{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:CHZ3VB2UHKJPGAEY6JLH7J7XPO","short_pith_number":"pith:CHZ3VB2U","canonical_record":{"source":{"id":"1812.01675","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-04T20:47:10Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"e019fe810941adf365e5f36fbbfad692187d3b961a6c494e65968d4fe31d373f","abstract_canon_sha256":"3fd56571d709dcc42ece4cc13b4979b928fa943d310d87b7083ead7e9b1811a6"},"schema_version":"1.0"},"canonical_sha256":"11f3ba87543a92f30098f2567fa7f77b826d67fa0e86c7bb22042a4d6d762c43","source":{"kind":"arxiv","id":"1812.01675","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.01675","created_at":"2026-05-17T23:58:18Z"},{"alias_kind":"arxiv_version","alias_value":"1812.01675v2","created_at":"2026-05-17T23:58:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.01675","created_at":"2026-05-17T23:58:18Z"},{"alias_kind":"pith_short_12","alias_value":"CHZ3VB2UHKJP","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CHZ3VB2UHKJPGAEY","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CHZ3VB2U","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:CHZ3VB2UHKJPGAEY6JLH7J7XPO","target":"record","payload":{"canonical_record":{"source":{"id":"1812.01675","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-04T20:47:10Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"e019fe810941adf365e5f36fbbfad692187d3b961a6c494e65968d4fe31d373f","abstract_canon_sha256":"3fd56571d709dcc42ece4cc13b4979b928fa943d310d87b7083ead7e9b1811a6"},"schema_version":"1.0"},"canonical_sha256":"11f3ba87543a92f30098f2567fa7f77b826d67fa0e86c7bb22042a4d6d762c43","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:18.737384Z","signature_b64":"XUgSt/WRHBrul52Lj7O4t0ZZrJx4vSzysps5WNQkowTe7xNrT0k85os+tpbTOsJc6Ydj2ki1xD6LbeWGyBI5BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11f3ba87543a92f30098f2567fa7f77b826d67fa0e86c7bb22042a4d6d762c43","last_reissued_at":"2026-05-17T23:58:18.736888Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:18.736888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.01675","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":"2026-05-17T23:58:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yLEsBhj+Hwo4gr2pUgkghKA1lmfOZub7ikRk/qMrd2oUM6GzNp+Yi93/yaqXOXO3YtwxJ0rPNnhdLbXi5tBRCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:31:52.605252Z"},"content_sha256":"e54a3b63043dd499d86c5806712659ff85dcb4d866caaf1cda7cca8a4301a47a","schema_version":"1.0","event_id":"sha256:e54a3b63043dd499d86c5806712659ff85dcb4d866caaf1cda7cca8a4301a47a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:CHZ3VB2UHKJPGAEY6JLH7J7XPO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deep quench approximation and optimal control of general Cahn-Hilliard systems with fractional operators and double obstacle potentials","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":"2018-12-04T20:47:10Z","abstract_excerpt":"The paper arXiv:1804.11290 contains well-posedness and regularity results for a system of evolutionary operator equations having the structure of a Cahn-Hilliard system. The operators appearing in the system equations were fractional versions in the spectral sense of general linear operators A and B having compact resolvents and are densely defined, unbounded, selfadjoint, and monotone in a Hilbert space of functions defined in a smooth domain. The associated double-well potentials driving the phase separation process modeled by the Cahn-Hilliard system could be of a very general type that inc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01675","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":"2026-05-17T23:58:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Igx3bau/0/3/iU3jixjpOGtKbM2+MdMdElFudJSsHgQ8sHo7cQQV1yzI2fd6ql2HnUY7mgGmJt7PR2DUJ2RcAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:31:52.606096Z"},"content_sha256":"18f335b1968a444191b7c7182c14d9efacc0ace2413e88099375d460778ca365","schema_version":"1.0","event_id":"sha256:18f335b1968a444191b7c7182c14d9efacc0ace2413e88099375d460778ca365"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CHZ3VB2UHKJPGAEY6JLH7J7XPO/bundle.json","state_url":"https://pith.science/pith/CHZ3VB2UHKJPGAEY6JLH7J7XPO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CHZ3VB2UHKJPGAEY6JLH7J7XPO/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":"2026-05-30T19:31:52Z","links":{"resolver":"https://pith.science/pith/CHZ3VB2UHKJPGAEY6JLH7J7XPO","bundle":"https://pith.science/pith/CHZ3VB2UHKJPGAEY6JLH7J7XPO/bundle.json","state":"https://pith.science/pith/CHZ3VB2UHKJPGAEY6JLH7J7XPO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CHZ3VB2UHKJPGAEY6JLH7J7XPO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CHZ3VB2UHKJPGAEY6JLH7J7XPO","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":"3fd56571d709dcc42ece4cc13b4979b928fa943d310d87b7083ead7e9b1811a6","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-04T20:47:10Z","title_canon_sha256":"e019fe810941adf365e5f36fbbfad692187d3b961a6c494e65968d4fe31d373f"},"schema_version":"1.0","source":{"id":"1812.01675","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.01675","created_at":"2026-05-17T23:58:18Z"},{"alias_kind":"arxiv_version","alias_value":"1812.01675v2","created_at":"2026-05-17T23:58:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.01675","created_at":"2026-05-17T23:58:18Z"},{"alias_kind":"pith_short_12","alias_value":"CHZ3VB2UHKJP","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CHZ3VB2UHKJPGAEY","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CHZ3VB2U","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:18f335b1968a444191b7c7182c14d9efacc0ace2413e88099375d460778ca365","target":"graph","created_at":"2026-05-17T23:58:18Z","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 paper arXiv:1804.11290 contains well-posedness and regularity results for a system of evolutionary operator equations having the structure of a Cahn-Hilliard system. The operators appearing in the system equations were fractional versions in the spectral sense of general linear operators A and B having compact resolvents and are densely defined, unbounded, selfadjoint, and monotone in a Hilbert space of functions defined in a smooth domain. The associated double-well potentials driving the phase separation process modeled by the Cahn-Hilliard system could be of a very general type that inc","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":"2018-12-04T20:47:10Z","title":"Deep quench approximation and optimal control of general Cahn-Hilliard systems with fractional operators and double obstacle potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01675","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:e54a3b63043dd499d86c5806712659ff85dcb4d866caaf1cda7cca8a4301a47a","target":"record","created_at":"2026-05-17T23:58:18Z","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":"3fd56571d709dcc42ece4cc13b4979b928fa943d310d87b7083ead7e9b1811a6","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-04T20:47:10Z","title_canon_sha256":"e019fe810941adf365e5f36fbbfad692187d3b961a6c494e65968d4fe31d373f"},"schema_version":"1.0","source":{"id":"1812.01675","kind":"arxiv","version":2}},"canonical_sha256":"11f3ba87543a92f30098f2567fa7f77b826d67fa0e86c7bb22042a4d6d762c43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11f3ba87543a92f30098f2567fa7f77b826d67fa0e86c7bb22042a4d6d762c43","first_computed_at":"2026-05-17T23:58:18.736888Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:18.736888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XUgSt/WRHBrul52Lj7O4t0ZZrJx4vSzysps5WNQkowTe7xNrT0k85os+tpbTOsJc6Ydj2ki1xD6LbeWGyBI5BA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:18.737384Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.01675","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e54a3b63043dd499d86c5806712659ff85dcb4d866caaf1cda7cca8a4301a47a","sha256:18f335b1968a444191b7c7182c14d9efacc0ace2413e88099375d460778ca365"],"state_sha256":"327329367bcc592970541be467c4fb34802f545af26add34001ccd61bd400ee3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"13TxIAljI6jtE5Vmz87rpDuKdTevgYVnSsnx3yuqYsZhBiUDGiOeQqEAiQ/pL5IJuNUccIqXY+fVsZxKblJhBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T19:31:52.610552Z","bundle_sha256":"8d9f4967faaf8f23b8ee03a2daf863c1f8b90464d585f0565e7b02361478ad14"}}