{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:V3XZJBRLPLHOEGXZ22MQRBY2GH","short_pith_number":"pith:V3XZJBRL","canonical_record":{"source":{"id":"1610.05913","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-19T08:50:54Z","cross_cats_sorted":[],"title_canon_sha256":"0b102cce990c3ba02c43f1978f63cdd6d92ecb942629a1975da46540b1db593b","abstract_canon_sha256":"7c12d08c81644f65b2de93fdeccef4284338fce79960980d68f9676e1dce6fb8"},"schema_version":"1.0"},"canonical_sha256":"aeef94862b7acee21af9d69908871a31e70f656dd64eefcdf755ff0c4397d57a","source":{"kind":"arxiv","id":"1610.05913","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05913","created_at":"2026-05-18T00:46:39Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05913v2","created_at":"2026-05-18T00:46:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05913","created_at":"2026-05-18T00:46:39Z"},{"alias_kind":"pith_short_12","alias_value":"V3XZJBRLPLHO","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"V3XZJBRLPLHOEGXZ","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"V3XZJBRL","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:V3XZJBRLPLHOEGXZ22MQRBY2GH","target":"record","payload":{"canonical_record":{"source":{"id":"1610.05913","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-19T08:50:54Z","cross_cats_sorted":[],"title_canon_sha256":"0b102cce990c3ba02c43f1978f63cdd6d92ecb942629a1975da46540b1db593b","abstract_canon_sha256":"7c12d08c81644f65b2de93fdeccef4284338fce79960980d68f9676e1dce6fb8"},"schema_version":"1.0"},"canonical_sha256":"aeef94862b7acee21af9d69908871a31e70f656dd64eefcdf755ff0c4397d57a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:39.390564Z","signature_b64":"2LLPGu74TtfK4EqwZFYEut0VTUF1Sksyqpv/y6vtAdyGEb/ol2oMx04BtYUDXejQlQbg+mBEzbiuB7/rk70tAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aeef94862b7acee21af9d69908871a31e70f656dd64eefcdf755ff0c4397d57a","last_reissued_at":"2026-05-18T00:46:39.389833Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:39.389833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.05913","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":"2026-05-18T00:46:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F5kXKkkLU5f7+GMSoCFvbCVcw4kN6DXqWyWzLWe9BbAZWRyRWaQWmG4L1oHYnoJFwhDPDOqwUcWeralaQl/FBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:14:09.114173Z"},"content_sha256":"9c77108c653744bc446ad03c782ec9f56a2768ea0018355af70e07339d19c0de","schema_version":"1.0","event_id":"sha256:9c77108c653744bc446ad03c782ec9f56a2768ea0018355af70e07339d19c0de"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:V3XZJBRLPLHOEGXZ22MQRBY2GH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The sharp lower bound of the lifespan of solutions to semilinear wave equations with low powers in two space dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hiroyuki Takamura, Kyouhei Wakasa, Masakazu Kato, Takuto Imai","submitted_at":"2016-10-19T08:50:54Z","abstract_excerpt":"This paper is devoted to a proof of the conjecture in Takamura(2015) on the lower bound of the lifespan of solutions to semilinear wave equations in two space dimensions. The result is divided into two cases according to the total integral of the initial speed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05913","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":"2026-05-18T00:46:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q5svC0U5s70K9hGNqV7/KKi/A1BzaEpukG1LGbR7zQFgp0dkKQ4Lbfrd2ZhQbYfcI+wQ/Dwdc7tG2vwVfw2KBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:14:09.114531Z"},"content_sha256":"cf5750454e33e1d45b10d35d09671a088e1e1c2101cb6596fdcfebbc8b1b4a8c","schema_version":"1.0","event_id":"sha256:cf5750454e33e1d45b10d35d09671a088e1e1c2101cb6596fdcfebbc8b1b4a8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V3XZJBRLPLHOEGXZ22MQRBY2GH/bundle.json","state_url":"https://pith.science/pith/V3XZJBRLPLHOEGXZ22MQRBY2GH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V3XZJBRLPLHOEGXZ22MQRBY2GH/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":"2026-06-22T14:14:09Z","links":{"resolver":"https://pith.science/pith/V3XZJBRLPLHOEGXZ22MQRBY2GH","bundle":"https://pith.science/pith/V3XZJBRLPLHOEGXZ22MQRBY2GH/bundle.json","state":"https://pith.science/pith/V3XZJBRLPLHOEGXZ22MQRBY2GH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V3XZJBRLPLHOEGXZ22MQRBY2GH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:V3XZJBRLPLHOEGXZ22MQRBY2GH","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":"7c12d08c81644f65b2de93fdeccef4284338fce79960980d68f9676e1dce6fb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-19T08:50:54Z","title_canon_sha256":"0b102cce990c3ba02c43f1978f63cdd6d92ecb942629a1975da46540b1db593b"},"schema_version":"1.0","source":{"id":"1610.05913","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05913","created_at":"2026-05-18T00:46:39Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05913v2","created_at":"2026-05-18T00:46:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05913","created_at":"2026-05-18T00:46:39Z"},{"alias_kind":"pith_short_12","alias_value":"V3XZJBRLPLHO","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"V3XZJBRLPLHOEGXZ","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"V3XZJBRL","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:cf5750454e33e1d45b10d35d09671a088e1e1c2101cb6596fdcfebbc8b1b4a8c","target":"graph","created_at":"2026-05-18T00:46:39Z","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":"This paper is devoted to a proof of the conjecture in Takamura(2015) on the lower bound of the lifespan of solutions to semilinear wave equations in two space dimensions. The result is divided into two cases according to the total integral of the initial speed.","authors_text":"Hiroyuki Takamura, Kyouhei Wakasa, Masakazu Kato, Takuto Imai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-19T08:50:54Z","title":"The sharp lower bound of the lifespan of solutions to semilinear wave equations with low powers in two space dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05913","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":"sha256:9c77108c653744bc446ad03c782ec9f56a2768ea0018355af70e07339d19c0de","target":"record","created_at":"2026-05-18T00:46:39Z","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":"7c12d08c81644f65b2de93fdeccef4284338fce79960980d68f9676e1dce6fb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-19T08:50:54Z","title_canon_sha256":"0b102cce990c3ba02c43f1978f63cdd6d92ecb942629a1975da46540b1db593b"},"schema_version":"1.0","source":{"id":"1610.05913","kind":"arxiv","version":2}},"canonical_sha256":"aeef94862b7acee21af9d69908871a31e70f656dd64eefcdf755ff0c4397d57a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aeef94862b7acee21af9d69908871a31e70f656dd64eefcdf755ff0c4397d57a","first_computed_at":"2026-05-18T00:46:39.389833Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:39.389833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2LLPGu74TtfK4EqwZFYEut0VTUF1Sksyqpv/y6vtAdyGEb/ol2oMx04BtYUDXejQlQbg+mBEzbiuB7/rk70tAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:39.390564Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.05913","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c77108c653744bc446ad03c782ec9f56a2768ea0018355af70e07339d19c0de","sha256:cf5750454e33e1d45b10d35d09671a088e1e1c2101cb6596fdcfebbc8b1b4a8c"],"state_sha256":"a2fb389902fb9c7e4bace612983fda23ce939c67fc7ab3c8d630efb40437212f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K8NB5FzOnyNB4MZwkOzkxZgffLflniGJ5tZrING3kanHDFOGqPjuvEw3u3voucTiunmTOLHOi6s/W9QDUslQCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T14:14:09.116526Z","bundle_sha256":"06c5b1d1cdb908d90d5d5c1de707b4704c278572817a1b6fe9b41f9f1603092c"}}