{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MB7SWAWFGNQS2BKI7QWFY5WK5P","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":"ac96b2fc31a878c1e09bd82e87bef4f5fc61cfabf0dcf06fc66fd27fb58f5c0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-30T21:33:03Z","title_canon_sha256":"4533b7555eb002400681e9cd069e5b71f0e162ad2049461bd6a1795baad4b9ec"},"schema_version":"1.0","source":{"id":"1204.0031","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.0031","created_at":"2026-05-18T03:58:50Z"},{"alias_kind":"arxiv_version","alias_value":"1204.0031v1","created_at":"2026-05-18T03:58:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0031","created_at":"2026-05-18T03:58:50Z"},{"alias_kind":"pith_short_12","alias_value":"MB7SWAWFGNQS","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MB7SWAWFGNQS2BKI","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MB7SWAWF","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:67c5af0d2f01c0a0a3a1ed84bf7b8888cba7f15257654b5f672fa8efd8c248fb","target":"graph","created_at":"2026-05-18T03:58:50Z","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"},"paper":{"abstract_excerpt":"In this paper, we describe the asymptotic behaviour of globally defined solutions and of bounded solutions blowing up in finite time of the radial energy-critical focusing non-linear wave equation in three space dimension.","authors_text":"Carlos Kenig, Frank Merle, Thomas Duyckaerts","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-30T21:33:03Z","title":"Classification of radial solutions of the focusing, energy-critical wave equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0031","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":"sha256:0c7dba706f1dcf8462d9aeb06f92631da6afb8d6051c4caa22ecef123d4b3508","target":"record","created_at":"2026-05-18T03:58:50Z","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":"ac96b2fc31a878c1e09bd82e87bef4f5fc61cfabf0dcf06fc66fd27fb58f5c0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-30T21:33:03Z","title_canon_sha256":"4533b7555eb002400681e9cd069e5b71f0e162ad2049461bd6a1795baad4b9ec"},"schema_version":"1.0","source":{"id":"1204.0031","kind":"arxiv","version":1}},"canonical_sha256":"607f2b02c533612d0548fc2c5c76caebccc80bfccc0cb7fb7cbb6996a88edf3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"607f2b02c533612d0548fc2c5c76caebccc80bfccc0cb7fb7cbb6996a88edf3b","first_computed_at":"2026-05-18T03:58:50.561694Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:50.561694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/RQsj3bMfBV00hbmjybXNI9T09h94QaFeEtEQwmlQiO+Oxdbt/8IVP9EGM33tLWqwrUZ+RY+uAj//F25sBzaBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:50.562374Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.0031","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c7dba706f1dcf8462d9aeb06f92631da6afb8d6051c4caa22ecef123d4b3508","sha256:67c5af0d2f01c0a0a3a1ed84bf7b8888cba7f15257654b5f672fa8efd8c248fb"],"state_sha256":"1ea6a94a843d81b837bc60c52b4e712011c8192677c8b9989f309f47945ca9e4"}