{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PGHDWO5FXE4UQDKFRC2VV3RTGO","short_pith_number":"pith:PGHDWO5F","canonical_record":{"source":{"id":"1508.07553","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-30T10:57:32Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"d70d7707e8628883c88daecf0adb9258f9a9dff8dfb66e9560adf2ec7367b9e6","abstract_canon_sha256":"c27b16c5333071d09f71e5203a4240a0fa4a0e94bca8b021b1a3e7f3a911e690"},"schema_version":"1.0"},"canonical_sha256":"798e3b3ba5b939480d4588b55aee33339e6442f27e32abe61c26eaf842a79d84","source":{"kind":"arxiv","id":"1508.07553","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07553","created_at":"2026-05-18T01:04:00Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07553v4","created_at":"2026-05-18T01:04:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07553","created_at":"2026-05-18T01:04:00Z"},{"alias_kind":"pith_short_12","alias_value":"PGHDWO5FXE4U","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PGHDWO5FXE4UQDKF","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PGHDWO5F","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PGHDWO5FXE4UQDKFRC2VV3RTGO","target":"record","payload":{"canonical_record":{"source":{"id":"1508.07553","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-30T10:57:32Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"d70d7707e8628883c88daecf0adb9258f9a9dff8dfb66e9560adf2ec7367b9e6","abstract_canon_sha256":"c27b16c5333071d09f71e5203a4240a0fa4a0e94bca8b021b1a3e7f3a911e690"},"schema_version":"1.0"},"canonical_sha256":"798e3b3ba5b939480d4588b55aee33339e6442f27e32abe61c26eaf842a79d84","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:00.101095Z","signature_b64":"yWOZ3JBOTrQPwW6qjxeNwCgxKMfPnQyFtrC/UPTOKTTUUllf9zingzKl79NitR84lSq8dXMDgN8axBLVX/uRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"798e3b3ba5b939480d4588b55aee33339e6442f27e32abe61c26eaf842a79d84","last_reissued_at":"2026-05-18T01:04:00.100451Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:00.100451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.07553","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"neGwk10XV7jUyTXVVM91uxWUWiALjscIxb6qHHY3DGRFwJnle3DME0AYmyeG5v+wDg0ypdm6OSSOsH3CPMomCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T20:01:08.760668Z"},"content_sha256":"59cafd4b3c59e4385e04d09e75cf25abbf0d7b455498da5c9fd8c10936e8e19e","schema_version":"1.0","event_id":"sha256:59cafd4b3c59e4385e04d09e75cf25abbf0d7b455498da5c9fd8c10936e8e19e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PGHDWO5FXE4UQDKFRC2VV3RTGO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Expansive actions of countable amenable groups, homoclinic pairs, and the Myhill property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"Michel Coornaert, Tullio Ceccherini-Silberstein","submitted_at":"2015-08-30T10:57:32Z","abstract_excerpt":"Let $X$ be a compact metrizable space equipped with a continuous action of a countable amenable group $G$. Suppose that the dynamical system $(X,G)$ is expansive and is the quotient by a uniformly bounded-to-one factor map of a strongly irreducible subshift. Let $\\tau \\colon X \\to X$ be a continuous map commuting with the action of $G$. We prove that if there is no pair of distinct $G$-homoclinic points in $X$ having the same image under $\\tau$, then $\\tau$ is surjective."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07553","kind":"arxiv","version":4},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MnygPuVchPD8BU0ICE2bbaJ3qrOp62dAal0AeB6X/FFZS+9nbOywIcE8BvzB3ohICQXmawuSQTovvJD723UZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T20:01:08.761017Z"},"content_sha256":"e1dea791f9088b3785873507e8471e46651518b2f1d82757df97d7bb960a1aa9","schema_version":"1.0","event_id":"sha256:e1dea791f9088b3785873507e8471e46651518b2f1d82757df97d7bb960a1aa9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PGHDWO5FXE4UQDKFRC2VV3RTGO/bundle.json","state_url":"https://pith.science/pith/PGHDWO5FXE4UQDKFRC2VV3RTGO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PGHDWO5FXE4UQDKFRC2VV3RTGO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T20:01:08Z","links":{"resolver":"https://pith.science/pith/PGHDWO5FXE4UQDKFRC2VV3RTGO","bundle":"https://pith.science/pith/PGHDWO5FXE4UQDKFRC2VV3RTGO/bundle.json","state":"https://pith.science/pith/PGHDWO5FXE4UQDKFRC2VV3RTGO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PGHDWO5FXE4UQDKFRC2VV3RTGO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PGHDWO5FXE4UQDKFRC2VV3RTGO","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":"c27b16c5333071d09f71e5203a4240a0fa4a0e94bca8b021b1a3e7f3a911e690","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-30T10:57:32Z","title_canon_sha256":"d70d7707e8628883c88daecf0adb9258f9a9dff8dfb66e9560adf2ec7367b9e6"},"schema_version":"1.0","source":{"id":"1508.07553","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07553","created_at":"2026-05-18T01:04:00Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07553v4","created_at":"2026-05-18T01:04:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07553","created_at":"2026-05-18T01:04:00Z"},{"alias_kind":"pith_short_12","alias_value":"PGHDWO5FXE4U","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PGHDWO5FXE4UQDKF","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PGHDWO5F","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:e1dea791f9088b3785873507e8471e46651518b2f1d82757df97d7bb960a1aa9","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 $X$ be a compact metrizable space equipped with a continuous action of a countable amenable group $G$. Suppose that the dynamical system $(X,G)$ is expansive and is the quotient by a uniformly bounded-to-one factor map of a strongly irreducible subshift. Let $\\tau \\colon X \\to X$ be a continuous map commuting with the action of $G$. We prove that if there is no pair of distinct $G$-homoclinic points in $X$ having the same image under $\\tau$, then $\\tau$ is surjective.","authors_text":"Michel Coornaert, Tullio Ceccherini-Silberstein","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-30T10:57:32Z","title":"Expansive actions of countable amenable groups, homoclinic pairs, and the Myhill property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07553","kind":"arxiv","version":4},"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":"sha256:59cafd4b3c59e4385e04d09e75cf25abbf0d7b455498da5c9fd8c10936e8e19e","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":"c27b16c5333071d09f71e5203a4240a0fa4a0e94bca8b021b1a3e7f3a911e690","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-30T10:57:32Z","title_canon_sha256":"d70d7707e8628883c88daecf0adb9258f9a9dff8dfb66e9560adf2ec7367b9e6"},"schema_version":"1.0","source":{"id":"1508.07553","kind":"arxiv","version":4}},"canonical_sha256":"798e3b3ba5b939480d4588b55aee33339e6442f27e32abe61c26eaf842a79d84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"798e3b3ba5b939480d4588b55aee33339e6442f27e32abe61c26eaf842a79d84","first_computed_at":"2026-05-18T01:04:00.100451Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:00.100451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yWOZ3JBOTrQPwW6qjxeNwCgxKMfPnQyFtrC/UPTOKTTUUllf9zingzKl79NitR84lSq8dXMDgN8axBLVX/uRDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:00.101095Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07553","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59cafd4b3c59e4385e04d09e75cf25abbf0d7b455498da5c9fd8c10936e8e19e","sha256:e1dea791f9088b3785873507e8471e46651518b2f1d82757df97d7bb960a1aa9"],"state_sha256":"dcc03fa1d4e9c2d8c152e9c4510b63f41290c09648696c4a959d09031d0cddd4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0D0FEIK7rmQ+seVgysmSMb336nsmYO9nyS0QNAAqEb/q0t674Tg02F4FYv2SrhAwxpMW0NObZFgZu6YaLvnECg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T20:01:08.762989Z","bundle_sha256":"f12a71351b0bc49558c7b7839d5af4ba92b8380cb459c46220c105261f1f6334"}}