{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:56QDU6AADDAKUIXJ2JWDIG6QWP","short_pith_number":"pith:56QDU6AA","schema_version":"1.0","canonical_sha256":"efa03a780018c0aa22e9d26c341bd0b3f280ed0c5b1343e179abf744f3e4dd33","source":{"kind":"arxiv","id":"1307.5295","version":2},"attestation_state":"computed","paper":{"title":"A decomposition based proof for fast mixing of a Markov chain over balanced realizations of a joint degree matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Istv\\'an Mikl\\'os, P\\'eter L. Erd\\H{o}s, Zolt\\'an Toroczkai","submitted_at":"2013-07-19T17:50:23Z","abstract_excerpt":"A joint degree matrix (JDM) specifies the number of connections between nodes of given degrees in a graph, for all degree pairs and uniquely determines the degree sequence of the graph. We consider the space of all balanced realizations of an arbitrary JDM, realizations in which the links between any two degree groups are placed as uniformly as possible. We prove that a swap Markov Chain Monte Carlo (MCMC) algorithm in the space of all balanced realizations of an {\\em arbitrary} graphical JDM mixes rapidly, i.e., the relaxation time of the chain is bounded from above by a polynomial in the num"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1307.5295","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-19T17:50:23Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"983112dc1a6d388450b460f91b51b667a359db982e01a38b62774ed452972f28","abstract_canon_sha256":"249b62d7a0ab6b02c630babe9a24f2c44c5b62a66248de4376cc1e55c232d46e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:02.611245Z","signature_b64":"5MKt4z+6faK1a1LhimGtwPmRMPOhFwElr+zzvOymipyBmUxubFdzDbidQ7EpV2cSr47fePynEwQbaZmiqE2PAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efa03a780018c0aa22e9d26c341bd0b3f280ed0c5b1343e179abf744f3e4dd33","last_reissued_at":"2026-05-18T01:37:02.610734Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:02.610734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A decomposition based proof for fast mixing of a Markov chain over balanced realizations of a joint degree matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Istv\\'an Mikl\\'os, P\\'eter L. Erd\\H{o}s, Zolt\\'an Toroczkai","submitted_at":"2013-07-19T17:50:23Z","abstract_excerpt":"A joint degree matrix (JDM) specifies the number of connections between nodes of given degrees in a graph, for all degree pairs and uniquely determines the degree sequence of the graph. We consider the space of all balanced realizations of an arbitrary JDM, realizations in which the links between any two degree groups are placed as uniformly as possible. We prove that a swap Markov Chain Monte Carlo (MCMC) algorithm in the space of all balanced realizations of an {\\em arbitrary} graphical JDM mixes rapidly, i.e., the relaxation time of the chain is bounded from above by a polynomial in the num"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5295","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1307.5295","created_at":"2026-05-18T01:37:02.610794+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.5295v2","created_at":"2026-05-18T01:37:02.610794+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5295","created_at":"2026-05-18T01:37:02.610794+00:00"},{"alias_kind":"pith_short_12","alias_value":"56QDU6AADDAK","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"56QDU6AADDAKUIXJ","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"56QDU6AA","created_at":"2026-05-18T12:27:34.582898+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/56QDU6AADDAKUIXJ2JWDIG6QWP","json":"https://pith.science/pith/56QDU6AADDAKUIXJ2JWDIG6QWP.json","graph_json":"https://pith.science/api/pith-number/56QDU6AADDAKUIXJ2JWDIG6QWP/graph.json","events_json":"https://pith.science/api/pith-number/56QDU6AADDAKUIXJ2JWDIG6QWP/events.json","paper":"https://pith.science/paper/56QDU6AA"},"agent_actions":{"view_html":"https://pith.science/pith/56QDU6AADDAKUIXJ2JWDIG6QWP","download_json":"https://pith.science/pith/56QDU6AADDAKUIXJ2JWDIG6QWP.json","view_paper":"https://pith.science/paper/56QDU6AA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.5295&json=true","fetch_graph":"https://pith.science/api/pith-number/56QDU6AADDAKUIXJ2JWDIG6QWP/graph.json","fetch_events":"https://pith.science/api/pith-number/56QDU6AADDAKUIXJ2JWDIG6QWP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/56QDU6AADDAKUIXJ2JWDIG6QWP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/56QDU6AADDAKUIXJ2JWDIG6QWP/action/storage_attestation","attest_author":"https://pith.science/pith/56QDU6AADDAKUIXJ2JWDIG6QWP/action/author_attestation","sign_citation":"https://pith.science/pith/56QDU6AADDAKUIXJ2JWDIG6QWP/action/citation_signature","submit_replication":"https://pith.science/pith/56QDU6AADDAKUIXJ2JWDIG6QWP/action/replication_record"}},"created_at":"2026-05-18T01:37:02.610794+00:00","updated_at":"2026-05-18T01:37:02.610794+00:00"}