{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JTNS73GSXDTK56XCW4WDYBWWFN","short_pith_number":"pith:JTNS73GS","canonical_record":{"source":{"id":"1608.07423","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-26T11:35:44Z","cross_cats_sorted":[],"title_canon_sha256":"756aedcdb1586e8d6830b9a1dd82d501cc91877c24a7de200be70b9b6681ed56","abstract_canon_sha256":"ac6165ecadf2464e8f2d2aa2b04a7b422792f34c2c6818d65e8172f809b9add0"},"schema_version":"1.0"},"canonical_sha256":"4cdb2fecd2b8e6aefae2b72c3c06d62b630b4700eb079e62612c3da402db8dd7","source":{"kind":"arxiv","id":"1608.07423","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07423","created_at":"2026-05-18T01:07:53Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07423v1","created_at":"2026-05-18T01:07:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07423","created_at":"2026-05-18T01:07:53Z"},{"alias_kind":"pith_short_12","alias_value":"JTNS73GSXDTK","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JTNS73GSXDTK56XC","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JTNS73GS","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JTNS73GSXDTK56XCW4WDYBWWFN","target":"record","payload":{"canonical_record":{"source":{"id":"1608.07423","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-26T11:35:44Z","cross_cats_sorted":[],"title_canon_sha256":"756aedcdb1586e8d6830b9a1dd82d501cc91877c24a7de200be70b9b6681ed56","abstract_canon_sha256":"ac6165ecadf2464e8f2d2aa2b04a7b422792f34c2c6818d65e8172f809b9add0"},"schema_version":"1.0"},"canonical_sha256":"4cdb2fecd2b8e6aefae2b72c3c06d62b630b4700eb079e62612c3da402db8dd7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:53.103941Z","signature_b64":"g1oOJ3fe4RUeiHDo083+lgJ20UtD/81UQazMtro85wWjNsdP3y8sCVjOenlBK/tfIvAqNLv4c+Ze8M66dWL4AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4cdb2fecd2b8e6aefae2b72c3c06d62b630b4700eb079e62612c3da402db8dd7","last_reissued_at":"2026-05-18T01:07:53.103535Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:53.103535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.07423","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":"2026-05-18T01:07:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D2v6DQ3eUNB/mmftj/9P1ri9nBKJ9rHzRj4SThb2W3QmKFO9iUzzlD/IKUk2dz5KQg+Ay8A48qbshmykp25vDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:23:33.499395Z"},"content_sha256":"992fc4d823c03f20db3e2f35b98d38f2fc76ed652fbd85861a2672445266750e","schema_version":"1.0","event_id":"sha256:992fc4d823c03f20db3e2f35b98d38f2fc76ed652fbd85861a2672445266750e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JTNS73GSXDTK56XCW4WDYBWWFN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multiple solutions of $p$-biharmonic equations with Navier boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Du\\v{s}an Repov\\v{s}, Giovanni Molica Bisci","submitted_at":"2016-08-26T11:35:44Z","abstract_excerpt":"In this paper, exploiting variational methods, the existence of multiple weak solutions for a class of elliptic Navier boundary problems involving the $p$-biharmonic operator is investigated. Moreover, a concrete example of an application is presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07423","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":"2026-05-18T01:07:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SzzZbIvw97CtEIHTm4udnweZBhrvj5G54xa1kbcieA/lpVabYWVGdqhBDhsDrimQcAMEtdN1FLmJjdjaX2WLBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:23:33.499743Z"},"content_sha256":"6a1a99a8ec0fa029ee3a0fbd4a51eea50abeaaa5ef9b27b2afaf1f83298a1bff","schema_version":"1.0","event_id":"sha256:6a1a99a8ec0fa029ee3a0fbd4a51eea50abeaaa5ef9b27b2afaf1f83298a1bff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JTNS73GSXDTK56XCW4WDYBWWFN/bundle.json","state_url":"https://pith.science/pith/JTNS73GSXDTK56XCW4WDYBWWFN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JTNS73GSXDTK56XCW4WDYBWWFN/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":"2026-06-12T06:23:33Z","links":{"resolver":"https://pith.science/pith/JTNS73GSXDTK56XCW4WDYBWWFN","bundle":"https://pith.science/pith/JTNS73GSXDTK56XCW4WDYBWWFN/bundle.json","state":"https://pith.science/pith/JTNS73GSXDTK56XCW4WDYBWWFN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JTNS73GSXDTK56XCW4WDYBWWFN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JTNS73GSXDTK56XCW4WDYBWWFN","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":"ac6165ecadf2464e8f2d2aa2b04a7b422792f34c2c6818d65e8172f809b9add0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-26T11:35:44Z","title_canon_sha256":"756aedcdb1586e8d6830b9a1dd82d501cc91877c24a7de200be70b9b6681ed56"},"schema_version":"1.0","source":{"id":"1608.07423","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07423","created_at":"2026-05-18T01:07:53Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07423v1","created_at":"2026-05-18T01:07:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07423","created_at":"2026-05-18T01:07:53Z"},{"alias_kind":"pith_short_12","alias_value":"JTNS73GSXDTK","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JTNS73GSXDTK56XC","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JTNS73GS","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:6a1a99a8ec0fa029ee3a0fbd4a51eea50abeaaa5ef9b27b2afaf1f83298a1bff","target":"graph","created_at":"2026-05-18T01:07:53Z","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":"In this paper, exploiting variational methods, the existence of multiple weak solutions for a class of elliptic Navier boundary problems involving the $p$-biharmonic operator is investigated. Moreover, a concrete example of an application is presented.","authors_text":"Du\\v{s}an Repov\\v{s}, Giovanni Molica Bisci","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-26T11:35:44Z","title":"Multiple solutions of $p$-biharmonic equations with Navier boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07423","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":"sha256:992fc4d823c03f20db3e2f35b98d38f2fc76ed652fbd85861a2672445266750e","target":"record","created_at":"2026-05-18T01:07:53Z","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":"ac6165ecadf2464e8f2d2aa2b04a7b422792f34c2c6818d65e8172f809b9add0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-26T11:35:44Z","title_canon_sha256":"756aedcdb1586e8d6830b9a1dd82d501cc91877c24a7de200be70b9b6681ed56"},"schema_version":"1.0","source":{"id":"1608.07423","kind":"arxiv","version":1}},"canonical_sha256":"4cdb2fecd2b8e6aefae2b72c3c06d62b630b4700eb079e62612c3da402db8dd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4cdb2fecd2b8e6aefae2b72c3c06d62b630b4700eb079e62612c3da402db8dd7","first_computed_at":"2026-05-18T01:07:53.103535Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:53.103535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g1oOJ3fe4RUeiHDo083+lgJ20UtD/81UQazMtro85wWjNsdP3y8sCVjOenlBK/tfIvAqNLv4c+Ze8M66dWL4AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:53.103941Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.07423","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:992fc4d823c03f20db3e2f35b98d38f2fc76ed652fbd85861a2672445266750e","sha256:6a1a99a8ec0fa029ee3a0fbd4a51eea50abeaaa5ef9b27b2afaf1f83298a1bff"],"state_sha256":"a45d2fd950897da05af45168e5f9db52b6d80dde6bdab7c7301860a740fb80da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o25H8ilhOMyYnU5OfZdkDlEXP+7+mUqmMNQdsJ+fBRMznOd4wV890NRKL2m5TWOXSKA2/yZzhEc/FPdDf2KsBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T06:23:33.502489Z","bundle_sha256":"377623acb78dcfdcb52a154737c71a953d0d6d0ae572e8c0fed9c31f5e127cfd"}}