{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:N5YRWAVK3S3LQZIQR5LI4NNKPH","short_pith_number":"pith:N5YRWAVK","canonical_record":{"source":{"id":"1012.0685","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-03T10:13:24Z","cross_cats_sorted":[],"title_canon_sha256":"9a15ae8ff8eeec2ccc135dd6cf4d60745b61869f25e2f55f3a59f8600c015753","abstract_canon_sha256":"63380438d2f34e2c739a6bcfd9133aed927687308ad6b247ecd7361ac78c9162"},"schema_version":"1.0"},"canonical_sha256":"6f711b02aadcb6b865108f568e35aa79d7dfbb6f282b3b342df4b5413d809163","source":{"kind":"arxiv","id":"1012.0685","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0685","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0685v1","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0685","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"pith_short_12","alias_value":"N5YRWAVK3S3L","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"N5YRWAVK3S3LQZIQ","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"N5YRWAVK","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:N5YRWAVK3S3LQZIQR5LI4NNKPH","target":"record","payload":{"canonical_record":{"source":{"id":"1012.0685","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-03T10:13:24Z","cross_cats_sorted":[],"title_canon_sha256":"9a15ae8ff8eeec2ccc135dd6cf4d60745b61869f25e2f55f3a59f8600c015753","abstract_canon_sha256":"63380438d2f34e2c739a6bcfd9133aed927687308ad6b247ecd7361ac78c9162"},"schema_version":"1.0"},"canonical_sha256":"6f711b02aadcb6b865108f568e35aa79d7dfbb6f282b3b342df4b5413d809163","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:09.598273Z","signature_b64":"Je6IwYgsXxX+0IzxX8FZGWDxRruZj1iO4JhR3teSxAI1vLbePNK+dBRU0kjEsiZUnHctw/LXOtUrooo9DWIEDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f711b02aadcb6b865108f568e35aa79d7dfbb6f282b3b342df4b5413d809163","last_reissued_at":"2026-05-18T04:34:09.597885Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:09.597885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.0685","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":"2026-05-18T04:34:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"25j3EdzfK7Xfr/tGaNtGa4xfX6WRlEowqq+Trig8ws96LI9+L8MEHPaJaY1Ri/MqX/fToO8mzXMalPkBRA6VCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:21:10.918279Z"},"content_sha256":"2a120e8222d332ba14fdae60232e01e5ff2699546c0ade9ffa837e3c690f4b0a","schema_version":"1.0","event_id":"sha256:2a120e8222d332ba14fdae60232e01e5ff2699546c0ade9ffa837e3c690f4b0a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:N5YRWAVK3S3LQZIQR5LI4NNKPH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some old and new results about rigidity of critical metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Gilles Carron (LMJL)","submitted_at":"2010-12-03T10:13:24Z","abstract_excerpt":"We present a new proof of a recent $\\epsilon$ regularity of G. Tian and J.Viaclovsky. Moreover, our idea also also works with a kind of $L^p, p<\\dim M/2$ assumptions on the curvature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0685","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":"2026-05-18T04:34:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KRGgimBkyU2qqPGfzSuKWBACtSBkXq86zhAWMM7GOALCjS1og5p/aLWhBfrCJYowrAYxrZFmHvtSjxTKiTYvAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:21:10.918939Z"},"content_sha256":"996586e55bc5691a19846d2b1085dcfd429c7129d7f06b8364a9f9b2f6263562","schema_version":"1.0","event_id":"sha256:996586e55bc5691a19846d2b1085dcfd429c7129d7f06b8364a9f9b2f6263562"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N5YRWAVK3S3LQZIQR5LI4NNKPH/bundle.json","state_url":"https://pith.science/pith/N5YRWAVK3S3LQZIQR5LI4NNKPH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N5YRWAVK3S3LQZIQR5LI4NNKPH/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":"2026-06-04T23:21:10Z","links":{"resolver":"https://pith.science/pith/N5YRWAVK3S3LQZIQR5LI4NNKPH","bundle":"https://pith.science/pith/N5YRWAVK3S3LQZIQR5LI4NNKPH/bundle.json","state":"https://pith.science/pith/N5YRWAVK3S3LQZIQR5LI4NNKPH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N5YRWAVK3S3LQZIQR5LI4NNKPH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:N5YRWAVK3S3LQZIQR5LI4NNKPH","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":"63380438d2f34e2c739a6bcfd9133aed927687308ad6b247ecd7361ac78c9162","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-03T10:13:24Z","title_canon_sha256":"9a15ae8ff8eeec2ccc135dd6cf4d60745b61869f25e2f55f3a59f8600c015753"},"schema_version":"1.0","source":{"id":"1012.0685","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0685","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0685v1","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0685","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"pith_short_12","alias_value":"N5YRWAVK3S3L","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"N5YRWAVK3S3LQZIQ","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"N5YRWAVK","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:996586e55bc5691a19846d2b1085dcfd429c7129d7f06b8364a9f9b2f6263562","target":"graph","created_at":"2026-05-18T04:34:09Z","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 present a new proof of a recent $\\epsilon$ regularity of G. Tian and J.Viaclovsky. Moreover, our idea also also works with a kind of $L^p, p<\\dim M/2$ assumptions on the curvature.","authors_text":"Gilles Carron (LMJL)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-03T10:13:24Z","title":"Some old and new results about rigidity of critical metric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0685","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":"sha256:2a120e8222d332ba14fdae60232e01e5ff2699546c0ade9ffa837e3c690f4b0a","target":"record","created_at":"2026-05-18T04:34:09Z","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":"63380438d2f34e2c739a6bcfd9133aed927687308ad6b247ecd7361ac78c9162","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-03T10:13:24Z","title_canon_sha256":"9a15ae8ff8eeec2ccc135dd6cf4d60745b61869f25e2f55f3a59f8600c015753"},"schema_version":"1.0","source":{"id":"1012.0685","kind":"arxiv","version":1}},"canonical_sha256":"6f711b02aadcb6b865108f568e35aa79d7dfbb6f282b3b342df4b5413d809163","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f711b02aadcb6b865108f568e35aa79d7dfbb6f282b3b342df4b5413d809163","first_computed_at":"2026-05-18T04:34:09.597885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:09.597885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Je6IwYgsXxX+0IzxX8FZGWDxRruZj1iO4JhR3teSxAI1vLbePNK+dBRU0kjEsiZUnHctw/LXOtUrooo9DWIEDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:09.598273Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.0685","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a120e8222d332ba14fdae60232e01e5ff2699546c0ade9ffa837e3c690f4b0a","sha256:996586e55bc5691a19846d2b1085dcfd429c7129d7f06b8364a9f9b2f6263562"],"state_sha256":"a84c03108c78b0e19a60860fabd7c66e0901f5a2044ab75b52054db9ed8ac9cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FHuV47/o4GhjRqH4N8tKONafqEj+0LXAfS4QuwTtmPV2lO1uSMLSGEPfnFc8y957gyPISdOwZRb2ffLf3XUwCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T23:21:10.922240Z","bundle_sha256":"80df63beada87567174bdd2530ffa90015c39b77c86ef4b21e7c10a0d35e2579"}}