{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:K5XUZXTKMV4R5L5VQN5GBNPJRP","short_pith_number":"pith:K5XUZXTK","canonical_record":{"source":{"id":"1605.07801","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-25T09:54:09Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"47ce84fa6a76f1059fb5b39eb06f7988fafb51b5e4eea59f396f342212691292","abstract_canon_sha256":"4a338b789c5a2412507d4b6e2e799a34a477f1c0d82a8201b33f2935b568519a"},"schema_version":"1.0"},"canonical_sha256":"576f4cde6a65791eafb5837a60b5e98bc48f87156aca13b95213c7e9cb299bc2","source":{"kind":"arxiv","id":"1605.07801","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.07801","created_at":"2026-05-18T01:04:32Z"},{"alias_kind":"arxiv_version","alias_value":"1605.07801v2","created_at":"2026-05-18T01:04:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07801","created_at":"2026-05-18T01:04:32Z"},{"alias_kind":"pith_short_12","alias_value":"K5XUZXTKMV4R","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"K5XUZXTKMV4R5L5V","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"K5XUZXTK","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:K5XUZXTKMV4R5L5VQN5GBNPJRP","target":"record","payload":{"canonical_record":{"source":{"id":"1605.07801","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-25T09:54:09Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"47ce84fa6a76f1059fb5b39eb06f7988fafb51b5e4eea59f396f342212691292","abstract_canon_sha256":"4a338b789c5a2412507d4b6e2e799a34a477f1c0d82a8201b33f2935b568519a"},"schema_version":"1.0"},"canonical_sha256":"576f4cde6a65791eafb5837a60b5e98bc48f87156aca13b95213c7e9cb299bc2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:32.711599Z","signature_b64":"u9vuauDKysAnD8peYcdH3N3TrIBLZVz48l08oVK5onDtK9mm/4Jo65OGmQMQ535o2BD2AREcE2guuYVMRB/IAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"576f4cde6a65791eafb5837a60b5e98bc48f87156aca13b95213c7e9cb299bc2","last_reissued_at":"2026-05-18T01:04:32.710782Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:32.710782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.07801","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YkBGn09PHWPA47C6NtXCMjmZFn+aEafZbaYRh7B4jdJb4Kow9SyG36CFUkZXioZKEvnKbQHlPw8atfKD6NrkDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:20:51.955434Z"},"content_sha256":"6c23b6f3951e3646f5fff6f404c8966d97ec85c1a56f0650f1718032de95bb90","schema_version":"1.0","event_id":"sha256:6c23b6f3951e3646f5fff6f404c8966d97ec85c1a56f0650f1718032de95bb90"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:K5XUZXTKMV4R5L5VQN5GBNPJRP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distributed optimal control of a nonstandard nonlocal phase field system","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":"2016-05-25T09:54:09Z","abstract_excerpt":"We investigate a distributed optimal control problem for a nonlocal phase field model of viscous Cahn-Hilliard type. The model constitutes a nonlocal version of a model for two-species phase segregation on an atomic lattice under the presence of diffusion that has been studied in a series of papers by P. Podio-Guidugli and the present authors. The model consists of a highly nonlinear parabolic equation coupled to an ordinary differential equation. The latter equation contains both nonlocal and singular terms that render the analysis difficult. Standard arguments of optimal control theory do no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07801","kind":"arxiv","version":2},"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":"2026-05-18T01:04:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MpW7cF21uxGuEE9fP3A/r+7vM1bK9tnghnVUEeoH19D5mXgnSshuxtK1mDd5mssHwq29ze+x5kfgxbcdJ3zAAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:20:51.956088Z"},"content_sha256":"4e1e7e847e9672d3e5257998de9a2df59e2a6c6d561a1d8e11f03d10b6ea4093","schema_version":"1.0","event_id":"sha256:4e1e7e847e9672d3e5257998de9a2df59e2a6c6d561a1d8e11f03d10b6ea4093"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K5XUZXTKMV4R5L5VQN5GBNPJRP/bundle.json","state_url":"https://pith.science/pith/K5XUZXTKMV4R5L5VQN5GBNPJRP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K5XUZXTKMV4R5L5VQN5GBNPJRP/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":"2026-06-07T02:20:51Z","links":{"resolver":"https://pith.science/pith/K5XUZXTKMV4R5L5VQN5GBNPJRP","bundle":"https://pith.science/pith/K5XUZXTKMV4R5L5VQN5GBNPJRP/bundle.json","state":"https://pith.science/pith/K5XUZXTKMV4R5L5VQN5GBNPJRP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K5XUZXTKMV4R5L5VQN5GBNPJRP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:K5XUZXTKMV4R5L5VQN5GBNPJRP","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":"4a338b789c5a2412507d4b6e2e799a34a477f1c0d82a8201b33f2935b568519a","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-25T09:54:09Z","title_canon_sha256":"47ce84fa6a76f1059fb5b39eb06f7988fafb51b5e4eea59f396f342212691292"},"schema_version":"1.0","source":{"id":"1605.07801","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.07801","created_at":"2026-05-18T01:04:32Z"},{"alias_kind":"arxiv_version","alias_value":"1605.07801v2","created_at":"2026-05-18T01:04:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07801","created_at":"2026-05-18T01:04:32Z"},{"alias_kind":"pith_short_12","alias_value":"K5XUZXTKMV4R","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"K5XUZXTKMV4R5L5V","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"K5XUZXTK","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:4e1e7e847e9672d3e5257998de9a2df59e2a6c6d561a1d8e11f03d10b6ea4093","target":"graph","created_at":"2026-05-18T01:04:32Z","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 investigate a distributed optimal control problem for a nonlocal phase field model of viscous Cahn-Hilliard type. The model constitutes a nonlocal version of a model for two-species phase segregation on an atomic lattice under the presence of diffusion that has been studied in a series of papers by P. Podio-Guidugli and the present authors. The model consists of a highly nonlinear parabolic equation coupled to an ordinary differential equation. The latter equation contains both nonlocal and singular terms that render the analysis difficult. Standard arguments of optimal control theory do no","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":"2016-05-25T09:54:09Z","title":"Distributed optimal control of a nonstandard nonlocal phase field system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07801","kind":"arxiv","version":2},"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":"sha256:6c23b6f3951e3646f5fff6f404c8966d97ec85c1a56f0650f1718032de95bb90","target":"record","created_at":"2026-05-18T01:04:32Z","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":"4a338b789c5a2412507d4b6e2e799a34a477f1c0d82a8201b33f2935b568519a","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-25T09:54:09Z","title_canon_sha256":"47ce84fa6a76f1059fb5b39eb06f7988fafb51b5e4eea59f396f342212691292"},"schema_version":"1.0","source":{"id":"1605.07801","kind":"arxiv","version":2}},"canonical_sha256":"576f4cde6a65791eafb5837a60b5e98bc48f87156aca13b95213c7e9cb299bc2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"576f4cde6a65791eafb5837a60b5e98bc48f87156aca13b95213c7e9cb299bc2","first_computed_at":"2026-05-18T01:04:32.710782Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:32.710782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u9vuauDKysAnD8peYcdH3N3TrIBLZVz48l08oVK5onDtK9mm/4Jo65OGmQMQ535o2BD2AREcE2guuYVMRB/IAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:32.711599Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.07801","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c23b6f3951e3646f5fff6f404c8966d97ec85c1a56f0650f1718032de95bb90","sha256:4e1e7e847e9672d3e5257998de9a2df59e2a6c6d561a1d8e11f03d10b6ea4093"],"state_sha256":"25be0c459284076e8b2d8d7467139e27049dbc17fd0cdebb70eb0345b5db30cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dinp1qXppOQ5eE8ihT+MUfZf5wMJcQpdM1a5mOi8Tq89CStl4l5CJOZHusSc4gPgpQoFkbtagkwYko9j1IbxBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T02:20:51.959588Z","bundle_sha256":"17cb4610129e02072b27894b4bb6f95eda6f7f2220ac17a6e1f0b988248764bb"}}