{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:AICUHZAKWZHPYC6XYNSJ3LGGIB","short_pith_number":"pith:AICUHZAK","canonical_record":{"source":{"id":"1906.03059","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2019-05-31T12:53:47Z","cross_cats_sorted":[],"title_canon_sha256":"93505a9f4d7e2681248af50827ba174e88a8254ddbb8e0bcfd92b30cb0bfb401","abstract_canon_sha256":"68866157c6159f057095c551dd97e0555478a444157a2f6257abf29f4f735ba8"},"schema_version":"1.0"},"canonical_sha256":"020543e40ab64efc0bd7c3649dacc64047f9c6af421172f6d7df348bbe1eeaa9","source":{"kind":"arxiv","id":"1906.03059","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.03059","created_at":"2026-05-17T23:43:55Z"},{"alias_kind":"arxiv_version","alias_value":"1906.03059v1","created_at":"2026-05-17T23:43:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.03059","created_at":"2026-05-17T23:43:55Z"},{"alias_kind":"pith_short_12","alias_value":"AICUHZAKWZHP","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"AICUHZAKWZHPYC6X","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"AICUHZAK","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:AICUHZAKWZHPYC6XYNSJ3LGGIB","target":"record","payload":{"canonical_record":{"source":{"id":"1906.03059","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2019-05-31T12:53:47Z","cross_cats_sorted":[],"title_canon_sha256":"93505a9f4d7e2681248af50827ba174e88a8254ddbb8e0bcfd92b30cb0bfb401","abstract_canon_sha256":"68866157c6159f057095c551dd97e0555478a444157a2f6257abf29f4f735ba8"},"schema_version":"1.0"},"canonical_sha256":"020543e40ab64efc0bd7c3649dacc64047f9c6af421172f6d7df348bbe1eeaa9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:55.200343Z","signature_b64":"VoMtzAFkvGNufXPiUCBSLS9pSY03CrxlwanchpU8QiaFmtzna+uS7MadyIFnxq+8q9pUOFBkhJ+Cp0cweIQLCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"020543e40ab64efc0bd7c3649dacc64047f9c6af421172f6d7df348bbe1eeaa9","last_reissued_at":"2026-05-17T23:43:55.199685Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:55.199685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.03059","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":"2026-05-17T23:43:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gupNxVhw6zgiqoHOz9HPDyZZZ4j2huQQ9VSnhl+SZb6tno+xYvOhwSx/4R1lSHvzuHmu2x8WVtzcMJ4auA2QBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T18:40:40.315926Z"},"content_sha256":"cf21642bf6559e6adf9b757199f90743e73b5eb22254559b294e6bd5657c1697","schema_version":"1.0","event_id":"sha256:cf21642bf6559e6adf9b757199f90743e73b5eb22254559b294e6bd5657c1697"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:AICUHZAKWZHPYC6XYNSJ3LGGIB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"R(p,q)-deformed combinatorics: full characterization and illustration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Fridolin Melong, Mahouton Norbert Hounkonnou","submitted_at":"2019-05-31T12:53:47Z","abstract_excerpt":"This paper addresses a theory of R(p,q)-deformed combinatorics in discrete probability. It mainly focuses on R(p,q)-deformed factorials, binomial coefficients, Vandermonde's formula, Cauchy's formula, binomial and negative binomial formulae, factorial and binomial moments, and Stirling numbers. Moreover, the R(p,q)-Stirling numbers of the second kind and the R(p,q)-Bell numbers for graphs are also derived. Related relevant properties are investigated and discussed. Finally, as a concrete illustration, the developed formalism is displayed for the well known generalized q-Quesne deformed quantum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03059","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":""},"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":"2026-05-17T23:43:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uOqjoRdMGcA1RdYr+dNskFXCrldbD5nw/JsDt+v5tsKeLOX77lTeZ+9WFG2AErJLZLryOmUraW/nj7jJVrIrDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T18:40:40.316280Z"},"content_sha256":"0e6efa19c9552f76f22bb1d000bf2ba6bd56de1ce9029a1fb7d5c0450441b08f","schema_version":"1.0","event_id":"sha256:0e6efa19c9552f76f22bb1d000bf2ba6bd56de1ce9029a1fb7d5c0450441b08f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AICUHZAKWZHPYC6XYNSJ3LGGIB/bundle.json","state_url":"https://pith.science/pith/AICUHZAKWZHPYC6XYNSJ3LGGIB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AICUHZAKWZHPYC6XYNSJ3LGGIB/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":"2026-06-20T18:40:40Z","links":{"resolver":"https://pith.science/pith/AICUHZAKWZHPYC6XYNSJ3LGGIB","bundle":"https://pith.science/pith/AICUHZAKWZHPYC6XYNSJ3LGGIB/bundle.json","state":"https://pith.science/pith/AICUHZAKWZHPYC6XYNSJ3LGGIB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AICUHZAKWZHPYC6XYNSJ3LGGIB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:AICUHZAKWZHPYC6XYNSJ3LGGIB","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":"68866157c6159f057095c551dd97e0555478a444157a2f6257abf29f4f735ba8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2019-05-31T12:53:47Z","title_canon_sha256":"93505a9f4d7e2681248af50827ba174e88a8254ddbb8e0bcfd92b30cb0bfb401"},"schema_version":"1.0","source":{"id":"1906.03059","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.03059","created_at":"2026-05-17T23:43:55Z"},{"alias_kind":"arxiv_version","alias_value":"1906.03059v1","created_at":"2026-05-17T23:43:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.03059","created_at":"2026-05-17T23:43:55Z"},{"alias_kind":"pith_short_12","alias_value":"AICUHZAKWZHP","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"AICUHZAKWZHPYC6X","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"AICUHZAK","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:0e6efa19c9552f76f22bb1d000bf2ba6bd56de1ce9029a1fb7d5c0450441b08f","target":"graph","created_at":"2026-05-17T23:43:55Z","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":"This paper addresses a theory of R(p,q)-deformed combinatorics in discrete probability. It mainly focuses on R(p,q)-deformed factorials, binomial coefficients, Vandermonde's formula, Cauchy's formula, binomial and negative binomial formulae, factorial and binomial moments, and Stirling numbers. Moreover, the R(p,q)-Stirling numbers of the second kind and the R(p,q)-Bell numbers for graphs are also derived. Related relevant properties are investigated and discussed. Finally, as a concrete illustration, the developed formalism is displayed for the well known generalized q-Quesne deformed quantum","authors_text":"Fridolin Melong, Mahouton Norbert Hounkonnou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2019-05-31T12:53:47Z","title":"R(p,q)-deformed combinatorics: full characterization and illustration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03059","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:cf21642bf6559e6adf9b757199f90743e73b5eb22254559b294e6bd5657c1697","target":"record","created_at":"2026-05-17T23:43:55Z","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":"68866157c6159f057095c551dd97e0555478a444157a2f6257abf29f4f735ba8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2019-05-31T12:53:47Z","title_canon_sha256":"93505a9f4d7e2681248af50827ba174e88a8254ddbb8e0bcfd92b30cb0bfb401"},"schema_version":"1.0","source":{"id":"1906.03059","kind":"arxiv","version":1}},"canonical_sha256":"020543e40ab64efc0bd7c3649dacc64047f9c6af421172f6d7df348bbe1eeaa9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"020543e40ab64efc0bd7c3649dacc64047f9c6af421172f6d7df348bbe1eeaa9","first_computed_at":"2026-05-17T23:43:55.199685Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:55.199685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VoMtzAFkvGNufXPiUCBSLS9pSY03CrxlwanchpU8QiaFmtzna+uS7MadyIFnxq+8q9pUOFBkhJ+Cp0cweIQLCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:55.200343Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.03059","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf21642bf6559e6adf9b757199f90743e73b5eb22254559b294e6bd5657c1697","sha256:0e6efa19c9552f76f22bb1d000bf2ba6bd56de1ce9029a1fb7d5c0450441b08f"],"state_sha256":"4585a74a343b58cbf14a11d7acb1406c969974c942a4f83f7f40463871faacbf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4GwF40bXL/c458wBd6reJQjplSKMMIe76ZXStMWLumeQoysMCUE8kX6rpCTmnKBstPJDqMHvha51iBy/Jy48AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T18:40:40.318256Z","bundle_sha256":"d2df87e2484a4954a2a0230ee9650671e3f8374fe047d21a73c56ce797c69d37"}}