{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:F55DT4LERG3KWTMIYDUQT5XASL","short_pith_number":"pith:F55DT4LE","schema_version":"1.0","canonical_sha256":"2f7a39f16489b6ab4d88c0e909f6e092cc6786726637b1c58831be11419130b5","source":{"kind":"arxiv","id":"2210.08866","version":1},"attestation_state":"computed","paper":{"title":"The intersection matrices of $X_0(p^r)$ and some applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chitrabhanu Chaudhuri, Debargha Banerjee, Priyanka Majumder","submitted_at":"2022-10-17T09:02:44Z","abstract_excerpt":"We compute intersection matrices for modular curves of the form $X_0(p^r)$ with $r \\in \\{3,4\\}$ and as an application, we compute an asymptotic expression for the Arakelov self-intersection number of the relative dualizing sheaf of Edixhoven's minimal regular model for the modular curve $X_0(p^r)$ over $\\qq$ with $r$ as above. This computation will be useful to understand an effective version of the Bogolomov conjecture for the stable models of modular curves $X_0(p^r)$ with $r \\in \\{3,4\\}$ and obtain a bound on the stable Faltings height for those curves."},"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":"2210.08866","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2022-10-17T09:02:44Z","cross_cats_sorted":[],"title_canon_sha256":"f577d4cfcec12913544920f412bfd016b707cb8f38c548350311f0b260bb6331","abstract_canon_sha256":"164e370ecdf09d6e6ddbf9013296a3226e8c57c0dc0fcad6903fcca7ed70b127"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:07:16.184947Z","signature_b64":"vVrFnFkOAs8EMti8RG7LtZpWXA+S82/2YyyILYdrpjzP2soQ+OIQ46qopPQghVpv+6gaiUrAD8zep0QLe4acDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f7a39f16489b6ab4d88c0e909f6e092cc6786726637b1c58831be11419130b5","last_reissued_at":"2026-07-05T05:07:16.184434Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:07:16.184434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The intersection matrices of $X_0(p^r)$ and some applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chitrabhanu Chaudhuri, Debargha Banerjee, Priyanka Majumder","submitted_at":"2022-10-17T09:02:44Z","abstract_excerpt":"We compute intersection matrices for modular curves of the form $X_0(p^r)$ with $r \\in \\{3,4\\}$ and as an application, we compute an asymptotic expression for the Arakelov self-intersection number of the relative dualizing sheaf of Edixhoven's minimal regular model for the modular curve $X_0(p^r)$ over $\\qq$ with $r$ as above. This computation will be useful to understand an effective version of the Bogolomov conjecture for the stable models of modular curves $X_0(p^r)$ with $r \\in \\{3,4\\}$ and obtain a bound on the stable Faltings height for those curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.08866","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/2210.08866/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":"2210.08866","created_at":"2026-07-05T05:07:16.184492+00:00"},{"alias_kind":"arxiv_version","alias_value":"2210.08866v1","created_at":"2026-07-05T05:07:16.184492+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.08866","created_at":"2026-07-05T05:07:16.184492+00:00"},{"alias_kind":"pith_short_12","alias_value":"F55DT4LERG3K","created_at":"2026-07-05T05:07:16.184492+00:00"},{"alias_kind":"pith_short_16","alias_value":"F55DT4LERG3KWTMI","created_at":"2026-07-05T05:07:16.184492+00:00"},{"alias_kind":"pith_short_8","alias_value":"F55DT4LE","created_at":"2026-07-05T05:07:16.184492+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/F55DT4LERG3KWTMIYDUQT5XASL","json":"https://pith.science/pith/F55DT4LERG3KWTMIYDUQT5XASL.json","graph_json":"https://pith.science/api/pith-number/F55DT4LERG3KWTMIYDUQT5XASL/graph.json","events_json":"https://pith.science/api/pith-number/F55DT4LERG3KWTMIYDUQT5XASL/events.json","paper":"https://pith.science/paper/F55DT4LE"},"agent_actions":{"view_html":"https://pith.science/pith/F55DT4LERG3KWTMIYDUQT5XASL","download_json":"https://pith.science/pith/F55DT4LERG3KWTMIYDUQT5XASL.json","view_paper":"https://pith.science/paper/F55DT4LE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2210.08866&json=true","fetch_graph":"https://pith.science/api/pith-number/F55DT4LERG3KWTMIYDUQT5XASL/graph.json","fetch_events":"https://pith.science/api/pith-number/F55DT4LERG3KWTMIYDUQT5XASL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F55DT4LERG3KWTMIYDUQT5XASL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F55DT4LERG3KWTMIYDUQT5XASL/action/storage_attestation","attest_author":"https://pith.science/pith/F55DT4LERG3KWTMIYDUQT5XASL/action/author_attestation","sign_citation":"https://pith.science/pith/F55DT4LERG3KWTMIYDUQT5XASL/action/citation_signature","submit_replication":"https://pith.science/pith/F55DT4LERG3KWTMIYDUQT5XASL/action/replication_record"}},"created_at":"2026-07-05T05:07:16.184492+00:00","updated_at":"2026-07-05T05:07:16.184492+00:00"}