{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XHSV2V5XTD4YAGKMUMUNU7JF6M","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":"74225bb46b4ef3c43342155e679d31eea4ce49f2a51891b0f6f48ae97333f5f5","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-01T07:53:41Z","title_canon_sha256":"7f2bd4a7f1e1629a317378b8683a04de29cefce1a16ee3aa97d2260371d223ab"},"schema_version":"1.0","source":{"id":"1705.00438","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00438","created_at":"2026-05-18T00:45:05Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00438v2","created_at":"2026-05-18T00:45:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00438","created_at":"2026-05-18T00:45:05Z"},{"alias_kind":"pith_short_12","alias_value":"XHSV2V5XTD4Y","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"XHSV2V5XTD4YAGKM","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"XHSV2V5X","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:52490ec9cd15077bd00f43c4aad053cd9f11d82c6ea382a5b6a47cdb0bea685e","target":"graph","created_at":"2026-05-18T00:45:05Z","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":"It is derived the explicit asymptotic expression in $n$ for the coefficient $c_n$ of the generating function for multiplicative structures with sub exponential rate of growth of $c_n,$ as $n\\to\\infty$.","authors_text":"Boris Granovsky","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-01T07:53:41Z","title":"Explicit asymptotic formulae for sub exponentially growing multiplicative structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00438","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:d6ca23060264c2f4e2e61189654f57fcf6713a0886a0557c430e7c84d9593178","target":"record","created_at":"2026-05-18T00:45:05Z","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":"74225bb46b4ef3c43342155e679d31eea4ce49f2a51891b0f6f48ae97333f5f5","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-01T07:53:41Z","title_canon_sha256":"7f2bd4a7f1e1629a317378b8683a04de29cefce1a16ee3aa97d2260371d223ab"},"schema_version":"1.0","source":{"id":"1705.00438","kind":"arxiv","version":2}},"canonical_sha256":"b9e55d57b798f980194ca328da7d25f326ac028b491e615d46ac88c84d1af2b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9e55d57b798f980194ca328da7d25f326ac028b491e615d46ac88c84d1af2b6","first_computed_at":"2026-05-18T00:45:05.946538Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:05.946538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y0ElFVviHyHkuMSdnLf3x9uRfo80fxr0XzokdSUTkzBAUEq4hOfVcroB2cuR07WWpmtSe/xGWSVTLdRgqY8iCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:05.947100Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.00438","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6ca23060264c2f4e2e61189654f57fcf6713a0886a0557c430e7c84d9593178","sha256:52490ec9cd15077bd00f43c4aad053cd9f11d82c6ea382a5b6a47cdb0bea685e"],"state_sha256":"54e78d14ad3bc764fab20100fb4345e8e8d4f8fe6cf6314a15690fbab672a4aa"}