{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PPIVH636FZ47T7V7E4ZCKOEXKZ","short_pith_number":"pith:PPIVH636","canonical_record":{"source":{"id":"1209.1872","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-10T03:06:41Z","cross_cats_sorted":[],"title_canon_sha256":"6a8b3b9ec561a4cfff5c988881dabf87f3e14b5797b00b24efe3cf09bf51874a","abstract_canon_sha256":"93d4cdbce754b961bc7be58f5c691683fe6a74bdad7e86644c2ac93a5986d1bb"},"schema_version":"1.0"},"canonical_sha256":"7bd153fb7e2e79f9febf27322538975659bd82c47be7002afde514cf0f972c83","source":{"kind":"arxiv","id":"1209.1872","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PPIVH636FZ47T7V7E4ZCKOEXKZ","target":"record","payload":{"canonical_record":{"source":{"id":"1209.1872","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-10T03:06:41Z","cross_cats_sorted":[],"title_canon_sha256":"6a8b3b9ec561a4cfff5c988881dabf87f3e14b5797b00b24efe3cf09bf51874a","abstract_canon_sha256":"93d4cdbce754b961bc7be58f5c691683fe6a74bdad7e86644c2ac93a5986d1bb"},"schema_version":"1.0"},"canonical_sha256":"7bd153fb7e2e79f9febf27322538975659bd82c47be7002afde514cf0f972c83","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:54.140751Z","signature_b64":"cQiRBIWcRbnYg0GI7oGYZrgmzyW3mTLu6vuEQFJ6v3lCaNdj6nRhKuqOJAdsE+6OewPfIaVEKlaAtuRy/M29AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bd153fb7e2e79f9febf27322538975659bd82c47be7002afde514cf0f972c83","last_reissued_at":"2026-05-18T03:45:54.140333Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:54.140333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.1872","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:45:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"efwl3ecZFXYZzhWajNPYENF80ZgZJnLDufPUgGtujJ/QaT24yLAb0Y6TuoN3eBKJhBs8qRfvFvgj8UbWsmGZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T10:45:15.649469Z"},"content_sha256":"dba5547bcf963691f86c83e47265b1bfa82bbfd4f1b9a59c303b4967b21d8d44","schema_version":"1.0","event_id":"sha256:dba5547bcf963691f86c83e47265b1bfa82bbfd4f1b9a59c303b4967b21d8d44"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PPIVH636FZ47T7V7E4ZCKOEXKZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Presentations of symbolic dynamical systems by labelled directed graphs (Notes for a \"mini-cours\", SDA2, Paris 4-5 October 2007)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Wolfgang Krieger","submitted_at":"2012-09-10T03:06:41Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1872","kind":"arxiv","version":1},"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":"2026-05-18T03:45:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wHPQ2GRzdkjCVOjl40bo8fziIfAib6Sws4cMft8S1MbFGm44pZ8ZVSsr/ohC8lQqLdJ7Cc5MMJYALZAc4PfHAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T10:45:15.649813Z"},"content_sha256":"da84cdb27f554f399859166849d7a4cca9809e95f76871a5cb88e5ceb0bd6466","schema_version":"1.0","event_id":"sha256:da84cdb27f554f399859166849d7a4cca9809e95f76871a5cb88e5ceb0bd6466"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PPIVH636FZ47T7V7E4ZCKOEXKZ/bundle.json","state_url":"https://pith.science/pith/PPIVH636FZ47T7V7E4ZCKOEXKZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PPIVH636FZ47T7V7E4ZCKOEXKZ/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":"2026-07-03T10:45:15Z","links":{"resolver":"https://pith.science/pith/PPIVH636FZ47T7V7E4ZCKOEXKZ","bundle":"https://pith.science/pith/PPIVH636FZ47T7V7E4ZCKOEXKZ/bundle.json","state":"https://pith.science/pith/PPIVH636FZ47T7V7E4ZCKOEXKZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PPIVH636FZ47T7V7E4ZCKOEXKZ/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hCFlowiJ7qFVDvfjXUynxeuIwgQj2oxYgWQZpf6mWqgGckh5PogLxrQjw57qirvVQFbwubgdPaXjqdFcKsqiDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T10:45:15.651764Z","bundle_sha256":"a0d1020721d65c48dab930183c05acd476bf35f02b18402257207813be6022e5"}}