{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PPIVH636FZ47T7V7E4ZCKOEXKZ","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":"93d4cdbce754b961bc7be58f5c691683fe6a74bdad7e86644c2ac93a5986d1bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-10T03:06:41Z","title_canon_sha256":"6a8b3b9ec561a4cfff5c988881dabf87f3e14b5797b00b24efe3cf09bf51874a"},"schema_version":"1.0","source":{"id":"1209.1872","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1872","created_at":"2026-05-18T03:45:54Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1872v1","created_at":"2026-05-18T03:45:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1872","created_at":"2026-05-18T03:45:54Z"},{"alias_kind":"pith_short_12","alias_value":"PPIVH636FZ47","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PPIVH636FZ47T7V7","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PPIVH636","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:da84cdb27f554f399859166849d7a4cca9809e95f76871a5cb88e5ceb0bd6466","target":"graph","created_at":"2026-05-18T03:45:54Z","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":"We develop some aspects of a general theory of presentations of subshifts by labelled directed graphs, in particular by compact graphs. Also considered are synchronization properties of subshifts that lead to presentations by countable graphs.","authors_text":"Wolfgang Krieger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-10T03:06:41Z","title":"Presentations of symbolic dynamical systems by labelled directed graphs (Notes for a \"mini-cours\", SDA2, Paris 4-5 October 2007)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1872","kind":"arxiv","version":1},"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:dba5547bcf963691f86c83e47265b1bfa82bbfd4f1b9a59c303b4967b21d8d44","target":"record","created_at":"2026-05-18T03:45:54Z","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":"93d4cdbce754b961bc7be58f5c691683fe6a74bdad7e86644c2ac93a5986d1bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-10T03:06:41Z","title_canon_sha256":"6a8b3b9ec561a4cfff5c988881dabf87f3e14b5797b00b24efe3cf09bf51874a"},"schema_version":"1.0","source":{"id":"1209.1872","kind":"arxiv","version":1}},"canonical_sha256":"7bd153fb7e2e79f9febf27322538975659bd82c47be7002afde514cf0f972c83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7bd153fb7e2e79f9febf27322538975659bd82c47be7002afde514cf0f972c83","first_computed_at":"2026-05-18T03:45:54.140333Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:54.140333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cQiRBIWcRbnYg0GI7oGYZrgmzyW3mTLu6vuEQFJ6v3lCaNdj6nRhKuqOJAdsE+6OewPfIaVEKlaAtuRy/M29AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:54.140751Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.1872","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dba5547bcf963691f86c83e47265b1bfa82bbfd4f1b9a59c303b4967b21d8d44","sha256:da84cdb27f554f399859166849d7a4cca9809e95f76871a5cb88e5ceb0bd6466"],"state_sha256":"6a4b62ddd81439186dd1079904e059c3f6f3b1b7ba9662f4ca37984083144cd7"}