{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:VVXERFUIKHJC4SHB5QWBUFLJIT","short_pith_number":"pith:VVXERFUI","schema_version":"1.0","canonical_sha256":"ad6e48968851d22e48e1ec2c1a156944fc72edbc33ced9c48e30b6b699adbb55","source":{"kind":"arxiv","id":"1710.10915","version":3},"attestation_state":"computed","paper":{"title":"Arakelov Self-intersection numbers of minimal regular models of modular curves $X_0(p^2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chitrabhanu Chaudhuri, Debargha Banerjee, Diganta Borah","submitted_at":"2017-10-30T12:59:15Z","abstract_excerpt":"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 $X_0(p^2)$ over $\\mathbb{Q}$. The computation of the self-intersection numbers are used to prove effective Bogolomov conjecture for the semi-stable models of modular curves $X_0(p^2)$ and obtain a bound on the stable Faltings height for those curves in a companion article arXiv:1802.06968."},"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":"1710.10915","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-30T12:59:15Z","cross_cats_sorted":[],"title_canon_sha256":"132c004b9ceb05e5655d0c6178648e8e8732b65752a970e3e4c32dc66194eb73","abstract_canon_sha256":"f96bf425d513b4bf83c62f09129338ab4030e48a331d856aa4f8cd2d8a45f6fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:28:14.817994Z","signature_b64":"WusaWeeuvHA52yU+DIV8q/JE4tRa+UXRVfHIlXnGSpnWeAMmvxK6YISs1sHTO6xdrppazZgB1KwQmPxyv+9QCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad6e48968851d22e48e1ec2c1a156944fc72edbc33ced9c48e30b6b699adbb55","last_reissued_at":"2026-07-05T02:28:14.817553Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:28:14.817553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Arakelov Self-intersection numbers of minimal regular models of modular curves $X_0(p^2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chitrabhanu Chaudhuri, Debargha Banerjee, Diganta Borah","submitted_at":"2017-10-30T12:59:15Z","abstract_excerpt":"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 $X_0(p^2)$ over $\\mathbb{Q}$. The computation of the self-intersection numbers are used to prove effective Bogolomov conjecture for the semi-stable models of modular curves $X_0(p^2)$ and obtain a bound on the stable Faltings height for those curves in a companion article arXiv:1802.06968."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10915","kind":"arxiv","version":3},"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/1710.10915/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":"1710.10915","created_at":"2026-07-05T02:28:14.817613+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.10915v3","created_at":"2026-07-05T02:28:14.817613+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10915","created_at":"2026-07-05T02:28:14.817613+00:00"},{"alias_kind":"pith_short_12","alias_value":"VVXERFUIKHJC","created_at":"2026-07-05T02:28:14.817613+00:00"},{"alias_kind":"pith_short_16","alias_value":"VVXERFUIKHJC4SHB","created_at":"2026-07-05T02:28:14.817613+00:00"},{"alias_kind":"pith_short_8","alias_value":"VVXERFUI","created_at":"2026-07-05T02:28:14.817613+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/VVXERFUIKHJC4SHB5QWBUFLJIT","json":"https://pith.science/pith/VVXERFUIKHJC4SHB5QWBUFLJIT.json","graph_json":"https://pith.science/api/pith-number/VVXERFUIKHJC4SHB5QWBUFLJIT/graph.json","events_json":"https://pith.science/api/pith-number/VVXERFUIKHJC4SHB5QWBUFLJIT/events.json","paper":"https://pith.science/paper/VVXERFUI"},"agent_actions":{"view_html":"https://pith.science/pith/VVXERFUIKHJC4SHB5QWBUFLJIT","download_json":"https://pith.science/pith/VVXERFUIKHJC4SHB5QWBUFLJIT.json","view_paper":"https://pith.science/paper/VVXERFUI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.10915&json=true","fetch_graph":"https://pith.science/api/pith-number/VVXERFUIKHJC4SHB5QWBUFLJIT/graph.json","fetch_events":"https://pith.science/api/pith-number/VVXERFUIKHJC4SHB5QWBUFLJIT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VVXERFUIKHJC4SHB5QWBUFLJIT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VVXERFUIKHJC4SHB5QWBUFLJIT/action/storage_attestation","attest_author":"https://pith.science/pith/VVXERFUIKHJC4SHB5QWBUFLJIT/action/author_attestation","sign_citation":"https://pith.science/pith/VVXERFUIKHJC4SHB5QWBUFLJIT/action/citation_signature","submit_replication":"https://pith.science/pith/VVXERFUIKHJC4SHB5QWBUFLJIT/action/replication_record"}},"created_at":"2026-07-05T02:28:14.817613+00:00","updated_at":"2026-07-05T02:28:14.817613+00:00"}