{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:JUD7WSVCZ6EFLE7YBZSKEAHZ3O","short_pith_number":"pith:JUD7WSVC","schema_version":"1.0","canonical_sha256":"4d07fb4aa2cf885593f80e64a200f9dba661d4fd81108175f3c1cd2b8932533f","source":{"kind":"arxiv","id":"1803.03541","version":1},"attestation_state":"computed","paper":{"title":"Homoclinically expansive actions and a Garden of Eden theorem for harmonic models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"Hanfeng Li, Michel Coornaert, Tullio Ceccherini-Silberstein","submitted_at":"2018-03-08T14:56:58Z","abstract_excerpt":"Let $\\Gamma$ be a countable Abelian group and $f \\in \\Z[\\Gamma]$, where $\\Z[\\Gamma]$ denotes the integral group ring of $\\Gamma$. Consider the Pontryagin dual $X_f$ of the cyclic $\\Z[\\Gamma]$-module $\\Z[\\Gamma]/\\Z[\\Gamma] f$ and suppose that $f$ is weakly expansive (e.g., $f$ is invertible in $\\ell^1(\\Gamma)$, or, when $\\Gamma$ is not virtually $\\Z$ or $\\Z^2$, $f$ is well-balanced) and that $X_f$ is connected. We prove that if $\\tau \\colon X_f \\to X_f$ is a $\\Gamma$-equivariant continuous map, then $\\tau$ is surjective if and only if the restriction of $\\tau$ to each $\\Gamma$-homoclinicity cla"},"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":"1803.03541","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-08T14:56:58Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"86675725753001882e4d1f0df898b6d5d546f76dce1de1d24d91cdd772398080","abstract_canon_sha256":"5736dd436f23f55709f1e0874222714f48254cef09aefb1f6387dda20b5d0456"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:31.490159Z","signature_b64":"CDyY6nX5GTq6PkQOsvNOoWA71F3/RdRaso7pbsHbTG051qkFTYQajy9+yUIq82McHPmPqWmSsSPcGO/6dzBzCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d07fb4aa2cf885593f80e64a200f9dba661d4fd81108175f3c1cd2b8932533f","last_reissued_at":"2026-05-17T23:53:31.489638Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:31.489638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homoclinically expansive actions and a Garden of Eden theorem for harmonic models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"Hanfeng Li, Michel Coornaert, Tullio Ceccherini-Silberstein","submitted_at":"2018-03-08T14:56:58Z","abstract_excerpt":"Let $\\Gamma$ be a countable Abelian group and $f \\in \\Z[\\Gamma]$, where $\\Z[\\Gamma]$ denotes the integral group ring of $\\Gamma$. Consider the Pontryagin dual $X_f$ of the cyclic $\\Z[\\Gamma]$-module $\\Z[\\Gamma]/\\Z[\\Gamma] f$ and suppose that $f$ is weakly expansive (e.g., $f$ is invertible in $\\ell^1(\\Gamma)$, or, when $\\Gamma$ is not virtually $\\Z$ or $\\Z^2$, $f$ is well-balanced) and that $X_f$ is connected. We prove that if $\\tau \\colon X_f \\to X_f$ is a $\\Gamma$-equivariant continuous map, then $\\tau$ is surjective if and only if the restriction of $\\tau$ to each $\\Gamma$-homoclinicity cla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03541","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":"1803.03541","created_at":"2026-05-17T23:53:31.489723+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.03541v1","created_at":"2026-05-17T23:53:31.489723+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03541","created_at":"2026-05-17T23:53:31.489723+00:00"},{"alias_kind":"pith_short_12","alias_value":"JUD7WSVCZ6EF","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"JUD7WSVCZ6EFLE7Y","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"JUD7WSVC","created_at":"2026-05-18T12:32:31.084164+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/JUD7WSVCZ6EFLE7YBZSKEAHZ3O","json":"https://pith.science/pith/JUD7WSVCZ6EFLE7YBZSKEAHZ3O.json","graph_json":"https://pith.science/api/pith-number/JUD7WSVCZ6EFLE7YBZSKEAHZ3O/graph.json","events_json":"https://pith.science/api/pith-number/JUD7WSVCZ6EFLE7YBZSKEAHZ3O/events.json","paper":"https://pith.science/paper/JUD7WSVC"},"agent_actions":{"view_html":"https://pith.science/pith/JUD7WSVCZ6EFLE7YBZSKEAHZ3O","download_json":"https://pith.science/pith/JUD7WSVCZ6EFLE7YBZSKEAHZ3O.json","view_paper":"https://pith.science/paper/JUD7WSVC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.03541&json=true","fetch_graph":"https://pith.science/api/pith-number/JUD7WSVCZ6EFLE7YBZSKEAHZ3O/graph.json","fetch_events":"https://pith.science/api/pith-number/JUD7WSVCZ6EFLE7YBZSKEAHZ3O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JUD7WSVCZ6EFLE7YBZSKEAHZ3O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JUD7WSVCZ6EFLE7YBZSKEAHZ3O/action/storage_attestation","attest_author":"https://pith.science/pith/JUD7WSVCZ6EFLE7YBZSKEAHZ3O/action/author_attestation","sign_citation":"https://pith.science/pith/JUD7WSVCZ6EFLE7YBZSKEAHZ3O/action/citation_signature","submit_replication":"https://pith.science/pith/JUD7WSVCZ6EFLE7YBZSKEAHZ3O/action/replication_record"}},"created_at":"2026-05-17T23:53:31.489723+00:00","updated_at":"2026-05-17T23:53:31.489723+00:00"}