{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:5CMRYB7Q43PDNMELABAG5RQIIM","short_pith_number":"pith:5CMRYB7Q","canonical_record":{"source":{"id":"2501.15869","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-01-27T08:44:48Z","cross_cats_sorted":["math.CO","math.PR"],"title_canon_sha256":"204aca94fb55ec15a1756edd65badaafd793ded7168fe4666a44e24209b24ee7","abstract_canon_sha256":"ba05082d3269a4d3f6c04b75fc710d6bfaef9473183edae12c4734fbc12a9a27"},"schema_version":"1.0"},"canonical_sha256":"e8991c07f0e6de36b08b00406ec60843009110f534483259d2d2c106ba30fd26","source":{"kind":"arxiv","id":"2501.15869","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.15869","created_at":"2026-07-05T11:40:51Z"},{"alias_kind":"arxiv_version","alias_value":"2501.15869v2","created_at":"2026-07-05T11:40:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.15869","created_at":"2026-07-05T11:40:51Z"},{"alias_kind":"pith_short_12","alias_value":"5CMRYB7Q43PD","created_at":"2026-07-05T11:40:51Z"},{"alias_kind":"pith_short_16","alias_value":"5CMRYB7Q43PDNMEL","created_at":"2026-07-05T11:40:51Z"},{"alias_kind":"pith_short_8","alias_value":"5CMRYB7Q","created_at":"2026-07-05T11:40:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:5CMRYB7Q43PDNMELABAG5RQIIM","target":"record","payload":{"canonical_record":{"source":{"id":"2501.15869","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-01-27T08:44:48Z","cross_cats_sorted":["math.CO","math.PR"],"title_canon_sha256":"204aca94fb55ec15a1756edd65badaafd793ded7168fe4666a44e24209b24ee7","abstract_canon_sha256":"ba05082d3269a4d3f6c04b75fc710d6bfaef9473183edae12c4734fbc12a9a27"},"schema_version":"1.0"},"canonical_sha256":"e8991c07f0e6de36b08b00406ec60843009110f534483259d2d2c106ba30fd26","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:40:51.939463Z","signature_b64":"3A/LnIrwr8hgA71qavHZN4gnbZh36ormUfqZzX+rHw5TZkeZBabDPl50sF+Eg+s8NbqiIYvcJvlIHOe+jeYxAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8991c07f0e6de36b08b00406ec60843009110f534483259d2d2c106ba30fd26","last_reissued_at":"2026-07-05T11:40:51.938985Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:40:51.938985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.15869","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:40:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eceSr3Hopcl5B7vBhD9BcBdfp3S7iF97RghmJ07kP8PTQGt8TlIAs+bQizbq1RxoZCyvMiho/lYRt5i3J3PmAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T15:37:00.626725Z"},"content_sha256":"f55ff4e0a72a7b87c2267cdcbc84785566e213b732400420c098442daeb5775f","schema_version":"1.0","event_id":"sha256:f55ff4e0a72a7b87c2267cdcbc84785566e213b732400420c098442daeb5775f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:5CMRYB7Q43PDNMELABAG5RQIIM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A divisor generating $q$-series and cumulants arising from random graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"math.NT","authors_text":"Archit Agarwal, Bibekananda Maji, Pramod Eyyunni, Subhash Chand Bhoria, Tanay Wakhare","submitted_at":"2025-01-27T08:44:48Z","abstract_excerpt":"Uchimura, in 1987, introduced a probability generating function for a random variable $X$ and using properties of this function he discovered an interesting $q$-series identity. He further showed that the $m$-th cumulant with respect to the random variable $X$ is nothing but the generating function for the generalized divisor function $\\sigma_{m-1}(n)$. Simon, Crippa, and Collenberg, in 1993, explored the $G_{n,p}$-model of a random acyclic digraph and defined a random variable $\\gamma_n^{*}(1)$. Quite interestingly, they found links between limit of its mean and the generating function for th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.15869","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.15869/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":"2026-07-05T11:40:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m+iUB0Q0foXOg/YxPlRBA3PVj45zhm4nHM+JCxrCjUAEkUBXH2kh5+3SjnK1JpKbzx0lalGSEtqNO8fcQ0oDBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T15:37:00.627287Z"},"content_sha256":"79b00bb0e9eb5b73291f8958b330ef3b7094b7a54ce9a17b9771d8239ccf62cb","schema_version":"1.0","event_id":"sha256:79b00bb0e9eb5b73291f8958b330ef3b7094b7a54ce9a17b9771d8239ccf62cb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5CMRYB7Q43PDNMELABAG5RQIIM/bundle.json","state_url":"https://pith.science/pith/5CMRYB7Q43PDNMELABAG5RQIIM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5CMRYB7Q43PDNMELABAG5RQIIM/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":"2026-08-03T15:37:00Z","links":{"resolver":"https://pith.science/pith/5CMRYB7Q43PDNMELABAG5RQIIM","bundle":"https://pith.science/pith/5CMRYB7Q43PDNMELABAG5RQIIM/bundle.json","state":"https://pith.science/pith/5CMRYB7Q43PDNMELABAG5RQIIM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5CMRYB7Q43PDNMELABAG5RQIIM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:5CMRYB7Q43PDNMELABAG5RQIIM","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":"ba05082d3269a4d3f6c04b75fc710d6bfaef9473183edae12c4734fbc12a9a27","cross_cats_sorted":["math.CO","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-01-27T08:44:48Z","title_canon_sha256":"204aca94fb55ec15a1756edd65badaafd793ded7168fe4666a44e24209b24ee7"},"schema_version":"1.0","source":{"id":"2501.15869","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.15869","created_at":"2026-07-05T11:40:51Z"},{"alias_kind":"arxiv_version","alias_value":"2501.15869v2","created_at":"2026-07-05T11:40:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.15869","created_at":"2026-07-05T11:40:51Z"},{"alias_kind":"pith_short_12","alias_value":"5CMRYB7Q43PD","created_at":"2026-07-05T11:40:51Z"},{"alias_kind":"pith_short_16","alias_value":"5CMRYB7Q43PDNMEL","created_at":"2026-07-05T11:40:51Z"},{"alias_kind":"pith_short_8","alias_value":"5CMRYB7Q","created_at":"2026-07-05T11:40:51Z"}],"graph_snapshots":[{"event_id":"sha256:79b00bb0e9eb5b73291f8958b330ef3b7094b7a54ce9a17b9771d8239ccf62cb","target":"graph","created_at":"2026-07-05T11:40:51Z","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/2501.15869/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Uchimura, in 1987, introduced a probability generating function for a random variable $X$ and using properties of this function he discovered an interesting $q$-series identity. He further showed that the $m$-th cumulant with respect to the random variable $X$ is nothing but the generating function for the generalized divisor function $\\sigma_{m-1}(n)$. Simon, Crippa, and Collenberg, in 1993, explored the $G_{n,p}$-model of a random acyclic digraph and defined a random variable $\\gamma_n^{*}(1)$. Quite interestingly, they found links between limit of its mean and the generating function for th","authors_text":"Archit Agarwal, Bibekananda Maji, Pramod Eyyunni, Subhash Chand Bhoria, Tanay Wakhare","cross_cats":["math.CO","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-01-27T08:44:48Z","title":"A divisor generating $q$-series and cumulants arising from random graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.15869","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:f55ff4e0a72a7b87c2267cdcbc84785566e213b732400420c098442daeb5775f","target":"record","created_at":"2026-07-05T11:40:51Z","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":"ba05082d3269a4d3f6c04b75fc710d6bfaef9473183edae12c4734fbc12a9a27","cross_cats_sorted":["math.CO","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-01-27T08:44:48Z","title_canon_sha256":"204aca94fb55ec15a1756edd65badaafd793ded7168fe4666a44e24209b24ee7"},"schema_version":"1.0","source":{"id":"2501.15869","kind":"arxiv","version":2}},"canonical_sha256":"e8991c07f0e6de36b08b00406ec60843009110f534483259d2d2c106ba30fd26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8991c07f0e6de36b08b00406ec60843009110f534483259d2d2c106ba30fd26","first_computed_at":"2026-07-05T11:40:51.938985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:40:51.938985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3A/LnIrwr8hgA71qavHZN4gnbZh36ormUfqZzX+rHw5TZkeZBabDPl50sF+Eg+s8NbqiIYvcJvlIHOe+jeYxAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:40:51.939463Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.15869","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f55ff4e0a72a7b87c2267cdcbc84785566e213b732400420c098442daeb5775f","sha256:79b00bb0e9eb5b73291f8958b330ef3b7094b7a54ce9a17b9771d8239ccf62cb"],"state_sha256":"21aa3d5cb964910e3770f61a541a4c5785ebac008b639491303f4b6064964ffc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PR2BGnwvuNmlwNk5doIEXgIVbEHoFpA83IoyOdiCcvzDY3clhJL8/FFwlS9EnYygEMrSTrwzcsltT60+j0ECBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T15:37:00.631022Z","bundle_sha256":"8b8fb24c6ed45f21191d760c094dbce96a876333d3f27ad60541a89676c8a0ce"}}