{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:KZZR6ERYGUOCJDLE7UUKMYVEVN","short_pith_number":"pith:KZZR6ERY","canonical_record":{"source":{"id":"1106.1249","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-06-07T02:19:35Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"aab6d32c5ac675d950a029cc13606101ec24fe04b4ee76ee82254aa61c351515","abstract_canon_sha256":"14e805b7cd321109fafba2dd8e65a22f974651f1c78253cd06fde214fcc63521"},"schema_version":"1.0"},"canonical_sha256":"56731f1238351c248d64fd28a662a4ab73b64918a13b86328c4bd77399e306fa","source":{"kind":"arxiv","id":"1106.1249","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1249","created_at":"2026-05-18T04:11:28Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1249v2","created_at":"2026-05-18T04:11:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1249","created_at":"2026-05-18T04:11:28Z"},{"alias_kind":"pith_short_12","alias_value":"KZZR6ERYGUOC","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"KZZR6ERYGUOCJDLE","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"KZZR6ERY","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:KZZR6ERYGUOCJDLE7UUKMYVEVN","target":"record","payload":{"canonical_record":{"source":{"id":"1106.1249","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-06-07T02:19:35Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"aab6d32c5ac675d950a029cc13606101ec24fe04b4ee76ee82254aa61c351515","abstract_canon_sha256":"14e805b7cd321109fafba2dd8e65a22f974651f1c78253cd06fde214fcc63521"},"schema_version":"1.0"},"canonical_sha256":"56731f1238351c248d64fd28a662a4ab73b64918a13b86328c4bd77399e306fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:28.538134Z","signature_b64":"QOV7VUCFE5qoB8Noql3PUd27iF32nTe8xrTPPfL2OGhJbrXv79/uGWoP7E27aVwccw6gFrFIKJQUUsuhBnZgBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56731f1238351c248d64fd28a662a4ab73b64918a13b86328c4bd77399e306fa","last_reissued_at":"2026-05-18T04:11:28.537457Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:28.537457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.1249","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":"2026-05-18T04:11:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VN8NAQx09G5ZPWPCFiBkAnVlUxk7xJgAeJBComGDaZAzWgMCZ9+akQQ461pyFW3XNVAaI1AMh255i27RVMm1AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:04:14.583361Z"},"content_sha256":"0862fb3bcbba48b8c932847d4cb97560450a9760d5f0b5480e972cfb6833e4c4","schema_version":"1.0","event_id":"sha256:0862fb3bcbba48b8c932847d4cb97560450a9760d5f0b5480e972cfb6833e4c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:KZZR6ERYGUOCJDLE7UUKMYVEVN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Obstruction-flat asymptotically locally Euclidean metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Antonio Ache, Jeff Viaclovsky","submitted_at":"2011-06-07T02:19:35Z","abstract_excerpt":"We show that any asymptotically locally Euclidean (ALE) metric which is obstruction-flat or extended obstruction-flat must be ALE of a certain optimal order. Moreover, our proof applies to very general elliptic systems and in any dimension $n \\geq 3$. The proof is based on the technique of Cheeger-Tian for Ricci-flat metrics. We also apply this method to obtain a singularity removal theorem for (extended) obstruction-flat metrics with isolated $C^0$-orbifold singular points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1249","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":"2026-05-18T04:11:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5KXsdco0fgyxmR/DJWGitaIBZWTuV6Dxm9/h9V3DZj5npR+reIWRQIZwBFkeR8TJl1X2Hx9iRm1U0hil+MUwAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:04:14.584084Z"},"content_sha256":"dcfcd3b4d1733a3fca19b2c0ad851ed18241819402c1b20feed39d893e43442a","schema_version":"1.0","event_id":"sha256:dcfcd3b4d1733a3fca19b2c0ad851ed18241819402c1b20feed39d893e43442a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KZZR6ERYGUOCJDLE7UUKMYVEVN/bundle.json","state_url":"https://pith.science/pith/KZZR6ERYGUOCJDLE7UUKMYVEVN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KZZR6ERYGUOCJDLE7UUKMYVEVN/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":"2026-05-28T20:04:14Z","links":{"resolver":"https://pith.science/pith/KZZR6ERYGUOCJDLE7UUKMYVEVN","bundle":"https://pith.science/pith/KZZR6ERYGUOCJDLE7UUKMYVEVN/bundle.json","state":"https://pith.science/pith/KZZR6ERYGUOCJDLE7UUKMYVEVN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KZZR6ERYGUOCJDLE7UUKMYVEVN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KZZR6ERYGUOCJDLE7UUKMYVEVN","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":"14e805b7cd321109fafba2dd8e65a22f974651f1c78253cd06fde214fcc63521","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-06-07T02:19:35Z","title_canon_sha256":"aab6d32c5ac675d950a029cc13606101ec24fe04b4ee76ee82254aa61c351515"},"schema_version":"1.0","source":{"id":"1106.1249","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1249","created_at":"2026-05-18T04:11:28Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1249v2","created_at":"2026-05-18T04:11:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1249","created_at":"2026-05-18T04:11:28Z"},{"alias_kind":"pith_short_12","alias_value":"KZZR6ERYGUOC","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"KZZR6ERYGUOCJDLE","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"KZZR6ERY","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:dcfcd3b4d1733a3fca19b2c0ad851ed18241819402c1b20feed39d893e43442a","target":"graph","created_at":"2026-05-18T04:11:28Z","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 show that any asymptotically locally Euclidean (ALE) metric which is obstruction-flat or extended obstruction-flat must be ALE of a certain optimal order. Moreover, our proof applies to very general elliptic systems and in any dimension $n \\geq 3$. The proof is based on the technique of Cheeger-Tian for Ricci-flat metrics. We also apply this method to obtain a singularity removal theorem for (extended) obstruction-flat metrics with isolated $C^0$-orbifold singular points.","authors_text":"Antonio Ache, Jeff Viaclovsky","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-06-07T02:19:35Z","title":"Obstruction-flat asymptotically locally Euclidean metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1249","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":"sha256:0862fb3bcbba48b8c932847d4cb97560450a9760d5f0b5480e972cfb6833e4c4","target":"record","created_at":"2026-05-18T04:11:28Z","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":"14e805b7cd321109fafba2dd8e65a22f974651f1c78253cd06fde214fcc63521","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-06-07T02:19:35Z","title_canon_sha256":"aab6d32c5ac675d950a029cc13606101ec24fe04b4ee76ee82254aa61c351515"},"schema_version":"1.0","source":{"id":"1106.1249","kind":"arxiv","version":2}},"canonical_sha256":"56731f1238351c248d64fd28a662a4ab73b64918a13b86328c4bd77399e306fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56731f1238351c248d64fd28a662a4ab73b64918a13b86328c4bd77399e306fa","first_computed_at":"2026-05-18T04:11:28.537457Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:28.537457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QOV7VUCFE5qoB8Noql3PUd27iF32nTe8xrTPPfL2OGhJbrXv79/uGWoP7E27aVwccw6gFrFIKJQUUsuhBnZgBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:28.538134Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.1249","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0862fb3bcbba48b8c932847d4cb97560450a9760d5f0b5480e972cfb6833e4c4","sha256:dcfcd3b4d1733a3fca19b2c0ad851ed18241819402c1b20feed39d893e43442a"],"state_sha256":"b3ee0fe8ef0704abf503700294412c9db8d0e480820cd8803993a69c017696d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+sux0rIDe7ZxHDjAjNZ7Nugu3yzq+Yxa8u9tvRZhFQbF/CLuWZ89Om5Yb6rVSmabiKeCoOeYS/ImWoBUPUZNDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:04:14.587961Z","bundle_sha256":"51128a6f1cd71ba11f3aca88780b3b20f276fbd39a93cc1961f1fd57be169247"}}