{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:3KW45PZVIKNFDFPSMAVF7WQ5FM","short_pith_number":"pith:3KW45PZV","canonical_record":{"source":{"id":"1607.01991","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-07T12:45:44Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"98103112bb8bcbc42cc74eced5221055fd9adb80a3a4dd18d1697965e9bf00c7","abstract_canon_sha256":"cefc356375aac23204b95ef742a7030f90777b8a58578d1f285244b6e9aab34a"},"schema_version":"1.0"},"canonical_sha256":"daadcebf35429a5195f2602a5fda1d2b2adce249952a3e1e32deda8ce8de07d8","source":{"kind":"arxiv","id":"1607.01991","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.01991","created_at":"2026-05-18T01:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"1607.01991v1","created_at":"2026-05-18T01:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01991","created_at":"2026-05-18T01:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"3KW45PZVIKNF","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3KW45PZVIKNFDFPS","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3KW45PZV","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:3KW45PZVIKNFDFPSMAVF7WQ5FM","target":"record","payload":{"canonical_record":{"source":{"id":"1607.01991","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-07T12:45:44Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"98103112bb8bcbc42cc74eced5221055fd9adb80a3a4dd18d1697965e9bf00c7","abstract_canon_sha256":"cefc356375aac23204b95ef742a7030f90777b8a58578d1f285244b6e9aab34a"},"schema_version":"1.0"},"canonical_sha256":"daadcebf35429a5195f2602a5fda1d2b2adce249952a3e1e32deda8ce8de07d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:22.857573Z","signature_b64":"eexOACBl3hPDVhEdeBsAJDxzKo6AsqlvKAGFbWbZCWRYmlYW0p/H9V/PIpaKqjtcEDvkxF+6UOSnlRt4ZixlBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"daadcebf35429a5195f2602a5fda1d2b2adce249952a3e1e32deda8ce8de07d8","last_reissued_at":"2026-05-18T01:11:22.857026Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:22.857026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.01991","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":"2026-05-18T01:11:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CgFkClqAIZuA0S1ls9xyJYQAxygQVm1Oiiuh3YdSQU6ZVj3/4DE3aQkl5Ir60RqfIS4IAWflkJkAUbmYTuQMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:40:47.876725Z"},"content_sha256":"5e42626b0c983bb417969a4a64ecaf915b0a2311143a375808978388ed2ba93c","schema_version":"1.0","event_id":"sha256:5e42626b0c983bb417969a4a64ecaf915b0a2311143a375808978388ed2ba93c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:3KW45PZVIKNFDFPSMAVF7WQ5FM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distributed optimal control of a nonstandard nonlocal phase field system with double obstacle potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Gianni Gilardi, J\\\"urgen Sprekels, Pierluigi Colli","submitted_at":"2016-07-07T12:45:44Z","abstract_excerpt":"This paper is concerned with a distributed optimal control problem for a nonlocal phase field model of Cahn-Hilliard type, which is a nonlocal version of a model for two-species phase segregation on an atomic lattice under the presence of diffusion. The local model has been investigated in a series of papers by P. Podio-Guidugli and the present authors; the nonlocal model studied here consists of a highly nonlinear parabolic equation coupled to an ordinary differential inclusion of subdifferential type. The inclusion originates from a free energy containing the indicator function of the interv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01991","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":"2026-05-18T01:11:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NttGz/Uu+eyludQ9gtuzNiynci6J4kBVS4vrlwVgFgnIpmx/q6tshcMsvCaCwTm3RFP3qyDtmgbCK0v6NA/yAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:40:47.877099Z"},"content_sha256":"4e2939130dccc22f77d7d80411ba34f1676117a2a96ccad370b73e1143000b02","schema_version":"1.0","event_id":"sha256:4e2939130dccc22f77d7d80411ba34f1676117a2a96ccad370b73e1143000b02"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3KW45PZVIKNFDFPSMAVF7WQ5FM/bundle.json","state_url":"https://pith.science/pith/3KW45PZVIKNFDFPSMAVF7WQ5FM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3KW45PZVIKNFDFPSMAVF7WQ5FM/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":"2026-05-30T08:40:47Z","links":{"resolver":"https://pith.science/pith/3KW45PZVIKNFDFPSMAVF7WQ5FM","bundle":"https://pith.science/pith/3KW45PZVIKNFDFPSMAVF7WQ5FM/bundle.json","state":"https://pith.science/pith/3KW45PZVIKNFDFPSMAVF7WQ5FM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3KW45PZVIKNFDFPSMAVF7WQ5FM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3KW45PZVIKNFDFPSMAVF7WQ5FM","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":"cefc356375aac23204b95ef742a7030f90777b8a58578d1f285244b6e9aab34a","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-07T12:45:44Z","title_canon_sha256":"98103112bb8bcbc42cc74eced5221055fd9adb80a3a4dd18d1697965e9bf00c7"},"schema_version":"1.0","source":{"id":"1607.01991","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.01991","created_at":"2026-05-18T01:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"1607.01991v1","created_at":"2026-05-18T01:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01991","created_at":"2026-05-18T01:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"3KW45PZVIKNF","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3KW45PZVIKNFDFPS","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3KW45PZV","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:4e2939130dccc22f77d7d80411ba34f1676117a2a96ccad370b73e1143000b02","target":"graph","created_at":"2026-05-18T01:11:22Z","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":"This paper is concerned with a distributed optimal control problem for a nonlocal phase field model of Cahn-Hilliard type, which is a nonlocal version of a model for two-species phase segregation on an atomic lattice under the presence of diffusion. The local model has been investigated in a series of papers by P. Podio-Guidugli and the present authors; the nonlocal model studied here consists of a highly nonlinear parabolic equation coupled to an ordinary differential inclusion of subdifferential type. The inclusion originates from a free energy containing the indicator function of the interv","authors_text":"Gianni Gilardi, J\\\"urgen Sprekels, Pierluigi Colli","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-07T12:45:44Z","title":"Distributed optimal control of a nonstandard nonlocal phase field system with double obstacle potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01991","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":"sha256:5e42626b0c983bb417969a4a64ecaf915b0a2311143a375808978388ed2ba93c","target":"record","created_at":"2026-05-18T01:11:22Z","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":"cefc356375aac23204b95ef742a7030f90777b8a58578d1f285244b6e9aab34a","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-07T12:45:44Z","title_canon_sha256":"98103112bb8bcbc42cc74eced5221055fd9adb80a3a4dd18d1697965e9bf00c7"},"schema_version":"1.0","source":{"id":"1607.01991","kind":"arxiv","version":1}},"canonical_sha256":"daadcebf35429a5195f2602a5fda1d2b2adce249952a3e1e32deda8ce8de07d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"daadcebf35429a5195f2602a5fda1d2b2adce249952a3e1e32deda8ce8de07d8","first_computed_at":"2026-05-18T01:11:22.857026Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:22.857026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eexOACBl3hPDVhEdeBsAJDxzKo6AsqlvKAGFbWbZCWRYmlYW0p/H9V/PIpaKqjtcEDvkxF+6UOSnlRt4ZixlBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:22.857573Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.01991","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e42626b0c983bb417969a4a64ecaf915b0a2311143a375808978388ed2ba93c","sha256:4e2939130dccc22f77d7d80411ba34f1676117a2a96ccad370b73e1143000b02"],"state_sha256":"f7657c86dcc568b4fab481bb63295f0e95aef11eb4945e61b3182a7f28a4d8d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7eKwX8WrYZhjmM6gcaMwvuBZ0xJ6P4xp9/PGfHLs7ENK6GtLaXuqONIyuBAYe6nfENYGnLiI2DljXtth15OYCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:40:47.882106Z","bundle_sha256":"f37ed85cdff84bec2b196755864e9ffde06576fb95f4284b9353ab49fc19abbb"}}