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In this note, we shall prove several new congruences modulo 125 and 11 by using some results of modular forms. For example, for all $n\\ge 0$, we have \\begin{align*} f(1250n+125)&\\equiv 0 \\pmod{125},\\\\ f(1250n+1125)&\\equiv 0 \\pmod{125},\\\\ f(2750n+825)&\\equiv 0 \\pmod{11},\\\\ f(2750n+1925)&\\equiv 0 \\pmod{11}. \\end{align*}"},"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":"1506.03169","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-10T05:15:29Z","cross_cats_sorted":[],"title_canon_sha256":"1033a3a07e308f86a4a274ba90781923d8f089d43e809e4f7d141e3a5d7c8c2f","abstract_canon_sha256":"1af0a592f86ea047049fa4235f8814c6a3bb07356c4a983c2b50410fd5508217"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:44.606099Z","signature_b64":"lRFgWtE5GFnBdCxQkfcqP5dyTysPPu7MvF9aHLDKWFG2DoV6wdnU4PHWXMeWEUn0NkpFBLzcqg44cqVJl/A8Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96ca4766922a5f477978b125b96ce1161052564c4d6714aaf47a8738427a7d92","last_reissued_at":"2026-05-18T00:42:44.605561Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:44.605561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Congruences for 1-shell totally symmetric plane partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Shane Chern","submitted_at":"2015-06-10T05:15:29Z","abstract_excerpt":"Let $f(n)$ denote the number of 1-shell totally symmetric plane partitions of weight $n$. Recently, Hirschhorn and Sellers, Yao, and Xia established a number of congruences modulo 2 and 5, 4 and 8, and 25 for $f(n)$, respectively. In this note, we shall prove several new congruences modulo 125 and 11 by using some results of modular forms. For example, for all $n\\ge 0$, we have \\begin{align*} f(1250n+125)&\\equiv 0 \\pmod{125},\\\\ f(1250n+1125)&\\equiv 0 \\pmod{125},\\\\ f(2750n+825)&\\equiv 0 \\pmod{11},\\\\ f(2750n+1925)&\\equiv 0 \\pmod{11}. \\end{align*}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03169","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":""},"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":"1506.03169","created_at":"2026-05-18T00:42:44.605664+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.03169v2","created_at":"2026-05-18T00:42:44.605664+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03169","created_at":"2026-05-18T00:42:44.605664+00:00"},{"alias_kind":"pith_short_12","alias_value":"S3FEOZUSFJPU","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"S3FEOZUSFJPUO6LY","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"S3FEOZUS","created_at":"2026-05-18T12:29:39.896362+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/S3FEOZUSFJPUO6LYWES3S3HBCY","json":"https://pith.science/pith/S3FEOZUSFJPUO6LYWES3S3HBCY.json","graph_json":"https://pith.science/api/pith-number/S3FEOZUSFJPUO6LYWES3S3HBCY/graph.json","events_json":"https://pith.science/api/pith-number/S3FEOZUSFJPUO6LYWES3S3HBCY/events.json","paper":"https://pith.science/paper/S3FEOZUS"},"agent_actions":{"view_html":"https://pith.science/pith/S3FEOZUSFJPUO6LYWES3S3HBCY","download_json":"https://pith.science/pith/S3FEOZUSFJPUO6LYWES3S3HBCY.json","view_paper":"https://pith.science/paper/S3FEOZUS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.03169&json=true","fetch_graph":"https://pith.science/api/pith-number/S3FEOZUSFJPUO6LYWES3S3HBCY/graph.json","fetch_events":"https://pith.science/api/pith-number/S3FEOZUSFJPUO6LYWES3S3HBCY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S3FEOZUSFJPUO6LYWES3S3HBCY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S3FEOZUSFJPUO6LYWES3S3HBCY/action/storage_attestation","attest_author":"https://pith.science/pith/S3FEOZUSFJPUO6LYWES3S3HBCY/action/author_attestation","sign_citation":"https://pith.science/pith/S3FEOZUSFJPUO6LYWES3S3HBCY/action/citation_signature","submit_replication":"https://pith.science/pith/S3FEOZUSFJPUO6LYWES3S3HBCY/action/replication_record"}},"created_at":"2026-05-18T00:42:44.605664+00:00","updated_at":"2026-05-18T00:42:44.605664+00:00"}