{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4R66PKKLWSJQY2QIT26K6Y3JDX","short_pith_number":"pith:4R66PKKL","canonical_record":{"source":{"id":"1801.05364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-01-16T16:59:53Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"5418d5491a4ba64307b6550ba235631cd6474a7dfc36a90c535803cd8d5ea0ec","abstract_canon_sha256":"d5f1a0cf80b31dbfc47f73dd6a38382bbb4e4ede4f79a521d7a363a1419d9fa0"},"schema_version":"1.0"},"canonical_sha256":"e47de7a94bb4930c6a089ebcaf63691dd81d185e1ef934e4cf39f0e1b30773c7","source":{"kind":"arxiv","id":"1801.05364","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.05364","created_at":"2026-05-18T00:25:46Z"},{"alias_kind":"arxiv_version","alias_value":"1801.05364v1","created_at":"2026-05-18T00:25:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.05364","created_at":"2026-05-18T00:25:46Z"},{"alias_kind":"pith_short_12","alias_value":"4R66PKKLWSJQ","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4R66PKKLWSJQY2QI","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4R66PKKL","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4R66PKKLWSJQY2QIT26K6Y3JDX","target":"record","payload":{"canonical_record":{"source":{"id":"1801.05364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-01-16T16:59:53Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"5418d5491a4ba64307b6550ba235631cd6474a7dfc36a90c535803cd8d5ea0ec","abstract_canon_sha256":"d5f1a0cf80b31dbfc47f73dd6a38382bbb4e4ede4f79a521d7a363a1419d9fa0"},"schema_version":"1.0"},"canonical_sha256":"e47de7a94bb4930c6a089ebcaf63691dd81d185e1ef934e4cf39f0e1b30773c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:46.991939Z","signature_b64":"9I1MdFomr8m+fTiqxJ+vDxA/HITgRj3QyZ8CInRPHWRmfbyIX9zPYAT9jQDmUCqSZh9uW/ACVlustkyxM407Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e47de7a94bb4930c6a089ebcaf63691dd81d185e1ef934e4cf39f0e1b30773c7","last_reissued_at":"2026-05-18T00:25:46.991284Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:46.991284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.05364","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":"2026-05-18T00:25:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MB6buwr4dX6psRgXbLJI/nQcWWCJ+my+noHZCW1v4j0CiF6BewFBlQbRdlMlKHd9jsP8S9eXip/VyL2sb3jADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:56:00.748040Z"},"content_sha256":"b39129addb19dea7c42b87f427efd89311718b76e3c0fdf5feca9d15d3f499ab","schema_version":"1.0","event_id":"sha256:b39129addb19dea7c42b87f427efd89311718b76e3c0fdf5feca9d15d3f499ab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4R66PKKLWSJQY2QIT26K6Y3JDX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An existence result and evolutionary $\\Gamma$-convergence for perturbed gradient systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alexander Mielke, Aras Bacho, Etienne Emmrich","submitted_at":"2018-01-16T16:59:53Z","abstract_excerpt":"The initial-value problem for the perturbed gradient flow \\[\n  B(t,u(t)) \\in \\partial\\Psi_{u(t)}(u'(t))+\\partial \\mathcal E_t(u(t)) \\text{ for a.a. } t\\in (0,T),\\qquad u(0)=u_0 \\] with a perturbation $B$ in a Banach space $V$ is investigated, where the dissipation potential $\\Psi_u: V\\rightarrow [0,+\\infty)$ and the energy functional $\\mathcal E_t:V\\rightarrow (-\\infty,+\\infty]$ are nonsmooth and supposed to be convex and nonconvex, respectively. The perturbation $B:[0,T]\\times V \\rightarrow V^*, (t,v)\\mapsto B(t,v)$ is assumed to be continuous and satisfies a growth condition. Under additiona"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05364","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":"2026-05-18T00:25:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UHXK0aY2uJBOp5iJTb8AxgWtZA15JOQeqFh8DslwCxS+YOQ9fgTL71x8hoHOfWl/h2t1BhyIhdBQlZF2MDpQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:56:00.748727Z"},"content_sha256":"c3b0b42eedecddfd4021d7efce3fe08123202adf347b55d5be2a058c10f7ae75","schema_version":"1.0","event_id":"sha256:c3b0b42eedecddfd4021d7efce3fe08123202adf347b55d5be2a058c10f7ae75"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4R66PKKLWSJQY2QIT26K6Y3JDX/bundle.json","state_url":"https://pith.science/pith/4R66PKKLWSJQY2QIT26K6Y3JDX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4R66PKKLWSJQY2QIT26K6Y3JDX/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":"2026-05-26T07:56:00Z","links":{"resolver":"https://pith.science/pith/4R66PKKLWSJQY2QIT26K6Y3JDX","bundle":"https://pith.science/pith/4R66PKKLWSJQY2QIT26K6Y3JDX/bundle.json","state":"https://pith.science/pith/4R66PKKLWSJQY2QIT26K6Y3JDX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4R66PKKLWSJQY2QIT26K6Y3JDX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4R66PKKLWSJQY2QIT26K6Y3JDX","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":"d5f1a0cf80b31dbfc47f73dd6a38382bbb4e4ede4f79a521d7a363a1419d9fa0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-01-16T16:59:53Z","title_canon_sha256":"5418d5491a4ba64307b6550ba235631cd6474a7dfc36a90c535803cd8d5ea0ec"},"schema_version":"1.0","source":{"id":"1801.05364","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.05364","created_at":"2026-05-18T00:25:46Z"},{"alias_kind":"arxiv_version","alias_value":"1801.05364v1","created_at":"2026-05-18T00:25:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.05364","created_at":"2026-05-18T00:25:46Z"},{"alias_kind":"pith_short_12","alias_value":"4R66PKKLWSJQ","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4R66PKKLWSJQY2QI","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4R66PKKL","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:c3b0b42eedecddfd4021d7efce3fe08123202adf347b55d5be2a058c10f7ae75","target":"graph","created_at":"2026-05-18T00:25:46Z","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":"The initial-value problem for the perturbed gradient flow \\[\n  B(t,u(t)) \\in \\partial\\Psi_{u(t)}(u'(t))+\\partial \\mathcal E_t(u(t)) \\text{ for a.a. } t\\in (0,T),\\qquad u(0)=u_0 \\] with a perturbation $B$ in a Banach space $V$ is investigated, where the dissipation potential $\\Psi_u: V\\rightarrow [0,+\\infty)$ and the energy functional $\\mathcal E_t:V\\rightarrow (-\\infty,+\\infty]$ are nonsmooth and supposed to be convex and nonconvex, respectively. The perturbation $B:[0,T]\\times V \\rightarrow V^*, (t,v)\\mapsto B(t,v)$ is assumed to be continuous and satisfies a growth condition. Under additiona","authors_text":"Alexander Mielke, Aras Bacho, Etienne Emmrich","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-01-16T16:59:53Z","title":"An existence result and evolutionary $\\Gamma$-convergence for perturbed gradient systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05364","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:b39129addb19dea7c42b87f427efd89311718b76e3c0fdf5feca9d15d3f499ab","target":"record","created_at":"2026-05-18T00:25:46Z","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":"d5f1a0cf80b31dbfc47f73dd6a38382bbb4e4ede4f79a521d7a363a1419d9fa0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-01-16T16:59:53Z","title_canon_sha256":"5418d5491a4ba64307b6550ba235631cd6474a7dfc36a90c535803cd8d5ea0ec"},"schema_version":"1.0","source":{"id":"1801.05364","kind":"arxiv","version":1}},"canonical_sha256":"e47de7a94bb4930c6a089ebcaf63691dd81d185e1ef934e4cf39f0e1b30773c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e47de7a94bb4930c6a089ebcaf63691dd81d185e1ef934e4cf39f0e1b30773c7","first_computed_at":"2026-05-18T00:25:46.991284Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:46.991284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9I1MdFomr8m+fTiqxJ+vDxA/HITgRj3QyZ8CInRPHWRmfbyIX9zPYAT9jQDmUCqSZh9uW/ACVlustkyxM407Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:46.991939Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.05364","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b39129addb19dea7c42b87f427efd89311718b76e3c0fdf5feca9d15d3f499ab","sha256:c3b0b42eedecddfd4021d7efce3fe08123202adf347b55d5be2a058c10f7ae75"],"state_sha256":"8af88b0ee7f575422527d86a238061c6e6653f7ea3134d0bdea1ad54fbb24e28"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IeUqGNObUUmb/IG29ot/y3Py+dh03ZoPrRSCtC1xecGEezTtUIEUzXDM7uWbfjh6JevhsGwCmoDJ7/Y7mAdhDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T07:56:00.752682Z","bundle_sha256":"a1127bd1e45e481dff2059c2750b179f11ce5afbbff148230d785913e966401b"}}