{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NOAU3OVGDYT4AQ44XPBXLIKIA4","short_pith_number":"pith:NOAU3OVG","canonical_record":{"source":{"id":"1806.03736","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-10T22:24:16Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"e593c37874ce8adedc3060720e75259f5b4a37b485818523f2b4ddacf27d2e5a","abstract_canon_sha256":"dc3226500b726c80501a1a7847d9b94e3901e6e3d5b117f3c2ee0f6c0c82f1cf"},"schema_version":"1.0"},"canonical_sha256":"6b814dbaa61e27c0439cbbc375a148073161ee9c3c9e458d776003ccc6372cb4","source":{"kind":"arxiv","id":"1806.03736","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03736","created_at":"2026-07-05T01:50:14Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03736v4","created_at":"2026-07-05T01:50:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03736","created_at":"2026-07-05T01:50:14Z"},{"alias_kind":"pith_short_12","alias_value":"NOAU3OVGDYT4","created_at":"2026-07-05T01:50:14Z"},{"alias_kind":"pith_short_16","alias_value":"NOAU3OVGDYT4AQ44","created_at":"2026-07-05T01:50:14Z"},{"alias_kind":"pith_short_8","alias_value":"NOAU3OVG","created_at":"2026-07-05T01:50:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NOAU3OVGDYT4AQ44XPBXLIKIA4","target":"record","payload":{"canonical_record":{"source":{"id":"1806.03736","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-10T22:24:16Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"e593c37874ce8adedc3060720e75259f5b4a37b485818523f2b4ddacf27d2e5a","abstract_canon_sha256":"dc3226500b726c80501a1a7847d9b94e3901e6e3d5b117f3c2ee0f6c0c82f1cf"},"schema_version":"1.0"},"canonical_sha256":"6b814dbaa61e27c0439cbbc375a148073161ee9c3c9e458d776003ccc6372cb4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:50:14.140818Z","signature_b64":"1Hh3rnznfH27j+TfkIqgj0TLiaRNPyb5ZONfQSBWkmJaiCnKyDvX+dwhr8MjD86KSZFu8Bb5b9u6NKR/tzIxCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b814dbaa61e27c0439cbbc375a148073161ee9c3c9e458d776003ccc6372cb4","last_reissued_at":"2026-07-05T01:50:14.140478Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:50:14.140478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.03736","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:50:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wMz/rbl0UkRVGO12PqEAcXZmlDzdjQh6qAfupTaTBzuJ1fX92W/61TaDzsMLm+8vFEElbO+9DRF2bcXTj1B/DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T18:32:37.579952Z"},"content_sha256":"c41302ea27d8241d5d7f7dc517a14ea0c0527ed92f45c73ab7e31f637f1abe7a","schema_version":"1.0","event_id":"sha256:c41302ea27d8241d5d7f7dc517a14ea0c0527ed92f45c73ab7e31f637f1abe7a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NOAU3OVGDYT4AQ44XPBXLIKIA4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The distribution of sandpile groups of random regular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Andr\\'as M\\'esz\\'aros","submitted_at":"2018-06-10T22:24:16Z","abstract_excerpt":"We study the distribution of the sandpile group of random d-regular graphs. For the directed model, we prove that it follows the Cohen-Lenstra heuristics, that is, the limiting probability that the $p$-Sylow subgroup of the sandpile group is a given $p$-group $P$, is proportional to $|Aut(P)|^{-1}$. For finitely many primes, these events get independent in the limit. Similar results hold for undirected random regular graphs, where for odd primes the limiting distributions are the ones given by Clancy, Leake and Payne.\n  This answers an open question of Frieze and Vu whether the adjacency matri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03736","kind":"arxiv","version":4},"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/1806.03736/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":"2026-07-05T01:50:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D06W2+5KSdTRhk+OOYbWWzC4WvuWLfCCbz0aUQ0kthkv546EQgZxpLdSytRMi58r6yF86sgTKsoean44QLpEDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T18:32:37.580600Z"},"content_sha256":"b2b687f9899b55da982848b9728e13b76652d883a422b19f38de0c2c0b8aa29a","schema_version":"1.0","event_id":"sha256:b2b687f9899b55da982848b9728e13b76652d883a422b19f38de0c2c0b8aa29a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NOAU3OVGDYT4AQ44XPBXLIKIA4/bundle.json","state_url":"https://pith.science/pith/NOAU3OVGDYT4AQ44XPBXLIKIA4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NOAU3OVGDYT4AQ44XPBXLIKIA4/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":"2026-08-17T18:32:37Z","links":{"resolver":"https://pith.science/pith/NOAU3OVGDYT4AQ44XPBXLIKIA4","bundle":"https://pith.science/pith/NOAU3OVGDYT4AQ44XPBXLIKIA4/bundle.json","state":"https://pith.science/pith/NOAU3OVGDYT4AQ44XPBXLIKIA4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NOAU3OVGDYT4AQ44XPBXLIKIA4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NOAU3OVGDYT4AQ44XPBXLIKIA4","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":"dc3226500b726c80501a1a7847d9b94e3901e6e3d5b117f3c2ee0f6c0c82f1cf","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-10T22:24:16Z","title_canon_sha256":"e593c37874ce8adedc3060720e75259f5b4a37b485818523f2b4ddacf27d2e5a"},"schema_version":"1.0","source":{"id":"1806.03736","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03736","created_at":"2026-07-05T01:50:14Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03736v4","created_at":"2026-07-05T01:50:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03736","created_at":"2026-07-05T01:50:14Z"},{"alias_kind":"pith_short_12","alias_value":"NOAU3OVGDYT4","created_at":"2026-07-05T01:50:14Z"},{"alias_kind":"pith_short_16","alias_value":"NOAU3OVGDYT4AQ44","created_at":"2026-07-05T01:50:14Z"},{"alias_kind":"pith_short_8","alias_value":"NOAU3OVG","created_at":"2026-07-05T01:50:14Z"}],"graph_snapshots":[{"event_id":"sha256:b2b687f9899b55da982848b9728e13b76652d883a422b19f38de0c2c0b8aa29a","target":"graph","created_at":"2026-07-05T01:50:14Z","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/1806.03736/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the distribution of the sandpile group of random d-regular graphs. For the directed model, we prove that it follows the Cohen-Lenstra heuristics, that is, the limiting probability that the $p$-Sylow subgroup of the sandpile group is a given $p$-group $P$, is proportional to $|Aut(P)|^{-1}$. For finitely many primes, these events get independent in the limit. Similar results hold for undirected random regular graphs, where for odd primes the limiting distributions are the ones given by Clancy, Leake and Payne.\n  This answers an open question of Frieze and Vu whether the adjacency matri","authors_text":"Andr\\'as M\\'esz\\'aros","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-10T22:24:16Z","title":"The distribution of sandpile groups of random regular graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03736","kind":"arxiv","version":4},"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:c41302ea27d8241d5d7f7dc517a14ea0c0527ed92f45c73ab7e31f637f1abe7a","target":"record","created_at":"2026-07-05T01:50:14Z","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":"dc3226500b726c80501a1a7847d9b94e3901e6e3d5b117f3c2ee0f6c0c82f1cf","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-10T22:24:16Z","title_canon_sha256":"e593c37874ce8adedc3060720e75259f5b4a37b485818523f2b4ddacf27d2e5a"},"schema_version":"1.0","source":{"id":"1806.03736","kind":"arxiv","version":4}},"canonical_sha256":"6b814dbaa61e27c0439cbbc375a148073161ee9c3c9e458d776003ccc6372cb4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b814dbaa61e27c0439cbbc375a148073161ee9c3c9e458d776003ccc6372cb4","first_computed_at":"2026-07-05T01:50:14.140478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:50:14.140478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Hh3rnznfH27j+TfkIqgj0TLiaRNPyb5ZONfQSBWkmJaiCnKyDvX+dwhr8MjD86KSZFu8Bb5b9u6NKR/tzIxCA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:50:14.140818Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.03736","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c41302ea27d8241d5d7f7dc517a14ea0c0527ed92f45c73ab7e31f637f1abe7a","sha256:b2b687f9899b55da982848b9728e13b76652d883a422b19f38de0c2c0b8aa29a"],"state_sha256":"421e3d7c44936999096eebd82ec1e9b8f88bed0add0c78bda111d713ae64ddcf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tyFBKhse71kZdDy8sHJdF8SbRs3QeSixCWkkxQ5ASEm3AIMmo82jHmCiXD/DBA+/ugft5eVGxtghz7f5DSq+DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T18:32:37.584214Z","bundle_sha256":"858c2223fbadb9c34a8fe588ae92f61d36191cc87475322e6ee21e7c90e6324e"}}