{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SZZT7LKEBSDXMT4SNVGEXYYIUH","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":"16e5b8f21c58f7f3718206ab0df5c9e1a74b3356b73c68b0aaf52f4cacb4227c","cross_cats_sorted":["math.CO","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-05T23:14:11Z","title_canon_sha256":"d2a0ec01875912d7074ca2c14d1f21d41e28b776eda6aa183facf54554af9272"},"schema_version":"1.0","source":{"id":"1704.01666","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.01666","created_at":"2026-05-18T00:46:54Z"},{"alias_kind":"arxiv_version","alias_value":"1704.01666v1","created_at":"2026-05-18T00:46:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01666","created_at":"2026-05-18T00:46:54Z"},{"alias_kind":"pith_short_12","alias_value":"SZZT7LKEBSDX","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SZZT7LKEBSDXMT4S","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SZZT7LKE","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:12d6151c112f470dbf322f950e49dde387ad44252fd9b3c98a5c1449449fe3e7","target":"graph","created_at":"2026-05-18T00:46:54Z","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 link the theory of optimal transportation to the theory of integer partitions. Let $\\mathscr P(n)$ denote the set of integer partitions of $n \\in \\mathbb N$ and write partitions $\\pi \\in \\mathscr P(n)$ as $(n_1, \\dots, n_{k(\\pi)})$. Using terminology from optimal transport, we characterize certain classes of partitions like symmetric partitions and those in Euler's identity\n  $|\\{ \\pi \\in \\mathscr P(n) |$ all $ n_i $ distinct $ \\} | = | \\{ \\pi \\in \\mathscr P(n) | $ all $ n_i $ odd $ \\}|$.\n  Then we sketch how optimal transport might help to understand higher dimensional partitions.","authors_text":"Sonja Hohloch","cross_cats":["math.CO","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-05T23:14:11Z","title":"Optimal transport and integer partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01666","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":"sha256:396cd5ba16b1d48d63fa6533b74db4142f3bee1b305aabbadc48e39b0cb280b5","target":"record","created_at":"2026-05-18T00:46:54Z","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":"16e5b8f21c58f7f3718206ab0df5c9e1a74b3356b73c68b0aaf52f4cacb4227c","cross_cats_sorted":["math.CO","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-05T23:14:11Z","title_canon_sha256":"d2a0ec01875912d7074ca2c14d1f21d41e28b776eda6aa183facf54554af9272"},"schema_version":"1.0","source":{"id":"1704.01666","kind":"arxiv","version":1}},"canonical_sha256":"96733fad440c87764f926d4c4be308a1fbb92b1f01c44f0c289c8593870b3b49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96733fad440c87764f926d4c4be308a1fbb92b1f01c44f0c289c8593870b3b49","first_computed_at":"2026-05-18T00:46:54.639782Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:54.639782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0B0rMoPCMzF3rmFM+PAiRXBHqLI+O+WPebqdEzeESqvEkjQ0HjFSAnklr7n0I6QNyifVYsgZdsswThGJX1xjBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:54.640350Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.01666","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:396cd5ba16b1d48d63fa6533b74db4142f3bee1b305aabbadc48e39b0cb280b5","sha256:12d6151c112f470dbf322f950e49dde387ad44252fd9b3c98a5c1449449fe3e7"],"state_sha256":"5cf059c2a11d55b048859783b6b047205c36e16dd52d583308f34652bbf776a8"}