{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:LIO7AXMY24MDKF7HQVSL2UR7YK","short_pith_number":"pith:LIO7AXMY","canonical_record":{"source":{"id":"2411.15528","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-11-23T11:42:28Z","cross_cats_sorted":[],"title_canon_sha256":"1b9dc3d05fb3df3e9d2e1d69c1b7f0f771f8c787ec86f8061a305ae079232f4e","abstract_canon_sha256":"910153f17ce790f2358079bb936a3cdbb02817a84d3133d08b68e3a336c38ec2"},"schema_version":"1.0"},"canonical_sha256":"5a1df05d98d7183517e78564bd523fc2bf430386a7d26035f7274a4999ff32e8","source":{"kind":"arxiv","id":"2411.15528","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15528","created_at":"2026-07-05T09:39:36Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15528v1","created_at":"2026-07-05T09:39:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15528","created_at":"2026-07-05T09:39:36Z"},{"alias_kind":"pith_short_12","alias_value":"LIO7AXMY24MD","created_at":"2026-07-05T09:39:36Z"},{"alias_kind":"pith_short_16","alias_value":"LIO7AXMY24MDKF7H","created_at":"2026-07-05T09:39:36Z"},{"alias_kind":"pith_short_8","alias_value":"LIO7AXMY","created_at":"2026-07-05T09:39:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:LIO7AXMY24MDKF7HQVSL2UR7YK","target":"record","payload":{"canonical_record":{"source":{"id":"2411.15528","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-11-23T11:42:28Z","cross_cats_sorted":[],"title_canon_sha256":"1b9dc3d05fb3df3e9d2e1d69c1b7f0f771f8c787ec86f8061a305ae079232f4e","abstract_canon_sha256":"910153f17ce790f2358079bb936a3cdbb02817a84d3133d08b68e3a336c38ec2"},"schema_version":"1.0"},"canonical_sha256":"5a1df05d98d7183517e78564bd523fc2bf430386a7d26035f7274a4999ff32e8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:39:36.563629Z","signature_b64":"5PGKacanygnLi5xnjEaH6UecxJgT/+EL3ZZWZ9XLOShxvtjee9eM/lW3sQUG5bDZpgirmdChWlyX9E2424yaAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a1df05d98d7183517e78564bd523fc2bf430386a7d26035f7274a4999ff32e8","last_reissued_at":"2026-07-05T09:39:36.563186Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:39:36.563186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.15528","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":"2026-07-05T09:39:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/D861ed4wY7/OBZ3yjoscYNLD4dNVWpAt8OQTC1TRPwo30hs+RPqkm2QgAh7gEIu1F5FdbFiy9MSbu14TTV4DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T04:09:28.843618Z"},"content_sha256":"04e5e9f1188c31d072dc45b1ec57bbbd1be35f87ea971e78a922667c592894ed","schema_version":"1.0","event_id":"sha256:04e5e9f1188c31d072dc45b1ec57bbbd1be35f87ea971e78a922667c592894ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:LIO7AXMY24MDKF7HQVSL2UR7YK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the wave equation with variable exponent nonlinearity and distributive delay","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mohammad Kafini","submitted_at":"2024-11-23T11:42:28Z","abstract_excerpt":"In this work, we are concerned with a nonlinear wave equation with variable exponents. A distributive delay is imposed into the damping term with variable exponents nonlinearity. Firstly, we show that the global nonexistence time can be dominated. Secondly, global existence of solutions is shown under some suitable conditions on the initial data. Finally, the decay rates of that solutions are established as well."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15528","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.15528/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:39:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"04ReEpV0lVJdIEO5W0W2jDwS1kFIAgFyQIYHKE0mwIvi9TTgqjtYdQApF74GdWcb+tH+JGXRIPbxv3Hzo1onDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T04:09:28.844321Z"},"content_sha256":"bb2ca7f875aa4f9f46ae1d8a19653c8e2dd62e2b5e363fa1f5a66c1d39711193","schema_version":"1.0","event_id":"sha256:bb2ca7f875aa4f9f46ae1d8a19653c8e2dd62e2b5e363fa1f5a66c1d39711193"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LIO7AXMY24MDKF7HQVSL2UR7YK/bundle.json","state_url":"https://pith.science/pith/LIO7AXMY24MDKF7HQVSL2UR7YK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LIO7AXMY24MDKF7HQVSL2UR7YK/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":"2026-08-13T04:09:28Z","links":{"resolver":"https://pith.science/pith/LIO7AXMY24MDKF7HQVSL2UR7YK","bundle":"https://pith.science/pith/LIO7AXMY24MDKF7HQVSL2UR7YK/bundle.json","state":"https://pith.science/pith/LIO7AXMY24MDKF7HQVSL2UR7YK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LIO7AXMY24MDKF7HQVSL2UR7YK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LIO7AXMY24MDKF7HQVSL2UR7YK","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":"910153f17ce790f2358079bb936a3cdbb02817a84d3133d08b68e3a336c38ec2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-11-23T11:42:28Z","title_canon_sha256":"1b9dc3d05fb3df3e9d2e1d69c1b7f0f771f8c787ec86f8061a305ae079232f4e"},"schema_version":"1.0","source":{"id":"2411.15528","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15528","created_at":"2026-07-05T09:39:36Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15528v1","created_at":"2026-07-05T09:39:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15528","created_at":"2026-07-05T09:39:36Z"},{"alias_kind":"pith_short_12","alias_value":"LIO7AXMY24MD","created_at":"2026-07-05T09:39:36Z"},{"alias_kind":"pith_short_16","alias_value":"LIO7AXMY24MDKF7H","created_at":"2026-07-05T09:39:36Z"},{"alias_kind":"pith_short_8","alias_value":"LIO7AXMY","created_at":"2026-07-05T09:39:36Z"}],"graph_snapshots":[{"event_id":"sha256:bb2ca7f875aa4f9f46ae1d8a19653c8e2dd62e2b5e363fa1f5a66c1d39711193","target":"graph","created_at":"2026-07-05T09:39:36Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.15528/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we are concerned with a nonlinear wave equation with variable exponents. A distributive delay is imposed into the damping term with variable exponents nonlinearity. Firstly, we show that the global nonexistence time can be dominated. Secondly, global existence of solutions is shown under some suitable conditions on the initial data. Finally, the decay rates of that solutions are established as well.","authors_text":"Mohammad Kafini","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-11-23T11:42:28Z","title":"On the wave equation with variable exponent nonlinearity and distributive delay"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15528","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":"sha256:04e5e9f1188c31d072dc45b1ec57bbbd1be35f87ea971e78a922667c592894ed","target":"record","created_at":"2026-07-05T09:39:36Z","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":"910153f17ce790f2358079bb936a3cdbb02817a84d3133d08b68e3a336c38ec2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-11-23T11:42:28Z","title_canon_sha256":"1b9dc3d05fb3df3e9d2e1d69c1b7f0f771f8c787ec86f8061a305ae079232f4e"},"schema_version":"1.0","source":{"id":"2411.15528","kind":"arxiv","version":1}},"canonical_sha256":"5a1df05d98d7183517e78564bd523fc2bf430386a7d26035f7274a4999ff32e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a1df05d98d7183517e78564bd523fc2bf430386a7d26035f7274a4999ff32e8","first_computed_at":"2026-07-05T09:39:36.563186Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:39:36.563186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5PGKacanygnLi5xnjEaH6UecxJgT/+EL3ZZWZ9XLOShxvtjee9eM/lW3sQUG5bDZpgirmdChWlyX9E2424yaAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:39:36.563629Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.15528","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04e5e9f1188c31d072dc45b1ec57bbbd1be35f87ea971e78a922667c592894ed","sha256:bb2ca7f875aa4f9f46ae1d8a19653c8e2dd62e2b5e363fa1f5a66c1d39711193"],"state_sha256":"b2d24a5a2b2a1e54e02e60fa7f8267995a77522f061fec57485536d409a3132b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mrx4anUDG4ccubJ5lwlGFHk9P8W9iABJTZyUbz2jRUKZnpHMEPqRXfe2KR1NlMTq9RviuaqFOQTAhfDz7gA4Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T04:09:28.850349Z","bundle_sha256":"8e84ffa1782829619400a7a58c57de41ba4ffedbdb9a390137ea659670757a65"}}