{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:SBMGAIBE6UFCSPK45555MXSZVO","short_pith_number":"pith:SBMGAIBE","schema_version":"1.0","canonical_sha256":"9058602024f50a293d5cef7bd65e59ab9813960154547791b1aaab376529337d","source":{"kind":"arxiv","id":"1709.08183","version":1},"attestation_state":"computed","paper":{"title":"Invariant measures for actions of congruent monotileable amenable groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mar\\'ia Isabel Cortez, Paulina Cecchi","submitted_at":"2017-09-24T11:11:22Z","abstract_excerpt":"In this paper we show that for every congruent monotileable amenable group $G$ and for every metrizable Choquet simplex $K$, there exists a minimal $G$-subshift, which is free on a full measure set, whose set of invariant probability measures is affine homeomorphic to $K$. If the group is virtually abelian, the subshift is free. Congruent monotileable amenable groups are a generalization of amenable residually finite groups. In particular, we show that this class contains all the infinite countable virtually nilpotent groups. This article is a generalization to congruent monotileable amenable "},"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":"1709.08183","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-24T11:11:22Z","cross_cats_sorted":[],"title_canon_sha256":"688187b89ec272de7b52c0d31a4cf99a870ecc52f029ee2f16e7370e83e7d2ac","abstract_canon_sha256":"6de2574e736955a8d01e6c6bdaa8aeecd847454916910618bd1c25e63d9acfb5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:27.781005Z","signature_b64":"XMZ9HZZnzqU6vpU655MM23aOiOoTtnOpFi/65xSGH365SBP8czdxPJ2EWktYKhmtnxw4RE4YzVnc2SNtC1jpDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9058602024f50a293d5cef7bd65e59ab9813960154547791b1aaab376529337d","last_reissued_at":"2026-05-18T00:34:27.780381Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:27.780381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariant measures for actions of congruent monotileable amenable groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mar\\'ia Isabel Cortez, Paulina Cecchi","submitted_at":"2017-09-24T11:11:22Z","abstract_excerpt":"In this paper we show that for every congruent monotileable amenable group $G$ and for every metrizable Choquet simplex $K$, there exists a minimal $G$-subshift, which is free on a full measure set, whose set of invariant probability measures is affine homeomorphic to $K$. If the group is virtually abelian, the subshift is free. Congruent monotileable amenable groups are a generalization of amenable residually finite groups. In particular, we show that this class contains all the infinite countable virtually nilpotent groups. This article is a generalization to congruent monotileable amenable "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08183","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":"1709.08183","created_at":"2026-05-18T00:34:27.780488+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.08183v1","created_at":"2026-05-18T00:34:27.780488+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08183","created_at":"2026-05-18T00:34:27.780488+00:00"},{"alias_kind":"pith_short_12","alias_value":"SBMGAIBE6UFC","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"SBMGAIBE6UFCSPK4","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"SBMGAIBE","created_at":"2026-05-18T12:31:43.269735+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/SBMGAIBE6UFCSPK45555MXSZVO","json":"https://pith.science/pith/SBMGAIBE6UFCSPK45555MXSZVO.json","graph_json":"https://pith.science/api/pith-number/SBMGAIBE6UFCSPK45555MXSZVO/graph.json","events_json":"https://pith.science/api/pith-number/SBMGAIBE6UFCSPK45555MXSZVO/events.json","paper":"https://pith.science/paper/SBMGAIBE"},"agent_actions":{"view_html":"https://pith.science/pith/SBMGAIBE6UFCSPK45555MXSZVO","download_json":"https://pith.science/pith/SBMGAIBE6UFCSPK45555MXSZVO.json","view_paper":"https://pith.science/paper/SBMGAIBE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.08183&json=true","fetch_graph":"https://pith.science/api/pith-number/SBMGAIBE6UFCSPK45555MXSZVO/graph.json","fetch_events":"https://pith.science/api/pith-number/SBMGAIBE6UFCSPK45555MXSZVO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SBMGAIBE6UFCSPK45555MXSZVO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SBMGAIBE6UFCSPK45555MXSZVO/action/storage_attestation","attest_author":"https://pith.science/pith/SBMGAIBE6UFCSPK45555MXSZVO/action/author_attestation","sign_citation":"https://pith.science/pith/SBMGAIBE6UFCSPK45555MXSZVO/action/citation_signature","submit_replication":"https://pith.science/pith/SBMGAIBE6UFCSPK45555MXSZVO/action/replication_record"}},"created_at":"2026-05-18T00:34:27.780488+00:00","updated_at":"2026-05-18T00:34:27.780488+00:00"}