{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5SSJW6HQZODRNQAWC2CHF4BHW3","short_pith_number":"pith:5SSJW6HQ","canonical_record":{"source":{"id":"1501.06696","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-01-27T09:11:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5835b1be58679dcd5def85df489e8ce262a83ac2361fc5327032248b2b2549dc","abstract_canon_sha256":"f229b3b85d1652f84b231748a6e70e5213315c2544a2f948d099673ce555d572"},"schema_version":"1.0"},"canonical_sha256":"eca49b78f0cb8716c016168472f027b6ea58e3da065f031e89654666d3a0a0be","source":{"kind":"arxiv","id":"1501.06696","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06696","created_at":"2026-05-18T01:17:37Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06696v1","created_at":"2026-05-18T01:17:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06696","created_at":"2026-05-18T01:17:37Z"},{"alias_kind":"pith_short_12","alias_value":"5SSJW6HQZODR","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5SSJW6HQZODRNQAW","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5SSJW6HQ","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5SSJW6HQZODRNQAWC2CHF4BHW3","target":"record","payload":{"canonical_record":{"source":{"id":"1501.06696","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-01-27T09:11:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5835b1be58679dcd5def85df489e8ce262a83ac2361fc5327032248b2b2549dc","abstract_canon_sha256":"f229b3b85d1652f84b231748a6e70e5213315c2544a2f948d099673ce555d572"},"schema_version":"1.0"},"canonical_sha256":"eca49b78f0cb8716c016168472f027b6ea58e3da065f031e89654666d3a0a0be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:37.659750Z","signature_b64":"KFqA11w9BJTGOtCsqfJK679YLA2NicG/tjHckx38FfDtQnAiXFM2zLulUL/BHYHuN3F+F2eBJH+Rlmdu4INICw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eca49b78f0cb8716c016168472f027b6ea58e3da065f031e89654666d3a0a0be","last_reissued_at":"2026-05-18T01:17:37.659012Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:37.659012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.06696","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":"2026-05-18T01:17:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TSE2UvOwVgCBcg4VKQioEe0+z/vJdj3Qvujj4r6wm4i0Sf1JDtlYeVrz1F62m+DnLn12VLmk8763DesmFBqABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:53:13.661979Z"},"content_sha256":"045eb41428b6a17c6f4fc69f3b3003a5d7fc95a2e083667f7799482089df2a75","schema_version":"1.0","event_id":"sha256:045eb41428b6a17c6f4fc69f3b3003a5d7fc95a2e083667f7799482089df2a75"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5SSJW6HQZODRNQAWC2CHF4BHW3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An axiomatic approach to gradients with applications to Dirichlet and obstacle problems beyond function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.FA","authors_text":"Anders Bj\\\"orn, Jana Bj\\\"orn, Joakim Arnlind","submitted_at":"2015-01-27T09:11:34Z","abstract_excerpt":"We develop a framework for studying variational problems in Banach spaces with respect to gradient relations, which encompasses many of the notions of generalized gradients that appear in the literature. We stress the fact that our approach is not dependent on function spaces and therefore applies equally well to functions on metric spaces as to operator algebras. In particular, we consider analogues of Dirichlet and obstacle problems, as well as first eigenvalue problems, and formulate conditions for the existence of solutions and their uniqueness. Moreover, we investigate to what extent a la"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06696","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":"2026-05-18T01:17:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9RSxdI53D4vUgl1/8+f5hC8n2EXtN3/U4GTsSaXaY+a6YoiwNJ1JF4oygwRDbRCZZkpplSm6Ql85L3SxkEDjCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:53:13.662645Z"},"content_sha256":"22f1e7626463451eb3d89cd5f544b4b1e8c8033aa7d4a6a4c0c56f43eef5b049","schema_version":"1.0","event_id":"sha256:22f1e7626463451eb3d89cd5f544b4b1e8c8033aa7d4a6a4c0c56f43eef5b049"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5SSJW6HQZODRNQAWC2CHF4BHW3/bundle.json","state_url":"https://pith.science/pith/5SSJW6HQZODRNQAWC2CHF4BHW3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5SSJW6HQZODRNQAWC2CHF4BHW3/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":"2026-05-27T11:53:13Z","links":{"resolver":"https://pith.science/pith/5SSJW6HQZODRNQAWC2CHF4BHW3","bundle":"https://pith.science/pith/5SSJW6HQZODRNQAWC2CHF4BHW3/bundle.json","state":"https://pith.science/pith/5SSJW6HQZODRNQAWC2CHF4BHW3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5SSJW6HQZODRNQAWC2CHF4BHW3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5SSJW6HQZODRNQAWC2CHF4BHW3","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":"f229b3b85d1652f84b231748a6e70e5213315c2544a2f948d099673ce555d572","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-01-27T09:11:34Z","title_canon_sha256":"5835b1be58679dcd5def85df489e8ce262a83ac2361fc5327032248b2b2549dc"},"schema_version":"1.0","source":{"id":"1501.06696","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06696","created_at":"2026-05-18T01:17:37Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06696v1","created_at":"2026-05-18T01:17:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06696","created_at":"2026-05-18T01:17:37Z"},{"alias_kind":"pith_short_12","alias_value":"5SSJW6HQZODR","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5SSJW6HQZODRNQAW","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5SSJW6HQ","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:22f1e7626463451eb3d89cd5f544b4b1e8c8033aa7d4a6a4c0c56f43eef5b049","target":"graph","created_at":"2026-05-18T01:17:37Z","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 develop a framework for studying variational problems in Banach spaces with respect to gradient relations, which encompasses many of the notions of generalized gradients that appear in the literature. We stress the fact that our approach is not dependent on function spaces and therefore applies equally well to functions on metric spaces as to operator algebras. In particular, we consider analogues of Dirichlet and obstacle problems, as well as first eigenvalue problems, and formulate conditions for the existence of solutions and their uniqueness. Moreover, we investigate to what extent a la","authors_text":"Anders Bj\\\"orn, Jana Bj\\\"orn, Joakim Arnlind","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-01-27T09:11:34Z","title":"An axiomatic approach to gradients with applications to Dirichlet and obstacle problems beyond function spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06696","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":"sha256:045eb41428b6a17c6f4fc69f3b3003a5d7fc95a2e083667f7799482089df2a75","target":"record","created_at":"2026-05-18T01:17:37Z","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":"f229b3b85d1652f84b231748a6e70e5213315c2544a2f948d099673ce555d572","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-01-27T09:11:34Z","title_canon_sha256":"5835b1be58679dcd5def85df489e8ce262a83ac2361fc5327032248b2b2549dc"},"schema_version":"1.0","source":{"id":"1501.06696","kind":"arxiv","version":1}},"canonical_sha256":"eca49b78f0cb8716c016168472f027b6ea58e3da065f031e89654666d3a0a0be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eca49b78f0cb8716c016168472f027b6ea58e3da065f031e89654666d3a0a0be","first_computed_at":"2026-05-18T01:17:37.659012Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:37.659012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KFqA11w9BJTGOtCsqfJK679YLA2NicG/tjHckx38FfDtQnAiXFM2zLulUL/BHYHuN3F+F2eBJH+Rlmdu4INICw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:37.659750Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.06696","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:045eb41428b6a17c6f4fc69f3b3003a5d7fc95a2e083667f7799482089df2a75","sha256:22f1e7626463451eb3d89cd5f544b4b1e8c8033aa7d4a6a4c0c56f43eef5b049"],"state_sha256":"9910f607c350b8b15523d70fb213de2fe4e54892280e2e5600c7cd9b03ada1ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L8BOUgqnTPlNcOrs/M71C9Rt9ReYpaub/EIa8a8UMQsmGh9p2l5wHfaLWYyjFTK7iv5niRXqsjro0s6svofVCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:53:13.666745Z","bundle_sha256":"6969d86564087997400d575a986b18c67620d6c5c447e7396d8454fe9c21d29b"}}