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We also show that a non-trivial group homomorphism $\\Phi: \\text{Diff}_c(M) \\to \\text{Diff}_c(N)$ implies that $\\dim(M) \\leq \\dim(N)$ and give a classification of such homomorphisms when $\\dim(M) = \\dim(N)$."},"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":"1307.4447","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-07-16T23:09:39Z","cross_cats_sorted":["math.DS","math.GN","math.GR"],"title_canon_sha256":"2a772d9ba35487f352a217c21df360ebc2f6b038341586a75b4d8e1450f43f6c","abstract_canon_sha256":"1aaf4e1a09beb85e03ab55ba25431e393694ecde84bbddec8abbf40abf13c3eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:03.623867Z","signature_b64":"ASFhQK0Ji/DPN17pFCAXBWHQsKmRqw2eRHW57PB2TegCkW19Ja1+r36CXtvOvu6BuQqOuwxDDaEGrPkXIJg1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70ca8ecaeafa86d042844f95f28dec0a76a9496a210c8ac7b807d83931a8be5c","last_reissued_at":"2026-05-18T01:11:03.623324Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:03.623324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Continuity of discrete homomorphisms of diffeomorphism groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GN","math.GR"],"primary_cat":"math.GT","authors_text":"Sebastian Hurtado","submitted_at":"2013-07-16T23:09:39Z","abstract_excerpt":"Let $M$ and $N$ be two closed $C^{\\infty}$ manifolds and let $\\text{Diff}_c(M)$ denote the group of $C^{\\infty}$ diffeomorphisms isotopic to the identity. 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We also show that a non-trivial group homomorphism $\\Phi: \\text{Diff}_c(M) \\to \\text{Diff}_c(N)$ implies that $\\dim(M) \\leq \\dim(N)$ and give a classification of such homomorphisms when $\\dim(M) = \\dim(N)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4447","kind":"arxiv","version":4},"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":"1307.4447","created_at":"2026-05-18T01:11:03.623407+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.4447v4","created_at":"2026-05-18T01:11:03.623407+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4447","created_at":"2026-05-18T01:11:03.623407+00:00"},{"alias_kind":"pith_short_12","alias_value":"ODFI5SXK7KDN","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"ODFI5SXK7KDNAQUE","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"ODFI5SXK","created_at":"2026-05-18T12:27:54.935989+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/ODFI5SXK7KDNAQUEJ6K7FDPMBJ","json":"https://pith.science/pith/ODFI5SXK7KDNAQUEJ6K7FDPMBJ.json","graph_json":"https://pith.science/api/pith-number/ODFI5SXK7KDNAQUEJ6K7FDPMBJ/graph.json","events_json":"https://pith.science/api/pith-number/ODFI5SXK7KDNAQUEJ6K7FDPMBJ/events.json","paper":"https://pith.science/paper/ODFI5SXK"},"agent_actions":{"view_html":"https://pith.science/pith/ODFI5SXK7KDNAQUEJ6K7FDPMBJ","download_json":"https://pith.science/pith/ODFI5SXK7KDNAQUEJ6K7FDPMBJ.json","view_paper":"https://pith.science/paper/ODFI5SXK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.4447&json=true","fetch_graph":"https://pith.science/api/pith-number/ODFI5SXK7KDNAQUEJ6K7FDPMBJ/graph.json","fetch_events":"https://pith.science/api/pith-number/ODFI5SXK7KDNAQUEJ6K7FDPMBJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ODFI5SXK7KDNAQUEJ6K7FDPMBJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ODFI5SXK7KDNAQUEJ6K7FDPMBJ/action/storage_attestation","attest_author":"https://pith.science/pith/ODFI5SXK7KDNAQUEJ6K7FDPMBJ/action/author_attestation","sign_citation":"https://pith.science/pith/ODFI5SXK7KDNAQUEJ6K7FDPMBJ/action/citation_signature","submit_replication":"https://pith.science/pith/ODFI5SXK7KDNAQUEJ6K7FDPMBJ/action/replication_record"}},"created_at":"2026-05-18T01:11:03.623407+00:00","updated_at":"2026-05-18T01:11:03.623407+00:00"}