{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:E7XU4K3KXWDD3IUUQG4QJGAUFY","short_pith_number":"pith:E7XU4K3K","canonical_record":{"source":{"id":"1707.03950","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-13T01:45:44Z","cross_cats_sorted":[],"title_canon_sha256":"bca4fa483851df9d6495641b9d5f1b5848c6848aa9bb3e0c3230aeae517214a0","abstract_canon_sha256":"5a9c21b1e6c1bdd0b5eaf892820043ec539bb6ef480b6ba1738cea63270659f8"},"schema_version":"1.0"},"canonical_sha256":"27ef4e2b6abd863da29481b90498142e2291efce59ad6cddee2cfd132a362462","source":{"kind":"arxiv","id":"1707.03950","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03950","created_at":"2026-05-18T00:40:23Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03950v1","created_at":"2026-05-18T00:40:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03950","created_at":"2026-05-18T00:40:23Z"},{"alias_kind":"pith_short_12","alias_value":"E7XU4K3KXWDD","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"E7XU4K3KXWDD3IUU","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"E7XU4K3K","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:E7XU4K3KXWDD3IUUQG4QJGAUFY","target":"record","payload":{"canonical_record":{"source":{"id":"1707.03950","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-13T01:45:44Z","cross_cats_sorted":[],"title_canon_sha256":"bca4fa483851df9d6495641b9d5f1b5848c6848aa9bb3e0c3230aeae517214a0","abstract_canon_sha256":"5a9c21b1e6c1bdd0b5eaf892820043ec539bb6ef480b6ba1738cea63270659f8"},"schema_version":"1.0"},"canonical_sha256":"27ef4e2b6abd863da29481b90498142e2291efce59ad6cddee2cfd132a362462","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:23.030841Z","signature_b64":"Ky4GX7/jrYu5GEfukTASr6EI2HpXnHw43TySK+fmhNJNKKpQDSFTX8bo803lS7aM4VioHxhIpDbWtoGkjT4PDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27ef4e2b6abd863da29481b90498142e2291efce59ad6cddee2cfd132a362462","last_reissued_at":"2026-05-18T00:40:23.030207Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:23.030207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.03950","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":"2026-05-18T00:40:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pVwUK9pHtPAw4rGIfjtNcZDFOxlMQXQad/P38fvm3DMmyKvhI0pMKbLAhol1Uy3PgA95/KLwCnluNOqNpcWxBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:25:17.482146Z"},"content_sha256":"bb50f2a3c20d88c6a7701f0cef3ccab49d51af58b9a2092bfd366f8eb5122ffd","schema_version":"1.0","event_id":"sha256:bb50f2a3c20d88c6a7701f0cef3ccab49d51af58b9a2092bfd366f8eb5122ffd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:E7XU4K3KXWDD3IUUQG4QJGAUFY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The sharp estimate of the lifespan for the semilinear wave equation with time-dependent damping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masahiro Ikeda, Takahisa Inui","submitted_at":"2017-07-13T01:45:44Z","abstract_excerpt":"We consider the following semilinear wave equation with time-dependent damping. \\begin{align} \\tag{NLDW} \\left\\{ \\begin{array}{ll} \\partial_t^2 u - \\Delta u + b(t)\\partial_t u = |u|^{p}, & (t,x) \\in [0,T) \\times \\mathbb{R}^n, \\\\ u(0,x)=\\varepsilon u_0(x), u_t(0,x)=\\varepsilon u_1(x), & x \\in \\mathbb{R}^n, \\end{array} \\right. \\end{align} where $n \\in \\mathbb{N}$, $p>1$, $\\varepsilon>0$, and $b(t)\\thickapprox (t+1)^{-\\beta}$ with $\\beta \\in [-1,1)$. It is known that small data blow-up occurs when $1<p< p_F$ and, on the other hand, small data global existence holds when $p>p_F$, where $p_F:=1+2/n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03950","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":"2026-05-18T00:40:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"abMN5L1BZAMW6P4iYPdKttETUdpvBqUlSFDr63VinSncrreWKCj7EgIlIR4UCsbfEOyeRCeD2jEQA9q8JSXpBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:25:17.482810Z"},"content_sha256":"774993f5710589c9dd4328ccb23466a06bb898ceb05f14eac8c0aab25b206d50","schema_version":"1.0","event_id":"sha256:774993f5710589c9dd4328ccb23466a06bb898ceb05f14eac8c0aab25b206d50"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E7XU4K3KXWDD3IUUQG4QJGAUFY/bundle.json","state_url":"https://pith.science/pith/E7XU4K3KXWDD3IUUQG4QJGAUFY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E7XU4K3KXWDD3IUUQG4QJGAUFY/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":"2026-06-12T03:25:17Z","links":{"resolver":"https://pith.science/pith/E7XU4K3KXWDD3IUUQG4QJGAUFY","bundle":"https://pith.science/pith/E7XU4K3KXWDD3IUUQG4QJGAUFY/bundle.json","state":"https://pith.science/pith/E7XU4K3KXWDD3IUUQG4QJGAUFY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E7XU4K3KXWDD3IUUQG4QJGAUFY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:E7XU4K3KXWDD3IUUQG4QJGAUFY","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":"5a9c21b1e6c1bdd0b5eaf892820043ec539bb6ef480b6ba1738cea63270659f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-13T01:45:44Z","title_canon_sha256":"bca4fa483851df9d6495641b9d5f1b5848c6848aa9bb3e0c3230aeae517214a0"},"schema_version":"1.0","source":{"id":"1707.03950","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03950","created_at":"2026-05-18T00:40:23Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03950v1","created_at":"2026-05-18T00:40:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03950","created_at":"2026-05-18T00:40:23Z"},{"alias_kind":"pith_short_12","alias_value":"E7XU4K3KXWDD","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"E7XU4K3KXWDD3IUU","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"E7XU4K3K","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:774993f5710589c9dd4328ccb23466a06bb898ceb05f14eac8c0aab25b206d50","target":"graph","created_at":"2026-05-18T00:40:23Z","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 consider the following semilinear wave equation with time-dependent damping. \\begin{align} \\tag{NLDW} \\left\\{ \\begin{array}{ll} \\partial_t^2 u - \\Delta u + b(t)\\partial_t u = |u|^{p}, & (t,x) \\in [0,T) \\times \\mathbb{R}^n, \\\\ u(0,x)=\\varepsilon u_0(x), u_t(0,x)=\\varepsilon u_1(x), & x \\in \\mathbb{R}^n, \\end{array} \\right. \\end{align} where $n \\in \\mathbb{N}$, $p>1$, $\\varepsilon>0$, and $b(t)\\thickapprox (t+1)^{-\\beta}$ with $\\beta \\in [-1,1)$. It is known that small data blow-up occurs when $1<p< p_F$ and, on the other hand, small data global existence holds when $p>p_F$, where $p_F:=1+2/n","authors_text":"Masahiro Ikeda, Takahisa Inui","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-13T01:45:44Z","title":"The sharp estimate of the lifespan for the semilinear wave equation with time-dependent damping"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03950","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:bb50f2a3c20d88c6a7701f0cef3ccab49d51af58b9a2092bfd366f8eb5122ffd","target":"record","created_at":"2026-05-18T00:40:23Z","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":"5a9c21b1e6c1bdd0b5eaf892820043ec539bb6ef480b6ba1738cea63270659f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-13T01:45:44Z","title_canon_sha256":"bca4fa483851df9d6495641b9d5f1b5848c6848aa9bb3e0c3230aeae517214a0"},"schema_version":"1.0","source":{"id":"1707.03950","kind":"arxiv","version":1}},"canonical_sha256":"27ef4e2b6abd863da29481b90498142e2291efce59ad6cddee2cfd132a362462","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27ef4e2b6abd863da29481b90498142e2291efce59ad6cddee2cfd132a362462","first_computed_at":"2026-05-18T00:40:23.030207Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:23.030207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ky4GX7/jrYu5GEfukTASr6EI2HpXnHw43TySK+fmhNJNKKpQDSFTX8bo803lS7aM4VioHxhIpDbWtoGkjT4PDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:23.030841Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.03950","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb50f2a3c20d88c6a7701f0cef3ccab49d51af58b9a2092bfd366f8eb5122ffd","sha256:774993f5710589c9dd4328ccb23466a06bb898ceb05f14eac8c0aab25b206d50"],"state_sha256":"2c11327b8d2c65cc5ebfbe614a41ddacfecb7289d77344d9609a7b3de6e0f829"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3bCtlpL4Hl2vdu5iBD2554xYna10kiplEHp6NdsBDV88d5z9S8gng++x4hNC2/03OKyLdtBAUunYBEfad9CXDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T03:25:17.486856Z","bundle_sha256":"b4aba4dd6e074743d10a42db579f51c41bcf916b53ccbdb44d7e68d9d62a4059"}}