{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:F4PTPPAZPLX5NJB4GR35D23KQZ","short_pith_number":"pith:F4PTPPAZ","canonical_record":{"source":{"id":"2210.03457","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-10-07T10:59:08Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"beb2e9e717f6a904d9a34bafee2fb033bad1cade5b8dbadd4e2d1816fdefddf3","abstract_canon_sha256":"35fc9cf368e9e7aafa99c97c8094c9bfa788bc44aac1ccb69953e071603e2a48"},"schema_version":"1.0"},"canonical_sha256":"2f1f37bc197aefd6a43c3477d1eb6a8664ef230643fd148a5fa4b11e89103f5d","source":{"kind":"arxiv","id":"2210.03457","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.03457","created_at":"2026-07-05T05:04:20Z"},{"alias_kind":"arxiv_version","alias_value":"2210.03457v1","created_at":"2026-07-05T05:04:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.03457","created_at":"2026-07-05T05:04:20Z"},{"alias_kind":"pith_short_12","alias_value":"F4PTPPAZPLX5","created_at":"2026-07-05T05:04:20Z"},{"alias_kind":"pith_short_16","alias_value":"F4PTPPAZPLX5NJB4","created_at":"2026-07-05T05:04:20Z"},{"alias_kind":"pith_short_8","alias_value":"F4PTPPAZ","created_at":"2026-07-05T05:04:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:F4PTPPAZPLX5NJB4GR35D23KQZ","target":"record","payload":{"canonical_record":{"source":{"id":"2210.03457","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-10-07T10:59:08Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"beb2e9e717f6a904d9a34bafee2fb033bad1cade5b8dbadd4e2d1816fdefddf3","abstract_canon_sha256":"35fc9cf368e9e7aafa99c97c8094c9bfa788bc44aac1ccb69953e071603e2a48"},"schema_version":"1.0"},"canonical_sha256":"2f1f37bc197aefd6a43c3477d1eb6a8664ef230643fd148a5fa4b11e89103f5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:04:20.426969Z","signature_b64":"f3luTWAGheBtUIAZ12/UadqR4abUepLfrmvjirdfTAJA0tX2Cx43YLSDgm5BN/mxDbRjT6CTQffyeBorn0S6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f1f37bc197aefd6a43c3477d1eb6a8664ef230643fd148a5fa4b11e89103f5d","last_reissued_at":"2026-07-05T05:04:20.426585Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:04:20.426585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2210.03457","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":"2026-07-05T05:04:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P1V2INfdUvQv3f7xLVg+425xtOfLkdgtApMjcbVK4FVBJE6E3P9EVu7tCxPprOUGz81MDR16aOYzomEAK1b6Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T15:56:43.905467Z"},"content_sha256":"d32b44c8d3f8fd7124c921ee5a4afe6a0f384d3a8072884f1bd1c0ee8eac2e5e","schema_version":"1.0","event_id":"sha256:d32b44c8d3f8fd7124c921ee5a4afe6a0f384d3a8072884f1bd1c0ee8eac2e5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:F4PTPPAZPLX5NJB4GR35D23KQZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bressoud-Subbarao type weighted partition identities for a generalized divisor function","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Archit Agarwal, Bibekananda Maji, Pramod Eyyunni, Subhash Chand Bhoria","submitted_at":"2022-10-07T10:59:08Z","abstract_excerpt":"In 1984, Bressoud and Subbarao obtained an interesting weighted partition identity for a generalized divisor function, by means of combinatorial arguments. Recently, the last three named authors found an analytic proof of the aforementioned identity of Bressoud and Subbarao starting from a $q$-series identity of Ramanujan. In the present paper, we revisit the combinatorial arguments of Bressoud and Subbarao, and derive a more general weighted partition identity. Furthermore, with the help of a fractional differential operator, we establish a few more Bressoud-Subbarao type weighted partition i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.03457","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/2210.03457/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":"2026-07-05T05:04:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jlc2ekgeJFLrl/uVfx/GR53WxgbLKhMbDOSzz7hN2s/FzB9fPiF5l+1f8iQJ+JShFIWxq1pMHYzg4bVUgWhrBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T15:56:43.905836Z"},"content_sha256":"da3180e9cc1c88fe207a32ebb80297c46e220dce5bee1e93282fea1047e278ba","schema_version":"1.0","event_id":"sha256:da3180e9cc1c88fe207a32ebb80297c46e220dce5bee1e93282fea1047e278ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F4PTPPAZPLX5NJB4GR35D23KQZ/bundle.json","state_url":"https://pith.science/pith/F4PTPPAZPLX5NJB4GR35D23KQZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F4PTPPAZPLX5NJB4GR35D23KQZ/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":"2026-07-08T15:56:43Z","links":{"resolver":"https://pith.science/pith/F4PTPPAZPLX5NJB4GR35D23KQZ","bundle":"https://pith.science/pith/F4PTPPAZPLX5NJB4GR35D23KQZ/bundle.json","state":"https://pith.science/pith/F4PTPPAZPLX5NJB4GR35D23KQZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F4PTPPAZPLX5NJB4GR35D23KQZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:F4PTPPAZPLX5NJB4GR35D23KQZ","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":"35fc9cf368e9e7aafa99c97c8094c9bfa788bc44aac1ccb69953e071603e2a48","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-10-07T10:59:08Z","title_canon_sha256":"beb2e9e717f6a904d9a34bafee2fb033bad1cade5b8dbadd4e2d1816fdefddf3"},"schema_version":"1.0","source":{"id":"2210.03457","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.03457","created_at":"2026-07-05T05:04:20Z"},{"alias_kind":"arxiv_version","alias_value":"2210.03457v1","created_at":"2026-07-05T05:04:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.03457","created_at":"2026-07-05T05:04:20Z"},{"alias_kind":"pith_short_12","alias_value":"F4PTPPAZPLX5","created_at":"2026-07-05T05:04:20Z"},{"alias_kind":"pith_short_16","alias_value":"F4PTPPAZPLX5NJB4","created_at":"2026-07-05T05:04:20Z"},{"alias_kind":"pith_short_8","alias_value":"F4PTPPAZ","created_at":"2026-07-05T05:04:20Z"}],"graph_snapshots":[{"event_id":"sha256:da3180e9cc1c88fe207a32ebb80297c46e220dce5bee1e93282fea1047e278ba","target":"graph","created_at":"2026-07-05T05:04:20Z","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/2210.03457/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In 1984, Bressoud and Subbarao obtained an interesting weighted partition identity for a generalized divisor function, by means of combinatorial arguments. Recently, the last three named authors found an analytic proof of the aforementioned identity of Bressoud and Subbarao starting from a $q$-series identity of Ramanujan. In the present paper, we revisit the combinatorial arguments of Bressoud and Subbarao, and derive a more general weighted partition identity. Furthermore, with the help of a fractional differential operator, we establish a few more Bressoud-Subbarao type weighted partition i","authors_text":"Archit Agarwal, Bibekananda Maji, Pramod Eyyunni, Subhash Chand Bhoria","cross_cats":["math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-10-07T10:59:08Z","title":"Bressoud-Subbarao type weighted partition identities for a generalized divisor function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.03457","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:d32b44c8d3f8fd7124c921ee5a4afe6a0f384d3a8072884f1bd1c0ee8eac2e5e","target":"record","created_at":"2026-07-05T05:04:20Z","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":"35fc9cf368e9e7aafa99c97c8094c9bfa788bc44aac1ccb69953e071603e2a48","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-10-07T10:59:08Z","title_canon_sha256":"beb2e9e717f6a904d9a34bafee2fb033bad1cade5b8dbadd4e2d1816fdefddf3"},"schema_version":"1.0","source":{"id":"2210.03457","kind":"arxiv","version":1}},"canonical_sha256":"2f1f37bc197aefd6a43c3477d1eb6a8664ef230643fd148a5fa4b11e89103f5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f1f37bc197aefd6a43c3477d1eb6a8664ef230643fd148a5fa4b11e89103f5d","first_computed_at":"2026-07-05T05:04:20.426585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:04:20.426585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f3luTWAGheBtUIAZ12/UadqR4abUepLfrmvjirdfTAJA0tX2Cx43YLSDgm5BN/mxDbRjT6CTQffyeBorn0S6Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:04:20.426969Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.03457","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d32b44c8d3f8fd7124c921ee5a4afe6a0f384d3a8072884f1bd1c0ee8eac2e5e","sha256:da3180e9cc1c88fe207a32ebb80297c46e220dce5bee1e93282fea1047e278ba"],"state_sha256":"dbfd20c89de39a1e48764874a293ee43b3369297a566dba38264b67054ea8495"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Km5yYiTIA5g98yGM7Qe4/d9xV+ecIH+NRZ4Qwkz0T7X90uj0FY3zy3cWiHqKkKP/Pe8vpOII42M7jsxAB1ltCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T15:56:43.907829Z","bundle_sha256":"1805ba8d132330df1aa930bb08a7680d616033fdb43e5a5ba3f13cb64ff2a38c"}}