{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CZ73DGXGOS6A56FTTUEKPLTXQV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1923ecf6c5f4376b3eef7b09190a8be01bf4706bbef3903c1aa28c3b35ad2611","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-06-23T11:14:20Z","title_canon_sha256":"6912857097a25e724d733987b3975db5d66de60ebf659f7aa35ed00e778b57dd"},"schema_version":"1.0","source":{"id":"1506.06945","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06945","created_at":"2026-05-18T01:04:00Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06945v8","created_at":"2026-05-18T01:04:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06945","created_at":"2026-05-18T01:04:00Z"},{"alias_kind":"pith_short_12","alias_value":"CZ73DGXGOS6A","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CZ73DGXGOS6A56FT","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CZ73DGXG","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:363363345ec25242f1351cc40c0b2c4b3b5218492f83df53e5de011a55b9c151","target":"graph","created_at":"2026-05-18T01:04:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Michel Coornaert, Tullio Ceccherini-Silberstein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-06-23T11:14:20Z","title":"A Garden of Eden theorem for Anosov diffeomorphisms on tori"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06945","kind":"arxiv","version":8},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8fba0d9a5a06e26723fbc4ba4d0e50f795ddd1150e9809cddb426f0d14e87a89","target":"record","created_at":"2026-05-18T01:04:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1923ecf6c5f4376b3eef7b09190a8be01bf4706bbef3903c1aa28c3b35ad2611","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-06-23T11:14:20Z","title_canon_sha256":"6912857097a25e724d733987b3975db5d66de60ebf659f7aa35ed00e778b57dd"},"schema_version":"1.0","source":{"id":"1506.06945","kind":"arxiv","version":8}},"canonical_sha256":"167fb19ae674bc0ef8b39d08a7ae778567feac4848b23a894526b6b8cb248ab1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"167fb19ae674bc0ef8b39d08a7ae778567feac4848b23a894526b6b8cb248ab1","first_computed_at":"2026-05-18T01:04:00.204021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:00.204021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QwtPWK0m4yoYXU0YVDVcZvqV+I7aL7eUAO74ZKoVbjSGHIu62alI2P0CC2sW4DI1xSW1S1z7FPEDEcI8dxYxAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:00.204637Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06945","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fba0d9a5a06e26723fbc4ba4d0e50f795ddd1150e9809cddb426f0d14e87a89","sha256:363363345ec25242f1351cc40c0b2c4b3b5218492f83df53e5de011a55b9c151"],"state_sha256":"a04b23fccb04699dcf1b0c33ba311e33f0e9fdf516f0541186348e8c6ee2cd1c"}