{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:UJP3IW6E2LPGDCYEOUHTKWQF7Q","short_pith_number":"pith:UJP3IW6E","schema_version":"1.0","canonical_sha256":"a25fb45bc4d2de618b04750f355a05fc2c105110efd7ebe4b2e0bf43cbf31db6","source":{"kind":"arxiv","id":"1907.05167","version":1},"attestation_state":"computed","paper":{"title":"Invariants of formal pseudodifferential operator algebras and algebraic modular forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.NT","authors_text":"Fran\\c{c}ois Dumas, Fran\\c{c}ois Martin","submitted_at":"2019-07-11T12:54:44Z","abstract_excerpt":"We study from an algebraic point of view the question of extending an action of a group \\(\\Gamma\\) on a commutative domain \\(R\\) to a formal pseudodifferential operator ring \\(B=R(\\!(x\\,;\\,d)\\!)\\) with coefficients in \\(R\\), as well as to some canonical quadratic extension \\(C=R(\\!(x^{1/2}\\,;\\,\\frac 12 d)\\!)_2\\) of \\(B\\). We give a necessary and sufficient condition of compatibility between the action and the derivation $d$ of $R$ for such an extension to exist, and we determine all possible extensions of the action to \\(B\\) and \\(C\\). We describe under suitable assumptions the invariant subal"},"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":"1907.05167","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-07-11T12:54:44Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"4d59e599629613bf87b85aa12abbf3920b8a17f836f70011b2cfd6c81f1ac025","abstract_canon_sha256":"bbdf30990119a40f25beb638f5971a0adf661659d97e3f1c22d208a21d2c85be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:53.769610Z","signature_b64":"487YeMYdT2YO8hArmioaWIYEt+Ik5qR+utk9pAXapFQWQ46+w0/D998AavnuqEBwS2QnxqBR95+GRErgIPnaCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a25fb45bc4d2de618b04750f355a05fc2c105110efd7ebe4b2e0bf43cbf31db6","last_reissued_at":"2026-05-17T23:40:53.768948Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:53.768948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariants of formal pseudodifferential operator algebras and algebraic modular forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.NT","authors_text":"Fran\\c{c}ois Dumas, Fran\\c{c}ois Martin","submitted_at":"2019-07-11T12:54:44Z","abstract_excerpt":"We study from an algebraic point of view the question of extending an action of a group \\(\\Gamma\\) on a commutative domain \\(R\\) to a formal pseudodifferential operator ring \\(B=R(\\!(x\\,;\\,d)\\!)\\) with coefficients in \\(R\\), as well as to some canonical quadratic extension \\(C=R(\\!(x^{1/2}\\,;\\,\\frac 12 d)\\!)_2\\) of \\(B\\). We give a necessary and sufficient condition of compatibility between the action and the derivation $d$ of $R$ for such an extension to exist, and we determine all possible extensions of the action to \\(B\\) and \\(C\\). We describe under suitable assumptions the invariant subal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05167","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":"1907.05167","created_at":"2026-05-17T23:40:53.769069+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.05167v1","created_at":"2026-05-17T23:40:53.769069+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.05167","created_at":"2026-05-17T23:40:53.769069+00:00"},{"alias_kind":"pith_short_12","alias_value":"UJP3IW6E2LPG","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"UJP3IW6E2LPGDCYE","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"UJP3IW6E","created_at":"2026-05-18T12:33:30.264802+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/UJP3IW6E2LPGDCYEOUHTKWQF7Q","json":"https://pith.science/pith/UJP3IW6E2LPGDCYEOUHTKWQF7Q.json","graph_json":"https://pith.science/api/pith-number/UJP3IW6E2LPGDCYEOUHTKWQF7Q/graph.json","events_json":"https://pith.science/api/pith-number/UJP3IW6E2LPGDCYEOUHTKWQF7Q/events.json","paper":"https://pith.science/paper/UJP3IW6E"},"agent_actions":{"view_html":"https://pith.science/pith/UJP3IW6E2LPGDCYEOUHTKWQF7Q","download_json":"https://pith.science/pith/UJP3IW6E2LPGDCYEOUHTKWQF7Q.json","view_paper":"https://pith.science/paper/UJP3IW6E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.05167&json=true","fetch_graph":"https://pith.science/api/pith-number/UJP3IW6E2LPGDCYEOUHTKWQF7Q/graph.json","fetch_events":"https://pith.science/api/pith-number/UJP3IW6E2LPGDCYEOUHTKWQF7Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UJP3IW6E2LPGDCYEOUHTKWQF7Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UJP3IW6E2LPGDCYEOUHTKWQF7Q/action/storage_attestation","attest_author":"https://pith.science/pith/UJP3IW6E2LPGDCYEOUHTKWQF7Q/action/author_attestation","sign_citation":"https://pith.science/pith/UJP3IW6E2LPGDCYEOUHTKWQF7Q/action/citation_signature","submit_replication":"https://pith.science/pith/UJP3IW6E2LPGDCYEOUHTKWQF7Q/action/replication_record"}},"created_at":"2026-05-17T23:40:53.769069+00:00","updated_at":"2026-05-17T23:40:53.769069+00:00"}