{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:AAK27RHFXXLOPU4P44ZRYLVWYY","short_pith_number":"pith:AAK27RHF","canonical_record":{"source":{"id":"1104.2395","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-13T07:01:21Z","cross_cats_sorted":[],"title_canon_sha256":"11cb56344fd9b3ed29dcec534b0624aa9b24aceadf119ac74dd602ccf6aa8c50","abstract_canon_sha256":"9a23161f176f7344f5c42fe724851f3e7025df2d8690498307a04a2a05b79344"},"schema_version":"1.0"},"canonical_sha256":"0015afc4e5bdd6e7d38fe7331c2eb6c60a2eab06528dc6e284bbfaa9f190d0eb","source":{"kind":"arxiv","id":"1104.2395","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.2395","created_at":"2026-05-18T04:24:34Z"},{"alias_kind":"arxiv_version","alias_value":"1104.2395v1","created_at":"2026-05-18T04:24:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2395","created_at":"2026-05-18T04:24:34Z"},{"alias_kind":"pith_short_12","alias_value":"AAK27RHFXXLO","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AAK27RHFXXLOPU4P","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AAK27RHF","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:AAK27RHFXXLOPU4P44ZRYLVWYY","target":"record","payload":{"canonical_record":{"source":{"id":"1104.2395","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-13T07:01:21Z","cross_cats_sorted":[],"title_canon_sha256":"11cb56344fd9b3ed29dcec534b0624aa9b24aceadf119ac74dd602ccf6aa8c50","abstract_canon_sha256":"9a23161f176f7344f5c42fe724851f3e7025df2d8690498307a04a2a05b79344"},"schema_version":"1.0"},"canonical_sha256":"0015afc4e5bdd6e7d38fe7331c2eb6c60a2eab06528dc6e284bbfaa9f190d0eb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:34.837238Z","signature_b64":"ZS/nI8HNTU5yb7Ho6qO9CjtImCszcOnL7kvui6s7WPlWFgwFtxUbnQhl917MTncaanpdoNqBxWIn3AJDeZWRCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0015afc4e5bdd6e7d38fe7331c2eb6c60a2eab06528dc6e284bbfaa9f190d0eb","last_reissued_at":"2026-05-18T04:24:34.836856Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:34.836856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.2395","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":"2026-05-18T04:24:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KkNQujO6aErTkbQNtLmaA0zXodnfpw50BO1t6He0dfcOtT8Gj6Uq6LTv/KjoZS5EnwfsUkenh3YlSeD+uPTBDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T06:46:06.583396Z"},"content_sha256":"4d1f8b9b9d30af965cd829890fcfa828f6806f3316c8c01ce74e1bc1547ede6e","schema_version":"1.0","event_id":"sha256:4d1f8b9b9d30af965cd829890fcfa828f6806f3316c8c01ce74e1bc1547ede6e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:AAK27RHFXXLOPU4P44ZRYLVWYY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence, blow-up and exponential decay estimates for a nonlinear wave equation with boundary conditions of two-point type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alain Pham Ngoc Dinh (MAPMO), Le Thi Phuong Ngoc, Le Xuan Truong, Nguyen Thanh Long (UNS-HCMC)","submitted_at":"2011-04-13T07:01:21Z","abstract_excerpt":"This paper is devoted to study a nonlinear wave equation with boundary conditions of two-point type. First, we state two local existence theorems and under suitable conditions, we prove that any weak solutions with negative initial energy will blow up in finite time. Next, we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions. Finally, we present numerical results"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2395","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":"2026-05-18T04:24:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zy94wxwy/+ZdoIsJlAcOkac9mffvFG0CtJ12cmFj9VLk+A+SbKk7QYTZl+pqSRKq/2IZhWgGAajYJYuwkYdRCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T06:46:06.583743Z"},"content_sha256":"f144f9d60265d94241eed790e2a2868761cadda1fee1ad6caf8d77dff24bbc3d","schema_version":"1.0","event_id":"sha256:f144f9d60265d94241eed790e2a2868761cadda1fee1ad6caf8d77dff24bbc3d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AAK27RHFXXLOPU4P44ZRYLVWYY/bundle.json","state_url":"https://pith.science/pith/AAK27RHFXXLOPU4P44ZRYLVWYY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AAK27RHFXXLOPU4P44ZRYLVWYY/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":"2026-06-21T06:46:06Z","links":{"resolver":"https://pith.science/pith/AAK27RHFXXLOPU4P44ZRYLVWYY","bundle":"https://pith.science/pith/AAK27RHFXXLOPU4P44ZRYLVWYY/bundle.json","state":"https://pith.science/pith/AAK27RHFXXLOPU4P44ZRYLVWYY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AAK27RHFXXLOPU4P44ZRYLVWYY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:AAK27RHFXXLOPU4P44ZRYLVWYY","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":"9a23161f176f7344f5c42fe724851f3e7025df2d8690498307a04a2a05b79344","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-13T07:01:21Z","title_canon_sha256":"11cb56344fd9b3ed29dcec534b0624aa9b24aceadf119ac74dd602ccf6aa8c50"},"schema_version":"1.0","source":{"id":"1104.2395","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.2395","created_at":"2026-05-18T04:24:34Z"},{"alias_kind":"arxiv_version","alias_value":"1104.2395v1","created_at":"2026-05-18T04:24:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2395","created_at":"2026-05-18T04:24:34Z"},{"alias_kind":"pith_short_12","alias_value":"AAK27RHFXXLO","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AAK27RHFXXLOPU4P","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AAK27RHF","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:f144f9d60265d94241eed790e2a2868761cadda1fee1ad6caf8d77dff24bbc3d","target":"graph","created_at":"2026-05-18T04:24:34Z","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 study a nonlinear wave equation with boundary conditions of two-point type. First, we state two local existence theorems and under suitable conditions, we prove that any weak solutions with negative initial energy will blow up in finite time. Next, we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions. Finally, we present numerical results","authors_text":"Alain Pham Ngoc Dinh (MAPMO), Le Thi Phuong Ngoc, Le Xuan Truong, Nguyen Thanh Long (UNS-HCMC)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-13T07:01:21Z","title":"Existence, blow-up and exponential decay estimates for a nonlinear wave equation with boundary conditions of two-point type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2395","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":"sha256:4d1f8b9b9d30af965cd829890fcfa828f6806f3316c8c01ce74e1bc1547ede6e","target":"record","created_at":"2026-05-18T04:24:34Z","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":"9a23161f176f7344f5c42fe724851f3e7025df2d8690498307a04a2a05b79344","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-13T07:01:21Z","title_canon_sha256":"11cb56344fd9b3ed29dcec534b0624aa9b24aceadf119ac74dd602ccf6aa8c50"},"schema_version":"1.0","source":{"id":"1104.2395","kind":"arxiv","version":1}},"canonical_sha256":"0015afc4e5bdd6e7d38fe7331c2eb6c60a2eab06528dc6e284bbfaa9f190d0eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0015afc4e5bdd6e7d38fe7331c2eb6c60a2eab06528dc6e284bbfaa9f190d0eb","first_computed_at":"2026-05-18T04:24:34.836856Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:34.836856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZS/nI8HNTU5yb7Ho6qO9CjtImCszcOnL7kvui6s7WPlWFgwFtxUbnQhl917MTncaanpdoNqBxWIn3AJDeZWRCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:34.837238Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.2395","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d1f8b9b9d30af965cd829890fcfa828f6806f3316c8c01ce74e1bc1547ede6e","sha256:f144f9d60265d94241eed790e2a2868761cadda1fee1ad6caf8d77dff24bbc3d"],"state_sha256":"3ac6e5a9caf47da2a0fb263233366ac24a9e0b38e412ec7877676d22ded668cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SFIqW9mvIHjojHwEMtjVAn6FPFqf2dn6RmZGCeFOkSCWXN2ERmQKDZpxw2WlRv51RLb1A0QjxyY0k2Sb1SkWCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T06:46:06.585623Z","bundle_sha256":"407cc1843b835377aca322fd211d9f3bec8c3a56460f8d50862b7747982893d9"}}