{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DY7HCAWR4I6YEBOQY23ESNTIIB","short_pith_number":"pith:DY7HCAWR","canonical_record":{"source":{"id":"1301.4378","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-18T13:34:02Z","cross_cats_sorted":[],"title_canon_sha256":"5fa6daf0cbb1573aba1f1fcffaa2d937e544ef20d871f3414caa73eba640a037","abstract_canon_sha256":"86b61704276170cf4d9675110eebdc373b6166511aece60587f15e5eaa9904fb"},"schema_version":"1.0"},"canonical_sha256":"1e3e7102d1e23d8205d0c6b649366840561b7e7ea87fcc2ef188d64b7f476001","source":{"kind":"arxiv","id":"1301.4378","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4378","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4378v4","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4378","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"pith_short_12","alias_value":"DY7HCAWR4I6Y","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DY7HCAWR4I6YEBOQ","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DY7HCAWR","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DY7HCAWR4I6YEBOQY23ESNTIIB","target":"record","payload":{"canonical_record":{"source":{"id":"1301.4378","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-18T13:34:02Z","cross_cats_sorted":[],"title_canon_sha256":"5fa6daf0cbb1573aba1f1fcffaa2d937e544ef20d871f3414caa73eba640a037","abstract_canon_sha256":"86b61704276170cf4d9675110eebdc373b6166511aece60587f15e5eaa9904fb"},"schema_version":"1.0"},"canonical_sha256":"1e3e7102d1e23d8205d0c6b649366840561b7e7ea87fcc2ef188d64b7f476001","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:39.722268Z","signature_b64":"Rtx9WwFvn/ksoB7cfB07iNN5dj8aJwsCgIZUGrfiLvTQnTkXETEQu6eNScIRcuNzqYCaZEtL0nSNi3wFRWm6BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e3e7102d1e23d8205d0c6b649366840561b7e7ea87fcc2ef188d64b7f476001","last_reissued_at":"2026-05-18T02:42:39.721602Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:39.721602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.4378","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:42:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PtPRFuLS4W2+jXkmlHSeoOfNBOWD+qlG7jNoWfDdAooVxfusxqGWLsm9VMj4u1nv3NsxBiwDYisdyYELxIa5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:43:00.283549Z"},"content_sha256":"fa4296b675ec406e6e98f19c52aea39b5d4fa53f4450d178e8f8379c6bed1d4a","schema_version":"1.0","event_id":"sha256:fa4296b675ec406e6e98f19c52aea39b5d4fa53f4450d178e8f8379c6bed1d4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DY7HCAWR4I6YEBOQY23ESNTIIB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On type I blow up formation for the critical NLW","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Joachim Krieger, Willie Wong","submitted_at":"2013-01-18T13:34:02Z","abstract_excerpt":"We introduce a suitable concept of weak evolution in the context of the radial quintic focussing semilinear wave equation on $\\mathbb{R}^{3+1}$, that is adapted to continuation past type II singularities. We show that the weak extension leads to type I singularity formation for initial data corresponding to: (i) the Kenig-Merle blow-up solutions with initial energy below the ground state and (ii) the Krieger-Nakanishi-Schlag blow-up solutions sitting initially near and \"above\" the ground state static solution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4378","kind":"arxiv","version":4},"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":"2026-05-18T02:42:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"esh7jqMr5Rv1QDjNfTn3RV6rt7ZPlRiDPUpCIvUlZsHDAlmwjW1hG495y+/USbO6O8YfbgFoNyWgey9Jj0WpCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:43:00.284281Z"},"content_sha256":"10e66a9dde447e4b6aa2aa76ed22395a0196de487941a90531e15e26c3d914bd","schema_version":"1.0","event_id":"sha256:10e66a9dde447e4b6aa2aa76ed22395a0196de487941a90531e15e26c3d914bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DY7HCAWR4I6YEBOQY23ESNTIIB/bundle.json","state_url":"https://pith.science/pith/DY7HCAWR4I6YEBOQY23ESNTIIB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DY7HCAWR4I6YEBOQY23ESNTIIB/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":"2026-05-26T01:43:00Z","links":{"resolver":"https://pith.science/pith/DY7HCAWR4I6YEBOQY23ESNTIIB","bundle":"https://pith.science/pith/DY7HCAWR4I6YEBOQY23ESNTIIB/bundle.json","state":"https://pith.science/pith/DY7HCAWR4I6YEBOQY23ESNTIIB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DY7HCAWR4I6YEBOQY23ESNTIIB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DY7HCAWR4I6YEBOQY23ESNTIIB","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":"86b61704276170cf4d9675110eebdc373b6166511aece60587f15e5eaa9904fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-18T13:34:02Z","title_canon_sha256":"5fa6daf0cbb1573aba1f1fcffaa2d937e544ef20d871f3414caa73eba640a037"},"schema_version":"1.0","source":{"id":"1301.4378","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4378","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4378v4","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4378","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"pith_short_12","alias_value":"DY7HCAWR4I6Y","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DY7HCAWR4I6YEBOQ","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DY7HCAWR","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:10e66a9dde447e4b6aa2aa76ed22395a0196de487941a90531e15e26c3d914bd","target":"graph","created_at":"2026-05-18T02:42:39Z","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 introduce a suitable concept of weak evolution in the context of the radial quintic focussing semilinear wave equation on $\\mathbb{R}^{3+1}$, that is adapted to continuation past type II singularities. We show that the weak extension leads to type I singularity formation for initial data corresponding to: (i) the Kenig-Merle blow-up solutions with initial energy below the ground state and (ii) the Krieger-Nakanishi-Schlag blow-up solutions sitting initially near and \"above\" the ground state static solution.","authors_text":"Joachim Krieger, Willie Wong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-18T13:34:02Z","title":"On type I blow up formation for the critical NLW"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4378","kind":"arxiv","version":4},"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:fa4296b675ec406e6e98f19c52aea39b5d4fa53f4450d178e8f8379c6bed1d4a","target":"record","created_at":"2026-05-18T02:42:39Z","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":"86b61704276170cf4d9675110eebdc373b6166511aece60587f15e5eaa9904fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-18T13:34:02Z","title_canon_sha256":"5fa6daf0cbb1573aba1f1fcffaa2d937e544ef20d871f3414caa73eba640a037"},"schema_version":"1.0","source":{"id":"1301.4378","kind":"arxiv","version":4}},"canonical_sha256":"1e3e7102d1e23d8205d0c6b649366840561b7e7ea87fcc2ef188d64b7f476001","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e3e7102d1e23d8205d0c6b649366840561b7e7ea87fcc2ef188d64b7f476001","first_computed_at":"2026-05-18T02:42:39.721602Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:39.721602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rtx9WwFvn/ksoB7cfB07iNN5dj8aJwsCgIZUGrfiLvTQnTkXETEQu6eNScIRcuNzqYCaZEtL0nSNi3wFRWm6BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:39.722268Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.4378","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa4296b675ec406e6e98f19c52aea39b5d4fa53f4450d178e8f8379c6bed1d4a","sha256:10e66a9dde447e4b6aa2aa76ed22395a0196de487941a90531e15e26c3d914bd"],"state_sha256":"098051e16a5ff9c84b6047915b1a57a77ba5f7fb63c7b160df96e47f15393f6b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R417QmcBunQ7lYJtTD4zDC/xkiCocd3A07jgQC95G5uYVf1lJx23rhj6tPjHgkY8etuHUWDHO835V/JD/f0pAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T01:43:00.287644Z","bundle_sha256":"440ab359012dea5766279eac896b45c68dbdb43cdec3d138f9af60f146c77642"}}