{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:CZ73DGXGOS6A56FTTUEKPLTXQV","short_pith_number":"pith:CZ73DGXG","schema_version":"1.0","canonical_sha256":"167fb19ae674bc0ef8b39d08a7ae778567feac4848b23a894526b6b8cb248ab1","source":{"kind":"arxiv","id":"1506.06945","version":8},"attestation_state":"computed","paper":{"title":"A Garden of Eden theorem for Anosov diffeomorphisms on tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Michel Coornaert, Tullio Ceccherini-Silberstein","submitted_at":"2015-06-23T11:14:20Z","abstract_excerpt":"Let $f$ be an Anosov diffeomorphism of the $n$-dimensional torus ${\\mathbb{T}}^n$ and $\\tau$ a continuous self-mapping of ${\\mathbb{T}}^n$ commuting with $f$. We prove that $\\tau$ is surjective if and only if the restriction of $\\tau$ to each homoclinicity class of $f$ is injective."},"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":"1506.06945","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-06-23T11:14:20Z","cross_cats_sorted":[],"title_canon_sha256":"6912857097a25e724d733987b3975db5d66de60ebf659f7aa35ed00e778b57dd","abstract_canon_sha256":"1923ecf6c5f4376b3eef7b09190a8be01bf4706bbef3903c1aa28c3b35ad2611"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:00.204637Z","signature_b64":"QwtPWK0m4yoYXU0YVDVcZvqV+I7aL7eUAO74ZKoVbjSGHIu62alI2P0CC2sW4DI1xSW1S1z7FPEDEcI8dxYxAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"167fb19ae674bc0ef8b39d08a7ae778567feac4848b23a894526b6b8cb248ab1","last_reissued_at":"2026-05-18T01:04:00.204021Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:00.204021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Garden of Eden theorem for Anosov diffeomorphisms on tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Michel Coornaert, Tullio Ceccherini-Silberstein","submitted_at":"2015-06-23T11:14:20Z","abstract_excerpt":"Let $f$ be an Anosov diffeomorphism of the $n$-dimensional torus ${\\mathbb{T}}^n$ and $\\tau$ a continuous self-mapping of ${\\mathbb{T}}^n$ commuting with $f$. We prove that $\\tau$ is surjective if and only if the restriction of $\\tau$ to each homoclinicity class of $f$ is injective."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06945","kind":"arxiv","version":8},"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":"1506.06945","created_at":"2026-05-18T01:04:00.204108+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.06945v8","created_at":"2026-05-18T01:04:00.204108+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06945","created_at":"2026-05-18T01:04:00.204108+00:00"},{"alias_kind":"pith_short_12","alias_value":"CZ73DGXGOS6A","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"CZ73DGXGOS6A56FT","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"CZ73DGXG","created_at":"2026-05-18T12:29:17.054201+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/CZ73DGXGOS6A56FTTUEKPLTXQV","json":"https://pith.science/pith/CZ73DGXGOS6A56FTTUEKPLTXQV.json","graph_json":"https://pith.science/api/pith-number/CZ73DGXGOS6A56FTTUEKPLTXQV/graph.json","events_json":"https://pith.science/api/pith-number/CZ73DGXGOS6A56FTTUEKPLTXQV/events.json","paper":"https://pith.science/paper/CZ73DGXG"},"agent_actions":{"view_html":"https://pith.science/pith/CZ73DGXGOS6A56FTTUEKPLTXQV","download_json":"https://pith.science/pith/CZ73DGXGOS6A56FTTUEKPLTXQV.json","view_paper":"https://pith.science/paper/CZ73DGXG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.06945&json=true","fetch_graph":"https://pith.science/api/pith-number/CZ73DGXGOS6A56FTTUEKPLTXQV/graph.json","fetch_events":"https://pith.science/api/pith-number/CZ73DGXGOS6A56FTTUEKPLTXQV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CZ73DGXGOS6A56FTTUEKPLTXQV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CZ73DGXGOS6A56FTTUEKPLTXQV/action/storage_attestation","attest_author":"https://pith.science/pith/CZ73DGXGOS6A56FTTUEKPLTXQV/action/author_attestation","sign_citation":"https://pith.science/pith/CZ73DGXGOS6A56FTTUEKPLTXQV/action/citation_signature","submit_replication":"https://pith.science/pith/CZ73DGXGOS6A56FTTUEKPLTXQV/action/replication_record"}},"created_at":"2026-05-18T01:04:00.204108+00:00","updated_at":"2026-05-18T01:04:00.204108+00:00"}