{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:RUVZVELKSTH2FEBHQDB4IAKIT3","short_pith_number":"pith:RUVZVELK","canonical_record":{"source":{"id":"1507.03393","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-13T11:07:34Z","cross_cats_sorted":[],"title_canon_sha256":"8576ee66477016feab1976309554e094d71f00852e2eb8d36e2c1cbaccd3bc1e","abstract_canon_sha256":"28410e74b853f517c811a04fa9021bb93d84368ca2b020407da12b91f7443eb3"},"schema_version":"1.0"},"canonical_sha256":"8d2b9a916a94cfa2902780c3c401489ed2720795e8db0d3189c7cc65c6e9e197","source":{"kind":"arxiv","id":"1507.03393","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.03393","created_at":"2026-05-18T00:03:29Z"},{"alias_kind":"arxiv_version","alias_value":"1507.03393v2","created_at":"2026-05-18T00:03:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03393","created_at":"2026-05-18T00:03:29Z"},{"alias_kind":"pith_short_12","alias_value":"RUVZVELKSTH2","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RUVZVELKSTH2FEBH","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RUVZVELK","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:RUVZVELKSTH2FEBHQDB4IAKIT3","target":"record","payload":{"canonical_record":{"source":{"id":"1507.03393","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-13T11:07:34Z","cross_cats_sorted":[],"title_canon_sha256":"8576ee66477016feab1976309554e094d71f00852e2eb8d36e2c1cbaccd3bc1e","abstract_canon_sha256":"28410e74b853f517c811a04fa9021bb93d84368ca2b020407da12b91f7443eb3"},"schema_version":"1.0"},"canonical_sha256":"8d2b9a916a94cfa2902780c3c401489ed2720795e8db0d3189c7cc65c6e9e197","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:29.850217Z","signature_b64":"zt6NCYl4V9PJ1BMSX5nrk87JRANC96FUbj3ZnnZxU3EcKKBydA3OGbCD9a532voRoNjr+UvXFeUCs3a7iYkOBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d2b9a916a94cfa2902780c3c401489ed2720795e8db0d3189c7cc65c6e9e197","last_reissued_at":"2026-05-18T00:03:29.849447Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:29.849447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.03393","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":"2026-05-18T00:03:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gRL5cnn7a2OF3WRAt3d8iH94sAsCmlbrznlxSSRAB8DpE//8r40+UhUpFtwNJ3JM/+yq64DWex4FTahnnCf0Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:54:10.859422Z"},"content_sha256":"add6598410dcab7e8970458a9f94b785738ab41c52f0e21ea7488a5861a566bf","schema_version":"1.0","event_id":"sha256:add6598410dcab7e8970458a9f94b785738ab41c52f0e21ea7488a5861a566bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:RUVZVELKSTH2FEBHQDB4IAKIT3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological Entropy of Formal Languages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Daniel Borchmann, Friedrich Martin Schneider","submitted_at":"2015-07-13T11:07:34Z","abstract_excerpt":"We introduce the notion of topological entropy of a formal languages as the topological entropy of the minimal topological automaton accepting it. Using a characterization of this notion in terms of approximations of the Myhill-Nerode congruence relation, we are able to compute the topological entropies of certain example languages. Those examples suggest that the notion of a \"simple\" formal language coincides with the language having zero entropy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03393","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":"2026-05-18T00:03:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V/NcMc6IDLGPOsfhHBlgk7IuQQqtmNuNZRMdQiqhX/bJ1ogx+FgzmEbet+rdrpSCSK0DSc1Ztnsa3rHD8ArtDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:54:10.859777Z"},"content_sha256":"e18abb451a4d4cea9360058545cde2871cdcca8b718499138801d54b95308e1a","schema_version":"1.0","event_id":"sha256:e18abb451a4d4cea9360058545cde2871cdcca8b718499138801d54b95308e1a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RUVZVELKSTH2FEBHQDB4IAKIT3/bundle.json","state_url":"https://pith.science/pith/RUVZVELKSTH2FEBHQDB4IAKIT3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RUVZVELKSTH2FEBHQDB4IAKIT3/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":"2026-06-23T02:54:10Z","links":{"resolver":"https://pith.science/pith/RUVZVELKSTH2FEBHQDB4IAKIT3","bundle":"https://pith.science/pith/RUVZVELKSTH2FEBHQDB4IAKIT3/bundle.json","state":"https://pith.science/pith/RUVZVELKSTH2FEBHQDB4IAKIT3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RUVZVELKSTH2FEBHQDB4IAKIT3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RUVZVELKSTH2FEBHQDB4IAKIT3","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":"28410e74b853f517c811a04fa9021bb93d84368ca2b020407da12b91f7443eb3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-13T11:07:34Z","title_canon_sha256":"8576ee66477016feab1976309554e094d71f00852e2eb8d36e2c1cbaccd3bc1e"},"schema_version":"1.0","source":{"id":"1507.03393","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.03393","created_at":"2026-05-18T00:03:29Z"},{"alias_kind":"arxiv_version","alias_value":"1507.03393v2","created_at":"2026-05-18T00:03:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03393","created_at":"2026-05-18T00:03:29Z"},{"alias_kind":"pith_short_12","alias_value":"RUVZVELKSTH2","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RUVZVELKSTH2FEBH","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RUVZVELK","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:e18abb451a4d4cea9360058545cde2871cdcca8b718499138801d54b95308e1a","target":"graph","created_at":"2026-05-18T00:03:29Z","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 introduce the notion of topological entropy of a formal languages as the topological entropy of the minimal topological automaton accepting it. Using a characterization of this notion in terms of approximations of the Myhill-Nerode congruence relation, we are able to compute the topological entropies of certain example languages. Those examples suggest that the notion of a \"simple\" formal language coincides with the language having zero entropy.","authors_text":"Daniel Borchmann, Friedrich Martin Schneider","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-13T11:07:34Z","title":"Topological Entropy of Formal Languages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03393","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:add6598410dcab7e8970458a9f94b785738ab41c52f0e21ea7488a5861a566bf","target":"record","created_at":"2026-05-18T00:03:29Z","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":"28410e74b853f517c811a04fa9021bb93d84368ca2b020407da12b91f7443eb3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-13T11:07:34Z","title_canon_sha256":"8576ee66477016feab1976309554e094d71f00852e2eb8d36e2c1cbaccd3bc1e"},"schema_version":"1.0","source":{"id":"1507.03393","kind":"arxiv","version":2}},"canonical_sha256":"8d2b9a916a94cfa2902780c3c401489ed2720795e8db0d3189c7cc65c6e9e197","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d2b9a916a94cfa2902780c3c401489ed2720795e8db0d3189c7cc65c6e9e197","first_computed_at":"2026-05-18T00:03:29.849447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:29.849447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zt6NCYl4V9PJ1BMSX5nrk87JRANC96FUbj3ZnnZxU3EcKKBydA3OGbCD9a532voRoNjr+UvXFeUCs3a7iYkOBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:29.850217Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.03393","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:add6598410dcab7e8970458a9f94b785738ab41c52f0e21ea7488a5861a566bf","sha256:e18abb451a4d4cea9360058545cde2871cdcca8b718499138801d54b95308e1a"],"state_sha256":"25b3e1c01bd21af972bcb31576c6ad874c4306330af8c607d86cdfd2f5c6dc3f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0jR5FX4hthB4eXIKugLEOK31rm8XvkumheskxTkfKSHqnJCXovIFwUFDqDPeTBJAMkz5PMZwHzpieX1KxSOGDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T02:54:10.862008Z","bundle_sha256":"69994a9a71d55363204e8faf7e4a43626ba7447d61eae9cf08617e7e806f395d"}}