{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7SDBS3HKC3ELQHOSJYVNGNOPFD","short_pith_number":"pith:7SDBS3HK","canonical_record":{"source":{"id":"1307.7890","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-30T09:44:21Z","cross_cats_sorted":[],"title_canon_sha256":"f7dda951c664964aa70692bc35765589512e3079befec3eaeaa8fe6c0aa96be9","abstract_canon_sha256":"39c7d43ae952d9027bc913b90591bd54a552338d92c56cf684d3c089bf5b4381"},"schema_version":"1.0"},"canonical_sha256":"fc86196cea16c8b81dd24e2ad335cf28e8d4d99077b9e1328b770bd25c0c43ee","source":{"kind":"arxiv","id":"1307.7890","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7890","created_at":"2026-05-18T03:17:13Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7890v1","created_at":"2026-05-18T03:17:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7890","created_at":"2026-05-18T03:17:13Z"},{"alias_kind":"pith_short_12","alias_value":"7SDBS3HKC3EL","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7SDBS3HKC3ELQHOS","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7SDBS3HK","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7SDBS3HKC3ELQHOSJYVNGNOPFD","target":"record","payload":{"canonical_record":{"source":{"id":"1307.7890","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-30T09:44:21Z","cross_cats_sorted":[],"title_canon_sha256":"f7dda951c664964aa70692bc35765589512e3079befec3eaeaa8fe6c0aa96be9","abstract_canon_sha256":"39c7d43ae952d9027bc913b90591bd54a552338d92c56cf684d3c089bf5b4381"},"schema_version":"1.0"},"canonical_sha256":"fc86196cea16c8b81dd24e2ad335cf28e8d4d99077b9e1328b770bd25c0c43ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:13.179536Z","signature_b64":"ttzApuPJp6o9JH2xRgPIj2B/z6b/jVmgBNtEt4vOj7sne0O4uFb6jn6FYTWc32qDRDniLEfCw/Uwstk6eXMtAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc86196cea16c8b81dd24e2ad335cf28e8d4d99077b9e1328b770bd25c0c43ee","last_reissued_at":"2026-05-18T03:17:13.178756Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:13.178756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.7890","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":"2026-05-18T03:17:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qa/SU5lBoZEZLAAm/+N/ra1kScodo/dFIEpZQLKtoQB7T9xX22Lbbfx8dsrCthfpYY/AEzL5xOTpUuQ5ZiEeAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:28:06.553803Z"},"content_sha256":"816710f553d3d338c4562b78355a128227aeadbeb6a1c6af3133749247ff80ac","schema_version":"1.0","event_id":"sha256:816710f553d3d338c4562b78355a128227aeadbeb6a1c6af3133749247ff80ac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7SDBS3HKC3ELQHOSJYVNGNOPFD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Remarks on decay of small solutions to systems of Klein-Gordon equations with dissipative nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Donghyun Kim, Hideaki Sunagawa","submitted_at":"2013-07-30T09:44:21Z","abstract_excerpt":"We consider the Cauchy problem for systems of cubic nonlinear Klein-Gordon equations in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the small amplitude solution gains an additional logarithmic decay in comparison with the free evolution in the sense of $L^p$, $2\\le p \\le \\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7890","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":"2026-05-18T03:17:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cQhzRot6LA3f2mPPu2hFH0bPUFyo4Ed+ENcD7NKPHpc18w2LukgRPShTM8pi9sIXtxmmZfse3JHm7DsLorLOCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:28:06.554248Z"},"content_sha256":"d62b3bab5b7df2079b85ed99d48f6280bcc69f2a12dd467f9208884e6fd6819a","schema_version":"1.0","event_id":"sha256:d62b3bab5b7df2079b85ed99d48f6280bcc69f2a12dd467f9208884e6fd6819a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7SDBS3HKC3ELQHOSJYVNGNOPFD/bundle.json","state_url":"https://pith.science/pith/7SDBS3HKC3ELQHOSJYVNGNOPFD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7SDBS3HKC3ELQHOSJYVNGNOPFD/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":"2026-06-07T14:28:06Z","links":{"resolver":"https://pith.science/pith/7SDBS3HKC3ELQHOSJYVNGNOPFD","bundle":"https://pith.science/pith/7SDBS3HKC3ELQHOSJYVNGNOPFD/bundle.json","state":"https://pith.science/pith/7SDBS3HKC3ELQHOSJYVNGNOPFD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7SDBS3HKC3ELQHOSJYVNGNOPFD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7SDBS3HKC3ELQHOSJYVNGNOPFD","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":"39c7d43ae952d9027bc913b90591bd54a552338d92c56cf684d3c089bf5b4381","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-30T09:44:21Z","title_canon_sha256":"f7dda951c664964aa70692bc35765589512e3079befec3eaeaa8fe6c0aa96be9"},"schema_version":"1.0","source":{"id":"1307.7890","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7890","created_at":"2026-05-18T03:17:13Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7890v1","created_at":"2026-05-18T03:17:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7890","created_at":"2026-05-18T03:17:13Z"},{"alias_kind":"pith_short_12","alias_value":"7SDBS3HKC3EL","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7SDBS3HKC3ELQHOS","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7SDBS3HK","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:d62b3bab5b7df2079b85ed99d48f6280bcc69f2a12dd467f9208884e6fd6819a","target":"graph","created_at":"2026-05-18T03:17:13Z","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 Cauchy problem for systems of cubic nonlinear Klein-Gordon equations in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the small amplitude solution gains an additional logarithmic decay in comparison with the free evolution in the sense of $L^p$, $2\\le p \\le \\infty$.","authors_text":"Donghyun Kim, Hideaki Sunagawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-30T09:44:21Z","title":"Remarks on decay of small solutions to systems of Klein-Gordon equations with dissipative nonlinearities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7890","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":"sha256:816710f553d3d338c4562b78355a128227aeadbeb6a1c6af3133749247ff80ac","target":"record","created_at":"2026-05-18T03:17:13Z","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":"39c7d43ae952d9027bc913b90591bd54a552338d92c56cf684d3c089bf5b4381","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-30T09:44:21Z","title_canon_sha256":"f7dda951c664964aa70692bc35765589512e3079befec3eaeaa8fe6c0aa96be9"},"schema_version":"1.0","source":{"id":"1307.7890","kind":"arxiv","version":1}},"canonical_sha256":"fc86196cea16c8b81dd24e2ad335cf28e8d4d99077b9e1328b770bd25c0c43ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc86196cea16c8b81dd24e2ad335cf28e8d4d99077b9e1328b770bd25c0c43ee","first_computed_at":"2026-05-18T03:17:13.178756Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:13.178756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ttzApuPJp6o9JH2xRgPIj2B/z6b/jVmgBNtEt4vOj7sne0O4uFb6jn6FYTWc32qDRDniLEfCw/Uwstk6eXMtAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:13.179536Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.7890","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:816710f553d3d338c4562b78355a128227aeadbeb6a1c6af3133749247ff80ac","sha256:d62b3bab5b7df2079b85ed99d48f6280bcc69f2a12dd467f9208884e6fd6819a"],"state_sha256":"8cdca9622504a992260e1b50da57fda8378d41cfa78ce540c7bba2c3c8c5768e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5dsKNpOvhm/thOwst6KQr2343vqSjZ+cw2mw7fk1E093WMkuzVWY5euFtCodOt1RiXrPyrB39eqQekyve2MjAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T14:28:06.557760Z","bundle_sha256":"d89c63b8ef62d4ce588ceda079418cdd691b6600ad4603290ff6497a4c7e5e32"}}