{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ECI2FKNWPSQV523ZSNJDCOQBKI","short_pith_number":"pith:ECI2FKNW","canonical_record":{"source":{"id":"1812.09781","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-23T21:46:44Z","cross_cats_sorted":[],"title_canon_sha256":"801a201fa1697410805b1472610e38284c3f0ff801401791e406e7425a62afc1","abstract_canon_sha256":"52659325d2af878206552790f3a0f391993c120e40a2a4aa372b93c28c36a94b"},"schema_version":"1.0"},"canonical_sha256":"2091a2a9b67ca15eeb799352313a01520440c29c7113247c5e4b4555a2937962","source":{"kind":"arxiv","id":"1812.09781","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09781","created_at":"2026-05-17T23:57:26Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09781v1","created_at":"2026-05-17T23:57:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09781","created_at":"2026-05-17T23:57:26Z"},{"alias_kind":"pith_short_12","alias_value":"ECI2FKNWPSQV","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"ECI2FKNWPSQV523Z","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"ECI2FKNW","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ECI2FKNWPSQV523ZSNJDCOQBKI","target":"record","payload":{"canonical_record":{"source":{"id":"1812.09781","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-23T21:46:44Z","cross_cats_sorted":[],"title_canon_sha256":"801a201fa1697410805b1472610e38284c3f0ff801401791e406e7425a62afc1","abstract_canon_sha256":"52659325d2af878206552790f3a0f391993c120e40a2a4aa372b93c28c36a94b"},"schema_version":"1.0"},"canonical_sha256":"2091a2a9b67ca15eeb799352313a01520440c29c7113247c5e4b4555a2937962","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:26.812371Z","signature_b64":"RcXwFTTC3mhRiXi3S7KHwwBPR8qLHvNTvZtxSaZra9nz8PW6vBeoxC3J6QEtxttfT/2j9avk7+MZe2zTcpc+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2091a2a9b67ca15eeb799352313a01520440c29c7113247c5e4b4555a2937962","last_reissued_at":"2026-05-17T23:57:26.811644Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:26.811644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.09781","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":"2026-05-17T23:57:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Q9XCxu4g3rmRaaRmRnC1ehB3TMFrDtQsPTk15QabuaQqTmdB5UrHB720RsbLdLT1VZMJk5WnWqG7ye2xF0XBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:54:46.614336Z"},"content_sha256":"b67803920b5a810dfb7ba3bc04a7baf79c8e73cd4315dbf30530d15113635c29","schema_version":"1.0","event_id":"sha256:b67803920b5a810dfb7ba3bc04a7baf79c8e73cd4315dbf30530d15113635c29"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ECI2FKNWPSQV523ZSNJDCOQBKI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global existence of weak solutions for strongly damped wave equations with nonlinear boundary conditions and balanced potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Joseph L. Shomberg","submitted_at":"2018-12-23T21:46:44Z","abstract_excerpt":"We demonstrate the global existence of weak solutions to a class of semilinear strongly damped wave equations possessing nonlinear hyperbolic dynamic boundary conditions. Our work assumes $(-\\Delta_W)^\\theta \\partial_tu$ with $\\theta\\in[\\frac{1}{2},1)$ and where $\\Delta_W$ is the Wentzell-Laplacian. Hence, the associated linear operator admits a compact resolvent. A balance condition is assumed to hold between the nonlinearity defined on the interior of the domain and the nonlinearity on the boundary. This allows for arbitrary (supercritical) polynomial growth on each potential, as well as mix"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09781","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":"2026-05-17T23:57:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+OEAxvA5hMwdXdeKg+OUp6OvYvT7s5wLWcVa+ndCdqiOocGYH7guYPcvTXAj6q/e/VGelaj2HH8gwCPvRHAVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:54:46.614704Z"},"content_sha256":"0ba6cc62769e20786998fc88dde0463785cf4eabbbe80b8e46ba821d12957e32","schema_version":"1.0","event_id":"sha256:0ba6cc62769e20786998fc88dde0463785cf4eabbbe80b8e46ba821d12957e32"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ECI2FKNWPSQV523ZSNJDCOQBKI/bundle.json","state_url":"https://pith.science/pith/ECI2FKNWPSQV523ZSNJDCOQBKI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ECI2FKNWPSQV523ZSNJDCOQBKI/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":"2026-06-02T21:54:46Z","links":{"resolver":"https://pith.science/pith/ECI2FKNWPSQV523ZSNJDCOQBKI","bundle":"https://pith.science/pith/ECI2FKNWPSQV523ZSNJDCOQBKI/bundle.json","state":"https://pith.science/pith/ECI2FKNWPSQV523ZSNJDCOQBKI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ECI2FKNWPSQV523ZSNJDCOQBKI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ECI2FKNWPSQV523ZSNJDCOQBKI","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":"52659325d2af878206552790f3a0f391993c120e40a2a4aa372b93c28c36a94b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-23T21:46:44Z","title_canon_sha256":"801a201fa1697410805b1472610e38284c3f0ff801401791e406e7425a62afc1"},"schema_version":"1.0","source":{"id":"1812.09781","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09781","created_at":"2026-05-17T23:57:26Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09781v1","created_at":"2026-05-17T23:57:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09781","created_at":"2026-05-17T23:57:26Z"},{"alias_kind":"pith_short_12","alias_value":"ECI2FKNWPSQV","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"ECI2FKNWPSQV523Z","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"ECI2FKNW","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:0ba6cc62769e20786998fc88dde0463785cf4eabbbe80b8e46ba821d12957e32","target":"graph","created_at":"2026-05-17T23:57:26Z","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 demonstrate the global existence of weak solutions to a class of semilinear strongly damped wave equations possessing nonlinear hyperbolic dynamic boundary conditions. Our work assumes $(-\\Delta_W)^\\theta \\partial_tu$ with $\\theta\\in[\\frac{1}{2},1)$ and where $\\Delta_W$ is the Wentzell-Laplacian. Hence, the associated linear operator admits a compact resolvent. A balance condition is assumed to hold between the nonlinearity defined on the interior of the domain and the nonlinearity on the boundary. This allows for arbitrary (supercritical) polynomial growth on each potential, as well as mix","authors_text":"Joseph L. Shomberg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-23T21:46:44Z","title":"Global existence of weak solutions for strongly damped wave equations with nonlinear boundary conditions and balanced potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09781","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:b67803920b5a810dfb7ba3bc04a7baf79c8e73cd4315dbf30530d15113635c29","target":"record","created_at":"2026-05-17T23:57:26Z","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":"52659325d2af878206552790f3a0f391993c120e40a2a4aa372b93c28c36a94b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-23T21:46:44Z","title_canon_sha256":"801a201fa1697410805b1472610e38284c3f0ff801401791e406e7425a62afc1"},"schema_version":"1.0","source":{"id":"1812.09781","kind":"arxiv","version":1}},"canonical_sha256":"2091a2a9b67ca15eeb799352313a01520440c29c7113247c5e4b4555a2937962","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2091a2a9b67ca15eeb799352313a01520440c29c7113247c5e4b4555a2937962","first_computed_at":"2026-05-17T23:57:26.811644Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:26.811644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RcXwFTTC3mhRiXi3S7KHwwBPR8qLHvNTvZtxSaZra9nz8PW6vBeoxC3J6QEtxttfT/2j9avk7+MZe2zTcpc+AQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:26.812371Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.09781","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b67803920b5a810dfb7ba3bc04a7baf79c8e73cd4315dbf30530d15113635c29","sha256:0ba6cc62769e20786998fc88dde0463785cf4eabbbe80b8e46ba821d12957e32"],"state_sha256":"ba47d95540ddc950bbec008855d24b9b0f40fef3c6623995d824b5ee93b55925"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kLBsGK5qwv/W/8syAYFr/KkaCmGqI9bkekKob8f16j1bkek8OR+Knf3+yTnJdXy6gqbHtlrmyI/3NWHgclpSAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:54:46.616728Z","bundle_sha256":"a3940008c02491f10b3a998b0888c23b109b3194635e4dd675c464762c2078f1"}}