{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:E2ZLESMS5PJROVWTRZ2P4B4N2P","short_pith_number":"pith:E2ZLESMS","canonical_record":{"source":{"id":"1702.06244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-21T02:44:12Z","cross_cats_sorted":[],"title_canon_sha256":"e6e4fd1cc1f8b0f6098a105142d30e700ccde6778af7cf3f07fc9589b572493b","abstract_canon_sha256":"e4414fccd292d3b725aec93c2bcb7acd63bba29e7b7a43a788b514c010254647"},"schema_version":"1.0"},"canonical_sha256":"26b2b24992ebd31756d38e74fe078dd3e328c0a6d8db89f0ecfd896debe9221d","source":{"kind":"arxiv","id":"1702.06244","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.06244","created_at":"2026-05-18T00:50:14Z"},{"alias_kind":"arxiv_version","alias_value":"1702.06244v1","created_at":"2026-05-18T00:50:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.06244","created_at":"2026-05-18T00:50:14Z"},{"alias_kind":"pith_short_12","alias_value":"E2ZLESMS5PJR","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"E2ZLESMS5PJROVWT","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"E2ZLESMS","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:E2ZLESMS5PJROVWTRZ2P4B4N2P","target":"record","payload":{"canonical_record":{"source":{"id":"1702.06244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-21T02:44:12Z","cross_cats_sorted":[],"title_canon_sha256":"e6e4fd1cc1f8b0f6098a105142d30e700ccde6778af7cf3f07fc9589b572493b","abstract_canon_sha256":"e4414fccd292d3b725aec93c2bcb7acd63bba29e7b7a43a788b514c010254647"},"schema_version":"1.0"},"canonical_sha256":"26b2b24992ebd31756d38e74fe078dd3e328c0a6d8db89f0ecfd896debe9221d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:14.620499Z","signature_b64":"zlO30AO29u7DQ0DNFhBtRc/UFZ1S/fBz/Nl6iC4OvLX8tDY3SaJZwoCs7g0kbIHy3MLVf4uPPx3zCP8HZi6ZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26b2b24992ebd31756d38e74fe078dd3e328c0a6d8db89f0ecfd896debe9221d","last_reissued_at":"2026-05-18T00:50:14.619939Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:14.619939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.06244","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":"2026-05-18T00:50:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ROJ8ljTCJtgN9KabQXTQFz4M9lDUxh91IufZXTolKpBQ5dp7tsk3gW7M5R9uYnbWzPncEg8XtaPg+wVL00bpDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:21:15.266013Z"},"content_sha256":"63f94a7ba9a64bc7843545ff45edfdc6762efcb2d95b3bd1c54ead9761d8750f","schema_version":"1.0","event_id":"sha256:63f94a7ba9a64bc7843545ff45edfdc6762efcb2d95b3bd1c54ead9761d8750f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:E2ZLESMS5PJROVWTRZ2P4B4N2P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An elliptic system with logarithmic nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abdelkrim Moussaoui, Claudianor O. Alves, Leandro da S. Tavares","submitted_at":"2017-02-21T02:44:12Z","abstract_excerpt":"In the present paper we study the existence of solutions for some classes of singular systems involving the p(x) and q(x) Laplacian operators. The approach is based on bifurcation theory and subsupersolution method for systems of quasilinear equations involving singular terms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06244","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":"2026-05-18T00:50:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z4zQYYNtDBXzhZ7M/hmC8/sKwzfGF8E+gz6OYHnlwX8qp32bO9AtAx8mhIimqp3HoQyOtPFvsYUXNMI11/2mBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:21:15.266389Z"},"content_sha256":"dd20558906c772b07eab9a4cfdd4c5590f8d52b871cb030f74aa90760eef88fb","schema_version":"1.0","event_id":"sha256:dd20558906c772b07eab9a4cfdd4c5590f8d52b871cb030f74aa90760eef88fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E2ZLESMS5PJROVWTRZ2P4B4N2P/bundle.json","state_url":"https://pith.science/pith/E2ZLESMS5PJROVWTRZ2P4B4N2P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E2ZLESMS5PJROVWTRZ2P4B4N2P/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":"2026-05-31T12:21:15Z","links":{"resolver":"https://pith.science/pith/E2ZLESMS5PJROVWTRZ2P4B4N2P","bundle":"https://pith.science/pith/E2ZLESMS5PJROVWTRZ2P4B4N2P/bundle.json","state":"https://pith.science/pith/E2ZLESMS5PJROVWTRZ2P4B4N2P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E2ZLESMS5PJROVWTRZ2P4B4N2P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:E2ZLESMS5PJROVWTRZ2P4B4N2P","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":"e4414fccd292d3b725aec93c2bcb7acd63bba29e7b7a43a788b514c010254647","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-21T02:44:12Z","title_canon_sha256":"e6e4fd1cc1f8b0f6098a105142d30e700ccde6778af7cf3f07fc9589b572493b"},"schema_version":"1.0","source":{"id":"1702.06244","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.06244","created_at":"2026-05-18T00:50:14Z"},{"alias_kind":"arxiv_version","alias_value":"1702.06244v1","created_at":"2026-05-18T00:50:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.06244","created_at":"2026-05-18T00:50:14Z"},{"alias_kind":"pith_short_12","alias_value":"E2ZLESMS5PJR","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"E2ZLESMS5PJROVWT","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"E2ZLESMS","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:dd20558906c772b07eab9a4cfdd4c5590f8d52b871cb030f74aa90760eef88fb","target":"graph","created_at":"2026-05-18T00:50:14Z","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 the present paper we study the existence of solutions for some classes of singular systems involving the p(x) and q(x) Laplacian operators. The approach is based on bifurcation theory and subsupersolution method for systems of quasilinear equations involving singular terms.","authors_text":"Abdelkrim Moussaoui, Claudianor O. Alves, Leandro da S. Tavares","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-21T02:44:12Z","title":"An elliptic system with logarithmic nonlinearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06244","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":"sha256:63f94a7ba9a64bc7843545ff45edfdc6762efcb2d95b3bd1c54ead9761d8750f","target":"record","created_at":"2026-05-18T00:50:14Z","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":"e4414fccd292d3b725aec93c2bcb7acd63bba29e7b7a43a788b514c010254647","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-21T02:44:12Z","title_canon_sha256":"e6e4fd1cc1f8b0f6098a105142d30e700ccde6778af7cf3f07fc9589b572493b"},"schema_version":"1.0","source":{"id":"1702.06244","kind":"arxiv","version":1}},"canonical_sha256":"26b2b24992ebd31756d38e74fe078dd3e328c0a6d8db89f0ecfd896debe9221d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26b2b24992ebd31756d38e74fe078dd3e328c0a6d8db89f0ecfd896debe9221d","first_computed_at":"2026-05-18T00:50:14.619939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:14.619939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zlO30AO29u7DQ0DNFhBtRc/UFZ1S/fBz/Nl6iC4OvLX8tDY3SaJZwoCs7g0kbIHy3MLVf4uPPx3zCP8HZi6ZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:14.620499Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.06244","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63f94a7ba9a64bc7843545ff45edfdc6762efcb2d95b3bd1c54ead9761d8750f","sha256:dd20558906c772b07eab9a4cfdd4c5590f8d52b871cb030f74aa90760eef88fb"],"state_sha256":"775b6a476c2b5fbab80dfed886e1bc4a65c55079ea5a2c23440a13f5e991eb1a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fLK6KeO7gVDiqfe6f1bS2m3IzsF/CvROvSLKeA2IyiCcIlhFExVpwwgaHJPIAnKAlSgr093gtUzvoVdeqrmWBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T12:21:15.269400Z","bundle_sha256":"5be1233cf75a8363b8638e9bb52e8bc46b48fc69235d0435b49ef3c500bbd603"}}