{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:XRYWLLLK2JEG7WU47CTXVJON6H","short_pith_number":"pith:XRYWLLLK","canonical_record":{"source":{"id":"1710.06780","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-18T15:23:58Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"db37f0bff3be67c718af353410acc97562c08300af8a1ab295ed5fc8f7dc7f89","abstract_canon_sha256":"986b29ac42b79bd1001cbd2b562ac571d226f671c72e40cdcbc6511b6d1dc6f9"},"schema_version":"1.0"},"canonical_sha256":"bc7165ad6ad2486fda9cf8a77aa5cdf1ce0d127a540c5d0865873a21f3bae126","source":{"kind":"arxiv","id":"1710.06780","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.06780","created_at":"2026-05-18T00:14:59Z"},{"alias_kind":"arxiv_version","alias_value":"1710.06780v2","created_at":"2026-05-18T00:14:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06780","created_at":"2026-05-18T00:14:59Z"},{"alias_kind":"pith_short_12","alias_value":"XRYWLLLK2JEG","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XRYWLLLK2JEG7WU4","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XRYWLLLK","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:XRYWLLLK2JEG7WU47CTXVJON6H","target":"record","payload":{"canonical_record":{"source":{"id":"1710.06780","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-18T15:23:58Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"db37f0bff3be67c718af353410acc97562c08300af8a1ab295ed5fc8f7dc7f89","abstract_canon_sha256":"986b29ac42b79bd1001cbd2b562ac571d226f671c72e40cdcbc6511b6d1dc6f9"},"schema_version":"1.0"},"canonical_sha256":"bc7165ad6ad2486fda9cf8a77aa5cdf1ce0d127a540c5d0865873a21f3bae126","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:59.835924Z","signature_b64":"+gTDfgGnWQmCSBklNXLvkQxdte75UG0QVsMvN2fkAqYd3jPrT4nUe3+PAicNk6oOJNU52Fcc6jIFZvjogBaHBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc7165ad6ad2486fda9cf8a77aa5cdf1ce0d127a540c5d0865873a21f3bae126","last_reissued_at":"2026-05-18T00:14:59.835118Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:59.835118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.06780","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":"2026-05-18T00:14:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UpqOqX0rTW8N+kUB3aSWmfoKdbJkaxnRiwH3/TVqlvo2NR/hlUMCcpWTroPf5Yo3QLtT1X2JiNntZzakPC2/CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:10:09.464720Z"},"content_sha256":"46770b79f2410d4745e6fbed1008c2349aa9d6126664215d97c2c3721a39f73a","schema_version":"1.0","event_id":"sha256:46770b79f2410d4745e6fbed1008c2349aa9d6126664215d97c2c3721a39f73a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:XRYWLLLK2JEG7WU47CTXVJON6H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Upper bound for lifespan of solutions to certain semilinear parabolic, dispersive and hyperbolic equations via a unified test function method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Masahiro Ikeda, Motohiro Sobajima","submitted_at":"2017-10-18T15:23:58Z","abstract_excerpt":"This paper is concerned with the blowup phenomena for initial-boundary value problem for certain semi linear parabolic, dispersive and hyperbolic equations in cone-like domain. The result proposes a unified treatment of estimates for lifespan of solutions to the problem by test function method. The Fujita exponent p=1 + 2/N appears as a threshold of blowup phenomena for small data when $C_{{\\Sigma}}=R^N$ , but the case of cone-like domain with boundary the threshold changes and explicitly given via the first eigenvalue of corresponding Laplace-Beltrami operator with Dirichlet boundary conditio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06780","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":"2026-05-18T00:14:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5SQe6O7KrTVvRA11C3a9vwDP08mgayHapaaA8zIpuRb5XNWK6FhpzoiHaZpZ166HuuhHV6iY19xEwrrpQzYuDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:10:09.465334Z"},"content_sha256":"673ada638ef508970d6f9aa6481c1fd5aac7a3d0588a360b10923d0256d3d1ba","schema_version":"1.0","event_id":"sha256:673ada638ef508970d6f9aa6481c1fd5aac7a3d0588a360b10923d0256d3d1ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XRYWLLLK2JEG7WU47CTXVJON6H/bundle.json","state_url":"https://pith.science/pith/XRYWLLLK2JEG7WU47CTXVJON6H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XRYWLLLK2JEG7WU47CTXVJON6H/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":"2026-05-28T22:10:09Z","links":{"resolver":"https://pith.science/pith/XRYWLLLK2JEG7WU47CTXVJON6H","bundle":"https://pith.science/pith/XRYWLLLK2JEG7WU47CTXVJON6H/bundle.json","state":"https://pith.science/pith/XRYWLLLK2JEG7WU47CTXVJON6H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XRYWLLLK2JEG7WU47CTXVJON6H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XRYWLLLK2JEG7WU47CTXVJON6H","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":"986b29ac42b79bd1001cbd2b562ac571d226f671c72e40cdcbc6511b6d1dc6f9","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-18T15:23:58Z","title_canon_sha256":"db37f0bff3be67c718af353410acc97562c08300af8a1ab295ed5fc8f7dc7f89"},"schema_version":"1.0","source":{"id":"1710.06780","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.06780","created_at":"2026-05-18T00:14:59Z"},{"alias_kind":"arxiv_version","alias_value":"1710.06780v2","created_at":"2026-05-18T00:14:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06780","created_at":"2026-05-18T00:14:59Z"},{"alias_kind":"pith_short_12","alias_value":"XRYWLLLK2JEG","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XRYWLLLK2JEG7WU4","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XRYWLLLK","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:673ada638ef508970d6f9aa6481c1fd5aac7a3d0588a360b10923d0256d3d1ba","target":"graph","created_at":"2026-05-18T00:14:59Z","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":"This paper is concerned with the blowup phenomena for initial-boundary value problem for certain semi linear parabolic, dispersive and hyperbolic equations in cone-like domain. The result proposes a unified treatment of estimates for lifespan of solutions to the problem by test function method. The Fujita exponent p=1 + 2/N appears as a threshold of blowup phenomena for small data when $C_{{\\Sigma}}=R^N$ , but the case of cone-like domain with boundary the threshold changes and explicitly given via the first eigenvalue of corresponding Laplace-Beltrami operator with Dirichlet boundary conditio","authors_text":"Masahiro Ikeda, Motohiro Sobajima","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-18T15:23:58Z","title":"Upper bound for lifespan of solutions to certain semilinear parabolic, dispersive and hyperbolic equations via a unified test function method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06780","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":"sha256:46770b79f2410d4745e6fbed1008c2349aa9d6126664215d97c2c3721a39f73a","target":"record","created_at":"2026-05-18T00:14:59Z","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":"986b29ac42b79bd1001cbd2b562ac571d226f671c72e40cdcbc6511b6d1dc6f9","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-18T15:23:58Z","title_canon_sha256":"db37f0bff3be67c718af353410acc97562c08300af8a1ab295ed5fc8f7dc7f89"},"schema_version":"1.0","source":{"id":"1710.06780","kind":"arxiv","version":2}},"canonical_sha256":"bc7165ad6ad2486fda9cf8a77aa5cdf1ce0d127a540c5d0865873a21f3bae126","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc7165ad6ad2486fda9cf8a77aa5cdf1ce0d127a540c5d0865873a21f3bae126","first_computed_at":"2026-05-18T00:14:59.835118Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:59.835118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+gTDfgGnWQmCSBklNXLvkQxdte75UG0QVsMvN2fkAqYd3jPrT4nUe3+PAicNk6oOJNU52Fcc6jIFZvjogBaHBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:59.835924Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.06780","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46770b79f2410d4745e6fbed1008c2349aa9d6126664215d97c2c3721a39f73a","sha256:673ada638ef508970d6f9aa6481c1fd5aac7a3d0588a360b10923d0256d3d1ba"],"state_sha256":"d9194abb0d52a6489188b72942807109d6db0cd033e2e2cf6eb3576d837076af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p6Sk7j3reMg+0rTecIA0ib4yYs+MlfyVyJ6PRge8toaktcQ9Qw2w2QzA5WZ6q3Aoa34XOxvzfBE2x5stn/pfDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:10:09.467952Z","bundle_sha256":"3f9c8e8248dc92076a3c8082b0e2d10aa53326e51eb595bc0a68a3778495a95e"}}