{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LHV6CYIG7NFWRKKEYMNYGZ5YC2","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":"bdae775ae37229bd45264e77f12c28c09a83f2e0757c068ddb4a3c4971d61709","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-22T09:40:15Z","title_canon_sha256":"db459cb4cb5aeb255f3f6ec6e9fc4263b9802acc58442218ccc8276b2935d06d"},"schema_version":"1.0","source":{"id":"1302.5529","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5529","created_at":"2026-05-17T23:57:54Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5529v2","created_at":"2026-05-17T23:57:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5529","created_at":"2026-05-17T23:57:54Z"},{"alias_kind":"pith_short_12","alias_value":"LHV6CYIG7NFW","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LHV6CYIG7NFWRKKE","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LHV6CYIG","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:8062a4a0da0b0f87b109a6729c64a986bbda09e0c853cc31f1e914be1413c7a7","target":"graph","created_at":"2026-05-17T23:57:54Z","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 consider the heat equation on the $N$-dimensional cube $(0,1)^N$ and impose different classes of integral conditions, instead of usual boundary ones. Well-posedness results for the heat equation under the condition that the moments of order 0 and 1 are conserved had been known so far only in the case of N=1 -- for which such conditions can be easily interpreted as conservation of mass and barycenter. In this paper we show that in the case of general $N$ the heat equation with such integral conditions is still well-posed, upon suitably relax the notion of solution.\n  Existence and uniqueness","authors_text":"Delio Mugnolo, Serge Nicaise","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-22T09:40:15Z","title":"The heat equation under linear conditions on the moments in higher dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5529","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":"sha256:25922bcc105a1f0365c9de4c3115d1e1aafc93ea5d11317f862e12ac374854a7","target":"record","created_at":"2026-05-17T23:57:54Z","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":"bdae775ae37229bd45264e77f12c28c09a83f2e0757c068ddb4a3c4971d61709","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-22T09:40:15Z","title_canon_sha256":"db459cb4cb5aeb255f3f6ec6e9fc4263b9802acc58442218ccc8276b2935d06d"},"schema_version":"1.0","source":{"id":"1302.5529","kind":"arxiv","version":2}},"canonical_sha256":"59ebe16106fb4b68a944c31b8367b8168169635a5df8aba2e3af5b1ca2cb2d63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59ebe16106fb4b68a944c31b8367b8168169635a5df8aba2e3af5b1ca2cb2d63","first_computed_at":"2026-05-17T23:57:54.509373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:54.509373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H9yDxFFbBdgKZ66CBXubzcmfuCQD01XJAgDb7oX9aw8xbQu52dPp/mSju+hm+lRYbpT3FvetUozBwgdDUQqeCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:54.509964Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.5529","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25922bcc105a1f0365c9de4c3115d1e1aafc93ea5d11317f862e12ac374854a7","sha256:8062a4a0da0b0f87b109a6729c64a986bbda09e0c853cc31f1e914be1413c7a7"],"state_sha256":"b3b080aed639d5697ebba0201489caf100eed1840bf385eff9079eab0230f70a"}