{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:DDPQETX2MU56TDMGKFNXWCIVQO","short_pith_number":"pith:DDPQETX2","schema_version":"1.0","canonical_sha256":"18df024efa653be98d86515b7b091583b2f430681bac688d38d5c3ed640e2432","source":{"kind":"arxiv","id":"2507.02720","version":1},"attestation_state":"computed","paper":{"title":"On Some New Congruences For Biregular Overpartitions","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anakha V","submitted_at":"2025-07-03T15:35:22Z","abstract_excerpt":"Inspired by the recent work by Nadji, Ahmia and Ram\\'irez, we examined the arithmetic properties of $\\bar{B}_{l_1,l_2} (n)$, the number of overpartitions of n whose parts are neither divisible by $l_1$ nor divisible by $l_2$. In particular, we establish some congruences modulo k in {4, 8, 6, 12} satisfied by $\\bar{B}_{l_1,l_2} (n)$ where $l_1$ and $l_2$ take values as arbitrary powers of 2 and 3. Moreover, we extend certain results proved in [26] and [15] for $l_1$ and $l_2$ with random powers of 2 and 3. Generating functions, dissection formulas, and theta functions are used to prove our main"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.02720","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NT","submitted_at":"2025-07-03T15:35:22Z","cross_cats_sorted":[],"title_canon_sha256":"6f69bc43811691b5694b2098cdb3ef955d3d2a1c4ab30a0124e4bf2bd65c2346","abstract_canon_sha256":"dacffeafe19598c86c9fe06b3d9be0ba026fd5efc55f297574509d1c02fa2412"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:31:33.682100Z","signature_b64":"hwT23hahjkZ245GX/aTHY6MnTdowG5PCO03VWfC4IPsh8D0KKtHAwBzxLBPF8MVGxjdEUo4wOtJuxdhnXLR2BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18df024efa653be98d86515b7b091583b2f430681bac688d38d5c3ed640e2432","last_reissued_at":"2026-07-05T11:31:33.681708Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:31:33.681708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Some New Congruences For Biregular Overpartitions","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anakha V","submitted_at":"2025-07-03T15:35:22Z","abstract_excerpt":"Inspired by the recent work by Nadji, Ahmia and Ram\\'irez, we examined the arithmetic properties of $\\bar{B}_{l_1,l_2} (n)$, the number of overpartitions of n whose parts are neither divisible by $l_1$ nor divisible by $l_2$. In particular, we establish some congruences modulo k in {4, 8, 6, 12} satisfied by $\\bar{B}_{l_1,l_2} (n)$ where $l_1$ and $l_2$ take values as arbitrary powers of 2 and 3. Moreover, we extend certain results proved in [26] and [15] for $l_1$ and $l_2$ with random powers of 2 and 3. Generating functions, dissection formulas, and theta functions are used to prove our main"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.02720","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/2507.02720/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2507.02720","created_at":"2026-07-05T11:31:33.681764+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.02720v1","created_at":"2026-07-05T11:31:33.681764+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.02720","created_at":"2026-07-05T11:31:33.681764+00:00"},{"alias_kind":"pith_short_12","alias_value":"DDPQETX2MU56","created_at":"2026-07-05T11:31:33.681764+00:00"},{"alias_kind":"pith_short_16","alias_value":"DDPQETX2MU56TDMG","created_at":"2026-07-05T11:31:33.681764+00:00"},{"alias_kind":"pith_short_8","alias_value":"DDPQETX2","created_at":"2026-07-05T11:31:33.681764+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DDPQETX2MU56TDMGKFNXWCIVQO","json":"https://pith.science/pith/DDPQETX2MU56TDMGKFNXWCIVQO.json","graph_json":"https://pith.science/api/pith-number/DDPQETX2MU56TDMGKFNXWCIVQO/graph.json","events_json":"https://pith.science/api/pith-number/DDPQETX2MU56TDMGKFNXWCIVQO/events.json","paper":"https://pith.science/paper/DDPQETX2"},"agent_actions":{"view_html":"https://pith.science/pith/DDPQETX2MU56TDMGKFNXWCIVQO","download_json":"https://pith.science/pith/DDPQETX2MU56TDMGKFNXWCIVQO.json","view_paper":"https://pith.science/paper/DDPQETX2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.02720&json=true","fetch_graph":"https://pith.science/api/pith-number/DDPQETX2MU56TDMGKFNXWCIVQO/graph.json","fetch_events":"https://pith.science/api/pith-number/DDPQETX2MU56TDMGKFNXWCIVQO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DDPQETX2MU56TDMGKFNXWCIVQO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DDPQETX2MU56TDMGKFNXWCIVQO/action/storage_attestation","attest_author":"https://pith.science/pith/DDPQETX2MU56TDMGKFNXWCIVQO/action/author_attestation","sign_citation":"https://pith.science/pith/DDPQETX2MU56TDMGKFNXWCIVQO/action/citation_signature","submit_replication":"https://pith.science/pith/DDPQETX2MU56TDMGKFNXWCIVQO/action/replication_record"}},"created_at":"2026-07-05T11:31:33.681764+00:00","updated_at":"2026-07-05T11:31:33.681764+00:00"}