{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:UU2UUM756QBWMSIGRDYBMHFOSY","short_pith_number":"pith:UU2UUM75","canonical_record":{"source":{"id":"1301.0471","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-03T14:52:06Z","cross_cats_sorted":[],"title_canon_sha256":"90ad94d10f9652aab357ae3b526a95bd2fb5266f9c52b6248b78417f643ad234","abstract_canon_sha256":"15e7b1e9c1f050f73d361219558a3da3c17117539c757b4d580b5dca34f07b90"},"schema_version":"1.0"},"canonical_sha256":"a5354a33fdf40366490688f0161cae960af110c29129936ccf4386fbdf406878","source":{"kind":"arxiv","id":"1301.0471","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0471","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0471v1","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0471","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"pith_short_12","alias_value":"UU2UUM756QBW","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UU2UUM756QBWMSIG","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UU2UUM75","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:UU2UUM756QBWMSIGRDYBMHFOSY","target":"record","payload":{"canonical_record":{"source":{"id":"1301.0471","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-03T14:52:06Z","cross_cats_sorted":[],"title_canon_sha256":"90ad94d10f9652aab357ae3b526a95bd2fb5266f9c52b6248b78417f643ad234","abstract_canon_sha256":"15e7b1e9c1f050f73d361219558a3da3c17117539c757b4d580b5dca34f07b90"},"schema_version":"1.0"},"canonical_sha256":"a5354a33fdf40366490688f0161cae960af110c29129936ccf4386fbdf406878","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:19.532816Z","signature_b64":"Yu6zCpcRVqFzps7YyJiGh5twC5hzdnobRYZx5z6l1p9qxdmTbIhZIkpvwVhfwEWUeYDeYe/d1FGsy8G3g9dQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5354a33fdf40366490688f0161cae960af110c29129936ccf4386fbdf406878","last_reissued_at":"2026-05-18T03:37:19.532120Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:19.532120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.0471","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":"2026-05-18T03:37:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/c4oDCQhIb52dELhMyt6ahYtihm8MEX4Z+vAeqnSO/y8sadbTfhaskLvSS7Yivoqp6hDbblJh6NjFbpMFz46BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:05:40.851590Z"},"content_sha256":"1bf37cf0ff2dbd56a4901789bd2122d004dcc57bd19d39f8476dc0dbadcf5c43","schema_version":"1.0","event_id":"sha256:1bf37cf0ff2dbd56a4901789bd2122d004dcc57bd19d39f8476dc0dbadcf5c43"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:UU2UUM756QBWMSIGRDYBMHFOSY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Blow-up behavior for the Klein-Gordon and other perturbed semilinear wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hatem Zaag, Mohamed-Ali Hamza","submitted_at":"2013-01-03T14:52:06Z","abstract_excerpt":"We give blow-up results for the Klein-Gordon equation and other perturbations of the semilinear wave equations with superlinear power nonlinearity, in one space dimension or in higher dimension under radial symmetry outside the origin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0471","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":"2026-05-18T03:37:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kaols+dY1oJVApWAtImxL+tD66LCy9Yj/4DPlVjis49++rmaEVSq4rcdCikvRZgDN9IAMWqivutweNS/XDu3AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:05:40.851971Z"},"content_sha256":"c72bbd52d9fa0636cd51eb763eb965a873b9c161ddd464f29585f6734101b2fe","schema_version":"1.0","event_id":"sha256:c72bbd52d9fa0636cd51eb763eb965a873b9c161ddd464f29585f6734101b2fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UU2UUM756QBWMSIGRDYBMHFOSY/bundle.json","state_url":"https://pith.science/pith/UU2UUM756QBWMSIGRDYBMHFOSY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UU2UUM756QBWMSIGRDYBMHFOSY/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":"2026-06-26T01:05:40Z","links":{"resolver":"https://pith.science/pith/UU2UUM756QBWMSIGRDYBMHFOSY","bundle":"https://pith.science/pith/UU2UUM756QBWMSIGRDYBMHFOSY/bundle.json","state":"https://pith.science/pith/UU2UUM756QBWMSIGRDYBMHFOSY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UU2UUM756QBWMSIGRDYBMHFOSY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UU2UUM756QBWMSIGRDYBMHFOSY","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":"15e7b1e9c1f050f73d361219558a3da3c17117539c757b4d580b5dca34f07b90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-03T14:52:06Z","title_canon_sha256":"90ad94d10f9652aab357ae3b526a95bd2fb5266f9c52b6248b78417f643ad234"},"schema_version":"1.0","source":{"id":"1301.0471","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0471","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0471v1","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0471","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"pith_short_12","alias_value":"UU2UUM756QBW","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UU2UUM756QBWMSIG","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UU2UUM75","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:c72bbd52d9fa0636cd51eb763eb965a873b9c161ddd464f29585f6734101b2fe","target":"graph","created_at":"2026-05-18T03:37:19Z","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 give blow-up results for the Klein-Gordon equation and other perturbations of the semilinear wave equations with superlinear power nonlinearity, in one space dimension or in higher dimension under radial symmetry outside the origin.","authors_text":"Hatem Zaag, Mohamed-Ali Hamza","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-03T14:52:06Z","title":"Blow-up behavior for the Klein-Gordon and other perturbed semilinear wave equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0471","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":"sha256:1bf37cf0ff2dbd56a4901789bd2122d004dcc57bd19d39f8476dc0dbadcf5c43","target":"record","created_at":"2026-05-18T03:37:19Z","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":"15e7b1e9c1f050f73d361219558a3da3c17117539c757b4d580b5dca34f07b90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-03T14:52:06Z","title_canon_sha256":"90ad94d10f9652aab357ae3b526a95bd2fb5266f9c52b6248b78417f643ad234"},"schema_version":"1.0","source":{"id":"1301.0471","kind":"arxiv","version":1}},"canonical_sha256":"a5354a33fdf40366490688f0161cae960af110c29129936ccf4386fbdf406878","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5354a33fdf40366490688f0161cae960af110c29129936ccf4386fbdf406878","first_computed_at":"2026-05-18T03:37:19.532120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:19.532120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yu6zCpcRVqFzps7YyJiGh5twC5hzdnobRYZx5z6l1p9qxdmTbIhZIkpvwVhfwEWUeYDeYe/d1FGsy8G3g9dQBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:19.532816Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.0471","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1bf37cf0ff2dbd56a4901789bd2122d004dcc57bd19d39f8476dc0dbadcf5c43","sha256:c72bbd52d9fa0636cd51eb763eb965a873b9c161ddd464f29585f6734101b2fe"],"state_sha256":"dcf4d63b52e5e7ec1ab2ca42d849c8afa158d5ad1c928e8be0ec028c190281ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kd4xRJHK0/octdEj5aTr1HrU3G4ieUbhqlGobpi1xCjyYt4usk2FC7LbKtDSNQwwZ0iBJTxTy6qfPmostSoUBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T01:05:40.853941Z","bundle_sha256":"ecd2f12befa94cb883a5b2ff673ac9a5973e09deb8d874a64a8e75cd054451a2"}}