{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:NL7GBRDUOPNI45YWX5ZG5PSJBX","short_pith_number":"pith:NL7GBRDU","canonical_record":{"source":{"id":"math-ph/0407001","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2004-07-01T13:15:16Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"79a0533f3eec8ff05995c7e158e78ad1f2cdc940144dacdf950060a69deea956","abstract_canon_sha256":"a3f312a185fa38685ee00aefdfbea8273ebc467d662207949d1a2ca8ed93aaa3"},"schema_version":"1.0"},"canonical_sha256":"6afe60c47473da8e7716bf726ebe490df46717b434104653b12690bfee841512","source":{"kind":"arxiv","id":"math-ph/0407001","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0407001","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0407001v2","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0407001","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"pith_short_12","alias_value":"NL7GBRDUOPNI","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"NL7GBRDUOPNI45YW","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"NL7GBRDU","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:NL7GBRDUOPNI45YWX5ZG5PSJBX","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0407001","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2004-07-01T13:15:16Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"79a0533f3eec8ff05995c7e158e78ad1f2cdc940144dacdf950060a69deea956","abstract_canon_sha256":"a3f312a185fa38685ee00aefdfbea8273ebc467d662207949d1a2ca8ed93aaa3"},"schema_version":"1.0"},"canonical_sha256":"6afe60c47473da8e7716bf726ebe490df46717b434104653b12690bfee841512","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:54.095007Z","signature_b64":"E77pJXaOT3ViDbPp3LYqjNxJqY6OzZhxPfEE7bal9arkBIS9O/ng4UYnhXRxWaI4Ab19D9ZI6qp3RyqrXgVPAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6afe60c47473da8e7716bf726ebe490df46717b434104653b12690bfee841512","last_reissued_at":"2026-05-18T04:41:54.094383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:54.094383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0407001","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":"2026-05-18T04:41:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qwvrTltOjHnzocGika6t3PyZcT5XAeP++AzwhGmxcZK4VX13hK2dejtn9UhzW0BKdWD3OTttiVQ95gBYuNN3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:02:50.651201Z"},"content_sha256":"60dd7f78c1f89c63e2cbdff1242c8d5ce119b9304074c9466aeab120634c8d16","schema_version":"1.0","event_id":"sha256:60dd7f78c1f89c63e2cbdff1242c8d5ce119b9304074c9466aeab120634c8d16"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:NL7GBRDUOPNI45YWX5ZG5PSJBX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Blow Up for the Semilinear Wave Equation in Schwarzschild Metric","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Davide Catania, Vladimir Georgiev","submitted_at":"2004-07-01T13:15:16Z","abstract_excerpt":"We study the semilinear wave equation in Schwarzschild metric (3+1 dimensional space--time). First, we establish that the problem is locally well--posed in $\\cs H^\\sigma$ for any $\\sigma \\geq 1$; then we prove the blow up of the solution for every real $p \\in ]1,1+\\sqrt{2}[$ and non--negative non--trivial initial data."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0407001","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":"2026-05-18T04:41:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GROfrJtFQ1c4CasWMiBKz6Xd6RLYmPky5wrqgRQl46RDDvAMZaO9uRGPIAEUuTvlQqXiCDQm4kWMaYQ63Yb2Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:02:50.651565Z"},"content_sha256":"b48f677e86cba4acb2db0daf3c7911d50f3a67525a4857a1310b8dc4715be168","schema_version":"1.0","event_id":"sha256:b48f677e86cba4acb2db0daf3c7911d50f3a67525a4857a1310b8dc4715be168"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NL7GBRDUOPNI45YWX5ZG5PSJBX/bundle.json","state_url":"https://pith.science/pith/NL7GBRDUOPNI45YWX5ZG5PSJBX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NL7GBRDUOPNI45YWX5ZG5PSJBX/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":"2026-06-23T07:02:50Z","links":{"resolver":"https://pith.science/pith/NL7GBRDUOPNI45YWX5ZG5PSJBX","bundle":"https://pith.science/pith/NL7GBRDUOPNI45YWX5ZG5PSJBX/bundle.json","state":"https://pith.science/pith/NL7GBRDUOPNI45YWX5ZG5PSJBX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NL7GBRDUOPNI45YWX5ZG5PSJBX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:NL7GBRDUOPNI45YWX5ZG5PSJBX","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":"a3f312a185fa38685ee00aefdfbea8273ebc467d662207949d1a2ca8ed93aaa3","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2004-07-01T13:15:16Z","title_canon_sha256":"79a0533f3eec8ff05995c7e158e78ad1f2cdc940144dacdf950060a69deea956"},"schema_version":"1.0","source":{"id":"math-ph/0407001","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0407001","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0407001v2","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0407001","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"pith_short_12","alias_value":"NL7GBRDUOPNI","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"NL7GBRDUOPNI45YW","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"NL7GBRDU","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:b48f677e86cba4acb2db0daf3c7911d50f3a67525a4857a1310b8dc4715be168","target":"graph","created_at":"2026-05-18T04:41:54Z","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 study the semilinear wave equation in Schwarzschild metric (3+1 dimensional space--time). First, we establish that the problem is locally well--posed in $\\cs H^\\sigma$ for any $\\sigma \\geq 1$; then we prove the blow up of the solution for every real $p \\in ]1,1+\\sqrt{2}[$ and non--negative non--trivial initial data.","authors_text":"Davide Catania, Vladimir Georgiev","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2004-07-01T13:15:16Z","title":"Blow Up for the Semilinear Wave Equation in Schwarzschild Metric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0407001","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":"sha256:60dd7f78c1f89c63e2cbdff1242c8d5ce119b9304074c9466aeab120634c8d16","target":"record","created_at":"2026-05-18T04:41:54Z","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":"a3f312a185fa38685ee00aefdfbea8273ebc467d662207949d1a2ca8ed93aaa3","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2004-07-01T13:15:16Z","title_canon_sha256":"79a0533f3eec8ff05995c7e158e78ad1f2cdc940144dacdf950060a69deea956"},"schema_version":"1.0","source":{"id":"math-ph/0407001","kind":"arxiv","version":2}},"canonical_sha256":"6afe60c47473da8e7716bf726ebe490df46717b434104653b12690bfee841512","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6afe60c47473da8e7716bf726ebe490df46717b434104653b12690bfee841512","first_computed_at":"2026-05-18T04:41:54.094383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:54.094383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E77pJXaOT3ViDbPp3LYqjNxJqY6OzZhxPfEE7bal9arkBIS9O/ng4UYnhXRxWaI4Ab19D9ZI6qp3RyqrXgVPAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:54.095007Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0407001","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60dd7f78c1f89c63e2cbdff1242c8d5ce119b9304074c9466aeab120634c8d16","sha256:b48f677e86cba4acb2db0daf3c7911d50f3a67525a4857a1310b8dc4715be168"],"state_sha256":"1b6cde7fa50ccf1bdb7da6537c52f0e42c6ddd67f3352e80006564790540e426"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xF8dpntHNjYjbO4vPXZoECDdYGMGTwgyETqlrVPRJ2JWHfcID37Pla7rUmsgLJsZUsIZeTRKOUVWvFUxA3RkAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T07:02:50.653573Z","bundle_sha256":"4d28de1041ca6824f65b16aedd79a987ff659887cf2989796662f095f7fbcddb"}}