{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:EHS2XXAA52622TTAXR57LLRBF5","short_pith_number":"pith:EHS2XXAA","canonical_record":{"source":{"id":"0810.4632","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-10-25T17:57:02Z","cross_cats_sorted":[],"title_canon_sha256":"22659f6366336652b9b91dd6da6736434f9f194c7193ffaaa6d1488f43553e58","abstract_canon_sha256":"58dbc58751c78d4eae2d8de28f97ce4aae4dd7c8eae994cde1764d81618141b5"},"schema_version":"1.0"},"canonical_sha256":"21e5abdc00eebdad4e60bc7bf5ae212f79db1d484289ff316d0b036580e7b487","source":{"kind":"arxiv","id":"0810.4632","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.4632","created_at":"2026-05-18T03:06:22Z"},{"alias_kind":"arxiv_version","alias_value":"0810.4632v2","created_at":"2026-05-18T03:06:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.4632","created_at":"2026-05-18T03:06:22Z"},{"alias_kind":"pith_short_12","alias_value":"EHS2XXAA5262","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"EHS2XXAA52622TTA","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"EHS2XXAA","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:EHS2XXAA52622TTAXR57LLRBF5","target":"record","payload":{"canonical_record":{"source":{"id":"0810.4632","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-10-25T17:57:02Z","cross_cats_sorted":[],"title_canon_sha256":"22659f6366336652b9b91dd6da6736434f9f194c7193ffaaa6d1488f43553e58","abstract_canon_sha256":"58dbc58751c78d4eae2d8de28f97ce4aae4dd7c8eae994cde1764d81618141b5"},"schema_version":"1.0"},"canonical_sha256":"21e5abdc00eebdad4e60bc7bf5ae212f79db1d484289ff316d0b036580e7b487","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:22.925527Z","signature_b64":"rcDlJGBwWp/XNjVVLbDdJOjt5yWO5LbMBUdfETJb62kD8G4dRu6apCdLZ16k4JSZzSQ0VdSvojz+Ye0WdDZ0DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21e5abdc00eebdad4e60bc7bf5ae212f79db1d484289ff316d0b036580e7b487","last_reissued_at":"2026-05-18T03:06:22.925015Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:22.925015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0810.4632","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:06:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VC2105GoFrnasSmm3zRWpuxTTKjKay7v2g34gr1NcFIrsgVg1uM5SW/VX0nrODsxGZ6C8O0Oxf7uJXmSWuu4BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:46:50.453271Z"},"content_sha256":"83dcdb9328afba9d7a1d280d844ad2ca1465af9a21e1b395a20686daba1b0a5f","schema_version":"1.0","event_id":"sha256:83dcdb9328afba9d7a1d280d844ad2ca1465af9a21e1b395a20686daba1b0a5f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:EHS2XXAA52622TTAXR57LLRBF5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the existence of open and bi-continuing codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Uijin Jung","submitted_at":"2008-10-25T17:57:02Z","abstract_excerpt":"Given an irreducible sofic shift X, we show that an an irreducible SFT Y of lower entropy is a factor of X if and only if it is a factor of X by an open bi-continuing code. If these equivalent conditions hold and Y is mixing, then any code from a proper subshift of X to Y can be extended to an open bi-continuing code on X. These results are still valid when X is assumed to be only an almost specified shift, i.e., a subshift satisfying an irreducible version of the specification property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.4632","kind":"arxiv","version":2},"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":"2026-05-18T03:06:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xQLsG3I7+QpVCBh3UO5ib61rWnFz7zanILxrqcERx+23CtfSrqbRXdApS/w2FYVonWWiORIhaWXMCGbDKe0iAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:46:50.453631Z"},"content_sha256":"d8b640f2b4188c6a9863951381ba0f3864c6223fde7ab213394652bb6b424d1e","schema_version":"1.0","event_id":"sha256:d8b640f2b4188c6a9863951381ba0f3864c6223fde7ab213394652bb6b424d1e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EHS2XXAA52622TTAXR57LLRBF5/bundle.json","state_url":"https://pith.science/pith/EHS2XXAA52622TTAXR57LLRBF5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EHS2XXAA52622TTAXR57LLRBF5/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":"2026-06-09T13:46:50Z","links":{"resolver":"https://pith.science/pith/EHS2XXAA52622TTAXR57LLRBF5","bundle":"https://pith.science/pith/EHS2XXAA52622TTAXR57LLRBF5/bundle.json","state":"https://pith.science/pith/EHS2XXAA52622TTAXR57LLRBF5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EHS2XXAA52622TTAXR57LLRBF5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:EHS2XXAA52622TTAXR57LLRBF5","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":"58dbc58751c78d4eae2d8de28f97ce4aae4dd7c8eae994cde1764d81618141b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-10-25T17:57:02Z","title_canon_sha256":"22659f6366336652b9b91dd6da6736434f9f194c7193ffaaa6d1488f43553e58"},"schema_version":"1.0","source":{"id":"0810.4632","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.4632","created_at":"2026-05-18T03:06:22Z"},{"alias_kind":"arxiv_version","alias_value":"0810.4632v2","created_at":"2026-05-18T03:06:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.4632","created_at":"2026-05-18T03:06:22Z"},{"alias_kind":"pith_short_12","alias_value":"EHS2XXAA5262","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"EHS2XXAA52622TTA","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"EHS2XXAA","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:d8b640f2b4188c6a9863951381ba0f3864c6223fde7ab213394652bb6b424d1e","target":"graph","created_at":"2026-05-18T03:06:22Z","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":"Given an irreducible sofic shift X, we show that an an irreducible SFT Y of lower entropy is a factor of X if and only if it is a factor of X by an open bi-continuing code. If these equivalent conditions hold and Y is mixing, then any code from a proper subshift of X to Y can be extended to an open bi-continuing code on X. These results are still valid when X is assumed to be only an almost specified shift, i.e., a subshift satisfying an irreducible version of the specification property.","authors_text":"Uijin Jung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-10-25T17:57:02Z","title":"On the existence of open and bi-continuing codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.4632","kind":"arxiv","version":2},"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":"sha256:83dcdb9328afba9d7a1d280d844ad2ca1465af9a21e1b395a20686daba1b0a5f","target":"record","created_at":"2026-05-18T03:06:22Z","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":"58dbc58751c78d4eae2d8de28f97ce4aae4dd7c8eae994cde1764d81618141b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-10-25T17:57:02Z","title_canon_sha256":"22659f6366336652b9b91dd6da6736434f9f194c7193ffaaa6d1488f43553e58"},"schema_version":"1.0","source":{"id":"0810.4632","kind":"arxiv","version":2}},"canonical_sha256":"21e5abdc00eebdad4e60bc7bf5ae212f79db1d484289ff316d0b036580e7b487","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21e5abdc00eebdad4e60bc7bf5ae212f79db1d484289ff316d0b036580e7b487","first_computed_at":"2026-05-18T03:06:22.925015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:22.925015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rcDlJGBwWp/XNjVVLbDdJOjt5yWO5LbMBUdfETJb62kD8G4dRu6apCdLZ16k4JSZzSQ0VdSvojz+Ye0WdDZ0DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:22.925527Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.4632","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83dcdb9328afba9d7a1d280d844ad2ca1465af9a21e1b395a20686daba1b0a5f","sha256:d8b640f2b4188c6a9863951381ba0f3864c6223fde7ab213394652bb6b424d1e"],"state_sha256":"c9a88dd1886d1188e1aca6206334dc52a8e6366504ffdcc2a4da0adf0061a87a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tpLvRLJoOMesxxYCOKLP6Sy0G77IK03xgL4Fyz2TsX516W11meLwwA7hfgZ2giMgypTydKfeNgQq/Z23+rAyAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T13:46:50.455541Z","bundle_sha256":"ade088d8cb60c97a2c00ea7ae822947e4afdecd75196253f885687293751fe38"}}