{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:3J2VHJS2LV3CW46JD7YESW5OWF","short_pith_number":"pith:3J2VHJS2","canonical_record":{"source":{"id":"2505.22875","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-28T21:17:03Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"bc15b044877833679116a081550a2d0141f21092c982921817c3bc32777a8af3","abstract_canon_sha256":"762cf578a3bd48865051f6983be950eebe4695404ac5064d3153e35ede54ca81"},"schema_version":"1.0"},"canonical_sha256":"da7553a65a5d762b73c91ff0495baeb1443961397e5087be72f27f8786960464","source":{"kind":"arxiv","id":"2505.22875","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.22875","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"2505.22875v1","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.22875","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"3J2VHJS2LV3C","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_16","alias_value":"3J2VHJS2LV3CW46J","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_8","alias_value":"3J2VHJS2","created_at":"2026-07-05T11:11:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:3J2VHJS2LV3CW46JD7YESW5OWF","target":"record","payload":{"canonical_record":{"source":{"id":"2505.22875","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-28T21:17:03Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"bc15b044877833679116a081550a2d0141f21092c982921817c3bc32777a8af3","abstract_canon_sha256":"762cf578a3bd48865051f6983be950eebe4695404ac5064d3153e35ede54ca81"},"schema_version":"1.0"},"canonical_sha256":"da7553a65a5d762b73c91ff0495baeb1443961397e5087be72f27f8786960464","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:11:51.298424Z","signature_b64":"KBr7RGTElZcrMBliom06gZv/7K7IPFNHJvZ9DzSogjuVNFRBsC/v0wSxrpvSL/ur/GzdfbL+LEgYRQsL+yhfCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da7553a65a5d762b73c91ff0495baeb1443961397e5087be72f27f8786960464","last_reissued_at":"2026-07-05T11:11:51.297923Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:11:51.297923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.22875","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:11:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pBmj7DA4NzzqX9pu/xwfTCzYgd3Sr7UCOcamvEi9xL3gMAEQSD1rEfPCVFBqW8hetSdF7Hcs8TrphDYOUxhRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T22:59:59.321056Z"},"content_sha256":"3f2335746f89586d1597f542a85c4431cce3976463bdc9883e541db65439d777","schema_version":"1.0","event_id":"sha256:3f2335746f89586d1597f542a85c4431cce3976463bdc9883e541db65439d777"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:3J2VHJS2LV3CW46JD7YESW5OWF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monotonicity and decompositions of random regular graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Adva Mond, Julien Portier, Lawrence Hollom, Lyuben Lichev, Yiting Wang","submitted_at":"2025-05-28T21:17:03Z","abstract_excerpt":"In this work we establish several monotonicity and decomposition results in the framework of random regular graphs. Among other results, we show that, for a wide range of parameters $d_1 \\leq d_2$, there exists a coupling of $G(n,d_1)$ and $G(n,d_2)$ satisfying that $G(n,d_1) \\subseteq G(n,d_2)$ with high probability, confirming a conjecture of Gao, Isaev and McKay in a new regime. Our contributions include new tools for analysing contiguity and total variation distance between random regular graph models, a novel procedure for generating unions of random edge-disjoint perfect matchings, and r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22875","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.22875/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:11:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l12uKkHuh2f81eXxlTNQLRmIbnJ8iZPBKbBokLsJzznJZBGWTmE+rUWUWBV5thr+AJ0Krnc6tJFITuY7/cC7DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T22:59:59.321428Z"},"content_sha256":"e564e7f9b7a3177d0515a547aa6a696285657ffd3683523f05f76ecca9bcd285","schema_version":"1.0","event_id":"sha256:e564e7f9b7a3177d0515a547aa6a696285657ffd3683523f05f76ecca9bcd285"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3J2VHJS2LV3CW46JD7YESW5OWF/bundle.json","state_url":"https://pith.science/pith/3J2VHJS2LV3CW46JD7YESW5OWF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3J2VHJS2LV3CW46JD7YESW5OWF/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":"2026-08-04T22:59:59Z","links":{"resolver":"https://pith.science/pith/3J2VHJS2LV3CW46JD7YESW5OWF","bundle":"https://pith.science/pith/3J2VHJS2LV3CW46JD7YESW5OWF/bundle.json","state":"https://pith.science/pith/3J2VHJS2LV3CW46JD7YESW5OWF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3J2VHJS2LV3CW46JD7YESW5OWF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3J2VHJS2LV3CW46JD7YESW5OWF","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":"762cf578a3bd48865051f6983be950eebe4695404ac5064d3153e35ede54ca81","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-28T21:17:03Z","title_canon_sha256":"bc15b044877833679116a081550a2d0141f21092c982921817c3bc32777a8af3"},"schema_version":"1.0","source":{"id":"2505.22875","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.22875","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"2505.22875v1","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.22875","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"3J2VHJS2LV3C","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_16","alias_value":"3J2VHJS2LV3CW46J","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_8","alias_value":"3J2VHJS2","created_at":"2026-07-05T11:11:51Z"}],"graph_snapshots":[{"event_id":"sha256:e564e7f9b7a3177d0515a547aa6a696285657ffd3683523f05f76ecca9bcd285","target":"graph","created_at":"2026-07-05T11:11:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.22875/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work we establish several monotonicity and decomposition results in the framework of random regular graphs. Among other results, we show that, for a wide range of parameters $d_1 \\leq d_2$, there exists a coupling of $G(n,d_1)$ and $G(n,d_2)$ satisfying that $G(n,d_1) \\subseteq G(n,d_2)$ with high probability, confirming a conjecture of Gao, Isaev and McKay in a new regime. Our contributions include new tools for analysing contiguity and total variation distance between random regular graph models, a novel procedure for generating unions of random edge-disjoint perfect matchings, and r","authors_text":"Adva Mond, Julien Portier, Lawrence Hollom, Lyuben Lichev, Yiting Wang","cross_cats":["math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-28T21:17:03Z","title":"Monotonicity and decompositions of random regular graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22875","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":"sha256:3f2335746f89586d1597f542a85c4431cce3976463bdc9883e541db65439d777","target":"record","created_at":"2026-07-05T11:11:51Z","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":"762cf578a3bd48865051f6983be950eebe4695404ac5064d3153e35ede54ca81","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-28T21:17:03Z","title_canon_sha256":"bc15b044877833679116a081550a2d0141f21092c982921817c3bc32777a8af3"},"schema_version":"1.0","source":{"id":"2505.22875","kind":"arxiv","version":1}},"canonical_sha256":"da7553a65a5d762b73c91ff0495baeb1443961397e5087be72f27f8786960464","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da7553a65a5d762b73c91ff0495baeb1443961397e5087be72f27f8786960464","first_computed_at":"2026-07-05T11:11:51.297923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:51.297923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KBr7RGTElZcrMBliom06gZv/7K7IPFNHJvZ9DzSogjuVNFRBsC/v0wSxrpvSL/ur/GzdfbL+LEgYRQsL+yhfCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:51.298424Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.22875","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f2335746f89586d1597f542a85c4431cce3976463bdc9883e541db65439d777","sha256:e564e7f9b7a3177d0515a547aa6a696285657ffd3683523f05f76ecca9bcd285"],"state_sha256":"57720ecb45cecb4b96529d8b6b1628b70a6a90dd8b46187980947f18f9ce92eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hvqufn9JL7h8Eu6X6gAlbMw7SG6Gh08KOdQHBYkRAip6NU6KNOm5uCIdXTsWjOkR0QHYrdGEnxu06UH/IPgtCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T22:59:59.324241Z","bundle_sha256":"8ce3c49f2071302cb845690d952defdd7c654eac1495a15e05a2c534f6a0c669"}}