{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:Z2CB4JJU2Z4WQCVSTDIAUGTFBW","short_pith_number":"pith:Z2CB4JJU","schema_version":"1.0","canonical_sha256":"ce841e2534d679680ab298d00a1a650d8073aca21b860d9977cdb85682883a1f","source":{"kind":"arxiv","id":"1404.7033","version":2},"attestation_state":"computed","paper":{"title":"An exotic zoo of diffeomorphism groups on $\\mathbb R^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.DG","authors_text":"Andreas Kriegl, Armin Rainer, Peter W. Michor","submitted_at":"2014-04-28T16:07:08Z","abstract_excerpt":"Let $C^{[M]}$ be a (local) Denjoy-Carleman class of Beurling or Roumieu type, where the weight sequence $M=(M_k)$ is log-convex and has moderate growth. We prove that the groups ${\\operatorname{Diff}}\\mathcal{B}^{[M]}(\\mathbb{R}^n)$, ${\\operatorname{Diff}}W^{[M],p}(\\mathbb{R}^n)$, ${\\operatorname{Diff}}{\\mathcal{S}}{}_{[L]}^{[M]}(\\mathbb{R}^n)$, and ${\\operatorname{Diff}}\\mathcal{D}^{[M]}(\\mathbb{R}^n)$ of $C^{[M]}$-diffeomorphisms on $\\mathbb{R}^n$ which differ from the identity by a mapping in $\\mathcal{B}^{[M]}$ (global Denjoy--Carleman), $W^{[M],p}$ (Sobolev-Denjoy-Carleman), ${\\mathcal{S}"},"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":"1404.7033","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-04-28T16:07:08Z","cross_cats_sorted":["math.AP","math.FA"],"title_canon_sha256":"6792f160eca6f926250ba4f8569995d95e74f6e87f0747d88cf1d21e050f1f13","abstract_canon_sha256":"f9c1822f05430a251eb34990ac44273ceac2a88eae986f9c187c9b3920ee60c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:19.140834Z","signature_b64":"Y7FLSY3f4vdmN4jbO32uM26LpdJiFPPZ4kKgJASnRf9D42EHy//pQ+iBAlgC4YvlGd1kYPjeVHcmVG9Ph1GQDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce841e2534d679680ab298d00a1a650d8073aca21b860d9977cdb85682883a1f","last_reissued_at":"2026-05-18T01:16:19.140195Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:19.140195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An exotic zoo of diffeomorphism groups on $\\mathbb R^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.DG","authors_text":"Andreas Kriegl, Armin Rainer, Peter W. Michor","submitted_at":"2014-04-28T16:07:08Z","abstract_excerpt":"Let $C^{[M]}$ be a (local) Denjoy-Carleman class of Beurling or Roumieu type, where the weight sequence $M=(M_k)$ is log-convex and has moderate growth. We prove that the groups ${\\operatorname{Diff}}\\mathcal{B}^{[M]}(\\mathbb{R}^n)$, ${\\operatorname{Diff}}W^{[M],p}(\\mathbb{R}^n)$, ${\\operatorname{Diff}}{\\mathcal{S}}{}_{[L]}^{[M]}(\\mathbb{R}^n)$, and ${\\operatorname{Diff}}\\mathcal{D}^{[M]}(\\mathbb{R}^n)$ of $C^{[M]}$-diffeomorphisms on $\\mathbb{R}^n$ which differ from the identity by a mapping in $\\mathcal{B}^{[M]}$ (global Denjoy--Carleman), $W^{[M],p}$ (Sobolev-Denjoy-Carleman), ${\\mathcal{S}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7033","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":"1404.7033","created_at":"2026-05-18T01:16:19.140299+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.7033v2","created_at":"2026-05-18T01:16:19.140299+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7033","created_at":"2026-05-18T01:16:19.140299+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z2CB4JJU2Z4W","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z2CB4JJU2Z4WQCVS","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z2CB4JJU","created_at":"2026-05-18T12:28:59.999130+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/Z2CB4JJU2Z4WQCVSTDIAUGTFBW","json":"https://pith.science/pith/Z2CB4JJU2Z4WQCVSTDIAUGTFBW.json","graph_json":"https://pith.science/api/pith-number/Z2CB4JJU2Z4WQCVSTDIAUGTFBW/graph.json","events_json":"https://pith.science/api/pith-number/Z2CB4JJU2Z4WQCVSTDIAUGTFBW/events.json","paper":"https://pith.science/paper/Z2CB4JJU"},"agent_actions":{"view_html":"https://pith.science/pith/Z2CB4JJU2Z4WQCVSTDIAUGTFBW","download_json":"https://pith.science/pith/Z2CB4JJU2Z4WQCVSTDIAUGTFBW.json","view_paper":"https://pith.science/paper/Z2CB4JJU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.7033&json=true","fetch_graph":"https://pith.science/api/pith-number/Z2CB4JJU2Z4WQCVSTDIAUGTFBW/graph.json","fetch_events":"https://pith.science/api/pith-number/Z2CB4JJU2Z4WQCVSTDIAUGTFBW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z2CB4JJU2Z4WQCVSTDIAUGTFBW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z2CB4JJU2Z4WQCVSTDIAUGTFBW/action/storage_attestation","attest_author":"https://pith.science/pith/Z2CB4JJU2Z4WQCVSTDIAUGTFBW/action/author_attestation","sign_citation":"https://pith.science/pith/Z2CB4JJU2Z4WQCVSTDIAUGTFBW/action/citation_signature","submit_replication":"https://pith.science/pith/Z2CB4JJU2Z4WQCVSTDIAUGTFBW/action/replication_record"}},"created_at":"2026-05-18T01:16:19.140299+00:00","updated_at":"2026-05-18T01:16:19.140299+00:00"}