{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:B4K7LHWWJU2Y45ULO7L7NEERHK","short_pith_number":"pith:B4K7LHWW","schema_version":"1.0","canonical_sha256":"0f15f59ed64d358e768b77d7f690913a8b6ff259a03a8acf83648a70d86e4de9","source":{"kind":"arxiv","id":"1409.5367","version":1},"attestation_state":"computed","paper":{"title":"Differential modular forms attached to newforms mod p","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandru Buium","submitted_at":"2014-09-18T16:35:33Z","abstract_excerpt":"In a previous paper we attached to classical complex newforms $f$ of weight $2$ certain $\\delta_p$-modular forms $f^{\\sharp}$ of order $2$ and weight $0$; the forms $f^{\\sharp}$ can be viewed as \"dual\" to $f$ and played a key role in some of the applications of the theory. The aim of this paper is to provide a higher weight version of this \"$\\sharp$-duality,\" by attaching to classical newforms mod $p$, $\\overline{f}$, of weight $\\kappa$ between $3$ and $p$, $\\delta_{\\pi}$-modular forms $f^{\\sharp}$ of order $2$ and weight $-\\kappa'$, with $\\kappa'$ between $1$ and $p-2$."},"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":"1409.5367","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-18T16:35:33Z","cross_cats_sorted":[],"title_canon_sha256":"1e5a9adcf5029200808c4c668c59deea8cfe041d4bbee9765a0f177fefd4ec98","abstract_canon_sha256":"d01121f34dd77da9768a84c34ddf74a487ee44ecf702c4bfa63a47d32bc51e57"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:29.696627Z","signature_b64":"IR2TvdEi3i4oAGj2eK/cXLvb3DMioKDfb6syyz5VO610TlLpN/+/lI85I4WsPHN5iiCnyVPV1tGvemleqk6ODg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f15f59ed64d358e768b77d7f690913a8b6ff259a03a8acf83648a70d86e4de9","last_reissued_at":"2026-05-18T02:42:29.695758Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:29.695758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Differential modular forms attached to newforms mod p","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandru Buium","submitted_at":"2014-09-18T16:35:33Z","abstract_excerpt":"In a previous paper we attached to classical complex newforms $f$ of weight $2$ certain $\\delta_p$-modular forms $f^{\\sharp}$ of order $2$ and weight $0$; the forms $f^{\\sharp}$ can be viewed as \"dual\" to $f$ and played a key role in some of the applications of the theory. The aim of this paper is to provide a higher weight version of this \"$\\sharp$-duality,\" by attaching to classical newforms mod $p$, $\\overline{f}$, of weight $\\kappa$ between $3$ and $p$, $\\delta_{\\pi}$-modular forms $f^{\\sharp}$ of order $2$ and weight $-\\kappa'$, with $\\kappa'$ between $1$ and $p-2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5367","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":""},"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":"1409.5367","created_at":"2026-05-18T02:42:29.695888+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.5367v1","created_at":"2026-05-18T02:42:29.695888+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5367","created_at":"2026-05-18T02:42:29.695888+00:00"},{"alias_kind":"pith_short_12","alias_value":"B4K7LHWWJU2Y","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"B4K7LHWWJU2Y45UL","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"B4K7LHWW","created_at":"2026-05-18T12:28:19.803747+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/B4K7LHWWJU2Y45ULO7L7NEERHK","json":"https://pith.science/pith/B4K7LHWWJU2Y45ULO7L7NEERHK.json","graph_json":"https://pith.science/api/pith-number/B4K7LHWWJU2Y45ULO7L7NEERHK/graph.json","events_json":"https://pith.science/api/pith-number/B4K7LHWWJU2Y45ULO7L7NEERHK/events.json","paper":"https://pith.science/paper/B4K7LHWW"},"agent_actions":{"view_html":"https://pith.science/pith/B4K7LHWWJU2Y45ULO7L7NEERHK","download_json":"https://pith.science/pith/B4K7LHWWJU2Y45ULO7L7NEERHK.json","view_paper":"https://pith.science/paper/B4K7LHWW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.5367&json=true","fetch_graph":"https://pith.science/api/pith-number/B4K7LHWWJU2Y45ULO7L7NEERHK/graph.json","fetch_events":"https://pith.science/api/pith-number/B4K7LHWWJU2Y45ULO7L7NEERHK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B4K7LHWWJU2Y45ULO7L7NEERHK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B4K7LHWWJU2Y45ULO7L7NEERHK/action/storage_attestation","attest_author":"https://pith.science/pith/B4K7LHWWJU2Y45ULO7L7NEERHK/action/author_attestation","sign_citation":"https://pith.science/pith/B4K7LHWWJU2Y45ULO7L7NEERHK/action/citation_signature","submit_replication":"https://pith.science/pith/B4K7LHWWJU2Y45ULO7L7NEERHK/action/replication_record"}},"created_at":"2026-05-18T02:42:29.695888+00:00","updated_at":"2026-05-18T02:42:29.695888+00:00"}