links":{"resolver":"https://pith.science/pith/XNYEN5376ZWNYOWKVVC5EPLYOY","bundle":"https://pith.science/pith/XNYEN5376ZWNYOWKVVC5EPLYOY/bundle.json","state":"https://pith.science/pith/XNYEN5376ZWNYOWKVVC5EPLYOY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XNYEN5376ZWNYOWKVVC5EPLYOY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:XNYEN5376ZWNYOWKVVC5EPLYOY","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":"fdbb720e1e51009f4e4bc65a189c22aef718abe185820187ddfb25f4096f2a24","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-09-24T17:57:09Z","title_canon_sha256":"9c244a61933aa0947dbcb9bab881d357c90e4fd8cbd2e0f2d57a61897981a4f6"},"schema_version":"1.0","source":{"id":"2009.11854","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.11854","created_at":"2026-07-05T01:37:50Z"},{"alias_kind":"arxiv_version","alias_value":"2009.11854v1","created_at":"2026-07-05T01:37:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.11854","created_at":"2026-07-05T01:37:50Z"},{"alias_kind":"pith_short_12","alias_value":"XNYEN5376ZWN","created_at":"2026-07-05T01:37:50Z"},{"alias_kind":"pith_short_16","alias_value":"XNYEN5376ZWNYOWK","created_at":"2026-07-05T01:37:50Z"},{"alias_kind":"pith_short_8","alias_value":"XNYEN537","created_at":"2026-07-05T01:37:50Z"}],"graph_snapshots":[{"event_id":"sha256:a883e02d391969dab7ab18037d6be1787fbba11fa7ec2e6ea0560fd2058696ce","target":"graph","created_at":"2026-07-05T01:37:50Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2009.11854/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove stability of integrable ALE manifolds with a parallel spinor under Ricci flow, given an initial metric which is close in $L^p \\cap L^\\infty$, for any $p \\in (1, n)$, where $n$ is the dimension of the manifold. In particular, our result applies to all known examples of $4$-dimensional gravitational instantons. Our decay rates are strong enough to prove positive scalar curvature rigidity in $L^p$, for each $p \\in \\left[1, \\frac{n}{n-2}\\right)$, generalizing a result by Appleton.","authors_text":"Klaus Kroencke, Oliver Lindblad Petersen","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-09-24T17:57:09Z","title":"$L^p$-stability and positive scalar curvature rigidity of Ricci-flat ALE manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.11854","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:ae5d4eda28e4582644d125511fb2ba422bf9f2b69eb471fa25ebc50c807e2753","target":"record","created_at":"2026-07-05T01:37:50Z","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":"fdbb720e1e51009f4e4bc65a189c22aef718abe185820187ddfb25f4096f2a24","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-09-24T17:57:09Z","title_canon_sha256":"9c244a61933aa0947dbcb9bab881d357c90e4fd8cbd2e0f2d57a61897981a4f6"},"schema_version":"1.0","source":{"id":"2009.11854","kind":"arxiv","version":1}},"canonical_sha256":"bb7046f77ff66cdc3acaad45d23d78761cb8aea993402968145daa923a370f04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb7046f77ff66cdc3acaad45d23d78761cb8aea993402968145daa923a370f04","first_computed_at":"2026-07-05T01:37:50.257148Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:37:50.257148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2ugBPdQ2GCTeTMPHOAPW3B+BjABHfk71iPoIyh+YqvqBn36sNOy3APvhPbdpvgqBqlyATo252TI5YShUCT8eBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:37:50.257664Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.11854","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae5d4eda28e4582644d125511fb2ba422bf9f2b69eb471fa25ebc50c807e2753","sha256:a883e02d391969dab7ab18037d6be1787fbba11fa7ec2e6ea0560fd2058696ce"],"state_sha256":"b6c4d7353e0ca9128f53c231c68115a9f87bb4d412f0c8c4755e1465adbd47f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qwrIYdKpG7+NHER6QDlqzvnSjZVo1CDbemz54fPXQ1U7/4/C90LuZ9ijOvt+I2/F2xB7xw+DdXeKPmqycBZSDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T12:23:09.424950Z","bundle_sha256":"4444074ab4f07801b10c955018c780a517543cbbd2ff00e8cbd73ea415d6621b"}}