{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:C3VKLMV5F6725T376R42NOO4SM","short_pith_number":"pith:C3VKLMV5","canonical_record":{"source":{"id":"1209.0347","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-03T13:29:17Z","cross_cats_sorted":[],"title_canon_sha256":"41c579d370281034313a26a2b9a9f0ebcc7c32307a77c0e8dadf406c714a4b10","abstract_canon_sha256":"67467d78a6d3269fae70d50de925e6c2a3707909cecddf9ce9c45d813715f44b"},"schema_version":"1.0"},"canonical_sha256":"16eaa5b2bd2fbfaecf7ff479a6b9dc931f51247a5cd171a1b632a019b9c71222","source":{"kind":"arxiv","id":"1209.0347","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0347","created_at":"2026-05-18T03:46:16Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0347v2","created_at":"2026-05-18T03:46:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0347","created_at":"2026-05-18T03:46:16Z"},{"alias_kind":"pith_short_12","alias_value":"C3VKLMV5F672","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"C3VKLMV5F6725T37","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"C3VKLMV5","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:C3VKLMV5F6725T376R42NOO4SM","target":"record","payload":{"canonical_record":{"source":{"id":"1209.0347","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-03T13:29:17Z","cross_cats_sorted":[],"title_canon_sha256":"41c579d370281034313a26a2b9a9f0ebcc7c32307a77c0e8dadf406c714a4b10","abstract_canon_sha256":"67467d78a6d3269fae70d50de925e6c2a3707909cecddf9ce9c45d813715f44b"},"schema_version":"1.0"},"canonical_sha256":"16eaa5b2bd2fbfaecf7ff479a6b9dc931f51247a5cd171a1b632a019b9c71222","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:16.289563Z","signature_b64":"fnHWnkUhfzPqKLDH4MBV0pLKFiBadzCCzsBJ3rbMPI7nsDcrRvJFScH5lY9mZC8ts1HXRvYytcR6UQcWLRNODQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16eaa5b2bd2fbfaecf7ff479a6b9dc931f51247a5cd171a1b632a019b9c71222","last_reissued_at":"2026-05-18T03:46:16.288810Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:16.288810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.0347","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":"2026-05-18T03:46:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JVqvAcXDUQxVumSHTTc61l2TYDwgvgEEQvLifNRqy/hZs1cORPXPgBXaLwImYB2JDe/E+ZnotvtXcY7ey8cABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:23:41.424366Z"},"content_sha256":"90e19b83327f14d4f824dfcab32047b964a4992029d7485f0300d8379ddeb89e","schema_version":"1.0","event_id":"sha256:90e19b83327f14d4f824dfcab32047b964a4992029d7485f0300d8379ddeb89e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:C3VKLMV5F6725T376R42NOO4SM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Threshold phenomenon for the quintic wave equation in three dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag","submitted_at":"2012-09-03T13:29:17Z","abstract_excerpt":"For the critical focusing wave equation $\\Box u = u^5$ on $\\R^{3+1}$ in the radial case, we establish the role of the \"center stable\" manifold $\\Sigma$ constructed in \\cite{KS} near the ground state $(W,0)$ as a threshold between type I blowup and scattering to zero, establishing a conjecture going back to numerical work by Bizo\\'n, Chmaj, Tabor. The underlying topology is stronger than the energy norm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0347","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":"2026-05-18T03:46:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b6gX14CACzOHWapbZqat2l/v8kQ0dLngmDAQ5Dx31NaXAVAP8J3ct+gLSGG1tWfZ8trsiJHJWYz3jgK0LhitCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:23:41.425106Z"},"content_sha256":"6869e27cf93f87fd6475ffdc786705ee07fe80cbf801b146f9b4b204b36c6f84","schema_version":"1.0","event_id":"sha256:6869e27cf93f87fd6475ffdc786705ee07fe80cbf801b146f9b4b204b36c6f84"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C3VKLMV5F6725T376R42NOO4SM/bundle.json","state_url":"https://pith.science/pith/C3VKLMV5F6725T376R42NOO4SM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C3VKLMV5F6725T376R42NOO4SM/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":"2026-05-25T19:23:41Z","links":{"resolver":"https://pith.science/pith/C3VKLMV5F6725T376R42NOO4SM","bundle":"https://pith.science/pith/C3VKLMV5F6725T376R42NOO4SM/bundle.json","state":"https://pith.science/pith/C3VKLMV5F6725T376R42NOO4SM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C3VKLMV5F6725T376R42NOO4SM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:C3VKLMV5F6725T376R42NOO4SM","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":"67467d78a6d3269fae70d50de925e6c2a3707909cecddf9ce9c45d813715f44b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-03T13:29:17Z","title_canon_sha256":"41c579d370281034313a26a2b9a9f0ebcc7c32307a77c0e8dadf406c714a4b10"},"schema_version":"1.0","source":{"id":"1209.0347","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0347","created_at":"2026-05-18T03:46:16Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0347v2","created_at":"2026-05-18T03:46:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0347","created_at":"2026-05-18T03:46:16Z"},{"alias_kind":"pith_short_12","alias_value":"C3VKLMV5F672","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"C3VKLMV5F6725T37","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"C3VKLMV5","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:6869e27cf93f87fd6475ffdc786705ee07fe80cbf801b146f9b4b204b36c6f84","target":"graph","created_at":"2026-05-18T03:46:16Z","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":"For the critical focusing wave equation $\\Box u = u^5$ on $\\R^{3+1}$ in the radial case, we establish the role of the \"center stable\" manifold $\\Sigma$ constructed in \\cite{KS} near the ground state $(W,0)$ as a threshold between type I blowup and scattering to zero, establishing a conjecture going back to numerical work by Bizo\\'n, Chmaj, Tabor. The underlying topology is stronger than the energy norm.","authors_text":"Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-03T13:29:17Z","title":"Threshold phenomenon for the quintic wave equation in three dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0347","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":"sha256:90e19b83327f14d4f824dfcab32047b964a4992029d7485f0300d8379ddeb89e","target":"record","created_at":"2026-05-18T03:46:16Z","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":"67467d78a6d3269fae70d50de925e6c2a3707909cecddf9ce9c45d813715f44b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-03T13:29:17Z","title_canon_sha256":"41c579d370281034313a26a2b9a9f0ebcc7c32307a77c0e8dadf406c714a4b10"},"schema_version":"1.0","source":{"id":"1209.0347","kind":"arxiv","version":2}},"canonical_sha256":"16eaa5b2bd2fbfaecf7ff479a6b9dc931f51247a5cd171a1b632a019b9c71222","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16eaa5b2bd2fbfaecf7ff479a6b9dc931f51247a5cd171a1b632a019b9c71222","first_computed_at":"2026-05-18T03:46:16.288810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:16.288810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fnHWnkUhfzPqKLDH4MBV0pLKFiBadzCCzsBJ3rbMPI7nsDcrRvJFScH5lY9mZC8ts1HXRvYytcR6UQcWLRNODQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:16.289563Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.0347","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90e19b83327f14d4f824dfcab32047b964a4992029d7485f0300d8379ddeb89e","sha256:6869e27cf93f87fd6475ffdc786705ee07fe80cbf801b146f9b4b204b36c6f84"],"state_sha256":"7c5d8bb5835aec51ff945d5b4b87248db6f13e292c51d0348e2037d23fd1f115"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dYams6clfK0aCE1ojm+OKECB9SJb9X6TlQVspe+9Bywe1bGpdiE4xKlB3+hNM73BGdGrKMscFeaxwZh56Z38AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:23:41.429167Z","bundle_sha256":"2c2f425e69c2f003b9998d766b903cc52682afc225f66b0737d2257429c8a656"}}