{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NJZXMD74DTH4FA6T2FQWIKTJ6B","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":"eec0e8b4513576101301d8da0797d79dc20857784b0ccc75384221e5d1addfe9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-07T16:08:07Z","title_canon_sha256":"62a00bc4d9039248b9fdb25503b407597063de9a2cdc53c7b792d99ccba91b6a"},"schema_version":"1.0","source":{"id":"1502.02156","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02156","created_at":"2026-05-18T01:16:53Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02156v1","created_at":"2026-05-18T01:16:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02156","created_at":"2026-05-18T01:16:53Z"},{"alias_kind":"pith_short_12","alias_value":"NJZXMD74DTH4","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NJZXMD74DTH4FA6T","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NJZXMD74","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:7bff62ff0db745890c0fedede288f869337ebe9cfccbc12e19bf2f51d1b8afdd","target":"graph","created_at":"2026-05-18T01:16:53Z","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":"In this paper, we continue the study of the hyperbolic relaxation of the Cahn-Hilliard-Oono equation with the sub-quintic non-linearity in the whole space $\\R^3$ started in our previous paper and verify that under the natural assumptions on the non-linearity and the external force, the fractal dimension of the associated global attractor in the natural energy space is finite.","authors_text":"Anton Savostianov, Sergey Zelik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-07T16:08:07Z","title":"Finite Dimensionality of the attractor for the hyperbolic Cahn-Hilliard-Oono Equation in R^3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02156","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":"sha256:7f3d0fabba3273a533c4ac415a59992ea12da64561bd34a030a097e0f47e7267","target":"record","created_at":"2026-05-18T01:16:53Z","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":"eec0e8b4513576101301d8da0797d79dc20857784b0ccc75384221e5d1addfe9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-07T16:08:07Z","title_canon_sha256":"62a00bc4d9039248b9fdb25503b407597063de9a2cdc53c7b792d99ccba91b6a"},"schema_version":"1.0","source":{"id":"1502.02156","kind":"arxiv","version":1}},"canonical_sha256":"6a73760ffc1ccfc283d3d161642a69f0795ad79ad4e8137a466ce99bbe7c78fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a73760ffc1ccfc283d3d161642a69f0795ad79ad4e8137a466ce99bbe7c78fd","first_computed_at":"2026-05-18T01:16:53.166787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:53.166787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IE/OCT1hSN/t32nIjVxmB/uzA5mT9hL0sZV7BFqn3+qE7fukWKPmH1QLHzPIs0Eco2F0qSJlBZOGaksn8lUJBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:53.167547Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.02156","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f3d0fabba3273a533c4ac415a59992ea12da64561bd34a030a097e0f47e7267","sha256:7bff62ff0db745890c0fedede288f869337ebe9cfccbc12e19bf2f51d1b8afdd"],"state_sha256":"1807ca43a1ff0f06a66f42db5c1745cb018d94f4bdac3a7ef8952c89411991cb"}