{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:U2TYQMXDOSSWBQLJZMCS3Q2JGH","short_pith_number":"pith:U2TYQMXD","canonical_record":{"source":{"id":"2106.05136","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-06-09T15:18:34Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"d5520f61b3fbc618659ed24d5fb87b05f734aebc1de2a4efb85f9d126c8b6998","abstract_canon_sha256":"58e58f0aeffa4feb60c1f31767096d0dbe36a025cb978920dcc10d00fb80a68b"},"schema_version":"1.0"},"canonical_sha256":"a6a78832e374a560c169cb052dc34931ec346a08ab009b88736b1148ec11de90","source":{"kind":"arxiv","id":"2106.05136","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.05136","created_at":"2026-07-05T02:47:53Z"},{"alias_kind":"arxiv_version","alias_value":"2106.05136v1","created_at":"2026-07-05T02:47:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.05136","created_at":"2026-07-05T02:47:53Z"},{"alias_kind":"pith_short_12","alias_value":"U2TYQMXDOSSW","created_at":"2026-07-05T02:47:53Z"},{"alias_kind":"pith_short_16","alias_value":"U2TYQMXDOSSWBQLJ","created_at":"2026-07-05T02:47:53Z"},{"alias_kind":"pith_short_8","alias_value":"U2TYQMXD","created_at":"2026-07-05T02:47:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:U2TYQMXDOSSWBQLJZMCS3Q2JGH","target":"record","payload":{"canonical_record":{"source":{"id":"2106.05136","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-06-09T15:18:34Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"d5520f61b3fbc618659ed24d5fb87b05f734aebc1de2a4efb85f9d126c8b6998","abstract_canon_sha256":"58e58f0aeffa4feb60c1f31767096d0dbe36a025cb978920dcc10d00fb80a68b"},"schema_version":"1.0"},"canonical_sha256":"a6a78832e374a560c169cb052dc34931ec346a08ab009b88736b1148ec11de90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:47:53.521454Z","signature_b64":"7ga4iD94IJHiIpIUQr/+bmMQd5/Mf/npjr2JWeQkKptIbQLREVs3fCw22LF8X1rgWELE22Ca+qXD+KdXLoyUDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6a78832e374a560c169cb052dc34931ec346a08ab009b88736b1148ec11de90","last_reissued_at":"2026-07-05T02:47:53.520959Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:47:53.520959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2106.05136","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":"2026-07-05T02:47:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"umxB48C2RkZmj7miqcyyq/XDBSq7igG9EicAanNY194zN7X1RF1mQB41r2hfNQqK9FGrveeNNZh6VIu/UXvSBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T19:55:43.820668Z"},"content_sha256":"f0881526c80949bc56c06c42ab55df4111726af6f74bc051d471910c4e15349a","schema_version":"1.0","event_id":"sha256:f0881526c80949bc56c06c42ab55df4111726af6f74bc051d471910c4e15349a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:U2TYQMXDOSSWBQLJZMCS3Q2JGH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hemivariational Inequalities on Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Anand Srivastav, Khalid Akhlil, Mourad El Ouali, Nouhayla Ait Oussaid, Sultana Ben Aadi","submitted_at":"2021-06-09T15:18:34Z","abstract_excerpt":"In this paper, a new class of hemivariational inequalities is introduced. It concerns Laplace operator on locally finite graphs together with multivalued nonmonotone nonlinearities expressed in terms of Clarke's subdifferential. First of all, we state and prove some results on the subdifferentiability of nonconvex functionals defined on graphs. Thereafter, an elliptic hemivariational inequality on locally finite graphs is considered and the existence and uniqueness of its weak solutions are proved by means of the well-known surjectivity result for pseudomonotone mappings. In the end of this pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.05136","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/2106.05136/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":"2026-07-05T02:47:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d6RRd6UpMCvTh3JC18Mr2Vl61OXkKjQeR8QBfcu6Ex3NHO9Xh935nxgkdk8DFbjzt5OClKcN2ya8T5Ybmcm7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T19:55:43.821148Z"},"content_sha256":"122f8d218fdbcb269c536861186a20eae7ee380b4f0e16bba0e3adddb0d3067d","schema_version":"1.0","event_id":"sha256:122f8d218fdbcb269c536861186a20eae7ee380b4f0e16bba0e3adddb0d3067d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U2TYQMXDOSSWBQLJZMCS3Q2JGH/bundle.json","state_url":"https://pith.science/pith/U2TYQMXDOSSWBQLJZMCS3Q2JGH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U2TYQMXDOSSWBQLJZMCS3Q2JGH/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":"2026-08-21T19:55:43Z","links":{"resolver":"https://pith.science/pith/U2TYQMXDOSSWBQLJZMCS3Q2JGH","bundle":"https://pith.science/pith/U2TYQMXDOSSWBQLJZMCS3Q2JGH/bundle.json","state":"https://pith.science/pith/U2TYQMXDOSSWBQLJZMCS3Q2JGH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U2TYQMXDOSSWBQLJZMCS3Q2JGH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:U2TYQMXDOSSWBQLJZMCS3Q2JGH","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":"58e58f0aeffa4feb60c1f31767096d0dbe36a025cb978920dcc10d00fb80a68b","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-06-09T15:18:34Z","title_canon_sha256":"d5520f61b3fbc618659ed24d5fb87b05f734aebc1de2a4efb85f9d126c8b6998"},"schema_version":"1.0","source":{"id":"2106.05136","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.05136","created_at":"2026-07-05T02:47:53Z"},{"alias_kind":"arxiv_version","alias_value":"2106.05136v1","created_at":"2026-07-05T02:47:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.05136","created_at":"2026-07-05T02:47:53Z"},{"alias_kind":"pith_short_12","alias_value":"U2TYQMXDOSSW","created_at":"2026-07-05T02:47:53Z"},{"alias_kind":"pith_short_16","alias_value":"U2TYQMXDOSSWBQLJ","created_at":"2026-07-05T02:47:53Z"},{"alias_kind":"pith_short_8","alias_value":"U2TYQMXD","created_at":"2026-07-05T02:47:53Z"}],"graph_snapshots":[{"event_id":"sha256:122f8d218fdbcb269c536861186a20eae7ee380b4f0e16bba0e3adddb0d3067d","target":"graph","created_at":"2026-07-05T02:47:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2106.05136/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, a new class of hemivariational inequalities is introduced. It concerns Laplace operator on locally finite graphs together with multivalued nonmonotone nonlinearities expressed in terms of Clarke's subdifferential. First of all, we state and prove some results on the subdifferentiability of nonconvex functionals defined on graphs. Thereafter, an elliptic hemivariational inequality on locally finite graphs is considered and the existence and uniqueness of its weak solutions are proved by means of the well-known surjectivity result for pseudomonotone mappings. In the end of this pa","authors_text":"Anand Srivastav, Khalid Akhlil, Mourad El Ouali, Nouhayla Ait Oussaid, Sultana Ben Aadi","cross_cats":["math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-06-09T15:18:34Z","title":"Hemivariational Inequalities on Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.05136","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:f0881526c80949bc56c06c42ab55df4111726af6f74bc051d471910c4e15349a","target":"record","created_at":"2026-07-05T02:47:53Z","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":"58e58f0aeffa4feb60c1f31767096d0dbe36a025cb978920dcc10d00fb80a68b","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-06-09T15:18:34Z","title_canon_sha256":"d5520f61b3fbc618659ed24d5fb87b05f734aebc1de2a4efb85f9d126c8b6998"},"schema_version":"1.0","source":{"id":"2106.05136","kind":"arxiv","version":1}},"canonical_sha256":"a6a78832e374a560c169cb052dc34931ec346a08ab009b88736b1148ec11de90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6a78832e374a560c169cb052dc34931ec346a08ab009b88736b1148ec11de90","first_computed_at":"2026-07-05T02:47:53.520959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:47:53.520959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7ga4iD94IJHiIpIUQr/+bmMQd5/Mf/npjr2JWeQkKptIbQLREVs3fCw22LF8X1rgWELE22Ca+qXD+KdXLoyUDA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:47:53.521454Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.05136","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0881526c80949bc56c06c42ab55df4111726af6f74bc051d471910c4e15349a","sha256:122f8d218fdbcb269c536861186a20eae7ee380b4f0e16bba0e3adddb0d3067d"],"state_sha256":"d38b4c7d8fe6592e401efc528dd064e2c34d26b3c2526bba5f2bf17aba11063a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nNtmJvsIOjqTG85ttLfE6fxv8bXfGGU/GotINFBG/0ataD8dzRIvGw7MEgq0BTbKRch+ajlYAVAs98LVoqDNBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T19:55:43.825588Z","bundle_sha256":"a9350ba664f90fc3e206dfa49d44430081c5046d2f8a24bbe9b9b23a97b81fe8"}}