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We show that if $K$ is neither the boundary of the $n$-simplex nor a cycle, then $\\mathrm{Aut}(\\mathcal{M}(K))\\cong \\mathrm{Aut}(K)$. In the case where $K= C_n$, a cycle of length $n$, we show that $\\mathrm{Aut}(\\mathcal{M}(C_n))\\cong \\mathrm{Aut}(C_{2n})$. In the case where $K=\\partial\\Delta^n$, we prove that $\\mathrm{Aut}(\\mathcal{M}(\\partial\\Delta^n))\\cong \\mathrm{Aut}(\\partial\\Delta^n)\\time"},"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":"1904.10907","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-04-24T16:29:06Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"89e0608a35d9688a3007c4cfd34948531248da255d4a2d60af27a9f9dc5600df","abstract_canon_sha256":"c89ccaa94220ba462b936de123019edd7295e6b037d6038136450886f9194c89"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:49.743908Z","signature_b64":"riv/1yVAO8WWUvI9CLBNvz6sr2pC4u+ucFVY5+uFpa4sG214B+XmIFkIFPFQZ+zqjbCGAJmWbYCc8pAiiUMWDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71d55bf36d4990c0f266ad4d3aa1741956aa37a37ef1e05f4894e9eb3b997827","last_reissued_at":"2026-05-17T23:47:49.743385Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:49.743385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the automorphism group of the Morse complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Maxwell Lin, Nicholas A. Scoville","submitted_at":"2019-04-24T16:29:06Z","abstract_excerpt":"Let $K$ be a finite, connected, abstract simplicial complex. The Morse complex of $K$, first introduced by Chari and Joswig, is the simplicial complex constructed from all gradient vector fields on $K$. We show that if $K$ is neither the boundary of the $n$-simplex nor a cycle, then $\\mathrm{Aut}(\\mathcal{M}(K))\\cong \\mathrm{Aut}(K)$. In the case where $K= C_n$, a cycle of length $n$, we show that $\\mathrm{Aut}(\\mathcal{M}(C_n))\\cong \\mathrm{Aut}(C_{2n})$. In the case where $K=\\partial\\Delta^n$, we prove that $\\mathrm{Aut}(\\mathcal{M}(\\partial\\Delta^n))\\cong \\mathrm{Aut}(\\partial\\Delta^n)\\time"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.10907","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":"1904.10907","created_at":"2026-05-17T23:47:49.743470+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.10907v1","created_at":"2026-05-17T23:47:49.743470+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.10907","created_at":"2026-05-17T23:47:49.743470+00:00"},{"alias_kind":"pith_short_12","alias_value":"OHKVX43NJGIM","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"OHKVX43NJGIMB4TG","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"OHKVX43N","created_at":"2026-05-18T12:33:24.271573+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/OHKVX43NJGIMB4TGVVGTVILUDF","json":"https://pith.science/pith/OHKVX43NJGIMB4TGVVGTVILUDF.json","graph_json":"https://pith.science/api/pith-number/OHKVX43NJGIMB4TGVVGTVILUDF/graph.json","events_json":"https://pith.science/api/pith-number/OHKVX43NJGIMB4TGVVGTVILUDF/events.json","paper":"https://pith.science/paper/OHKVX43N"},"agent_actions":{"view_html":"https://pith.science/pith/OHKVX43NJGIMB4TGVVGTVILUDF","download_json":"https://pith.science/pith/OHKVX43NJGIMB4TGVVGTVILUDF.json","view_paper":"https://pith.science/paper/OHKVX43N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.10907&json=true","fetch_graph":"https://pith.science/api/pith-number/OHKVX43NJGIMB4TGVVGTVILUDF/graph.json","fetch_events":"https://pith.science/api/pith-number/OHKVX43NJGIMB4TGVVGTVILUDF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OHKVX43NJGIMB4TGVVGTVILUDF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OHKVX43NJGIMB4TGVVGTVILUDF/action/storage_attestation","attest_author":"https://pith.science/pith/OHKVX43NJGIMB4TGVVGTVILUDF/action/author_attestation","sign_citation":"https://pith.science/pith/OHKVX43NJGIMB4TGVVGTVILUDF/action/citation_signature","submit_replication":"https://pith.science/pith/OHKVX43NJGIMB4TGVVGTVILUDF/action/replication_record"}},"created_at":"2026-05-17T23:47:49.743470+00:00","updated_at":"2026-05-17T23:47:49.743470+00:00"}