{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:5M7BGGFB4M5LGSJDGCSUKKTFRT","short_pith_number":"pith:5M7BGGFB","canonical_record":{"source":{"id":"1902.00209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2019-02-01T07:44:43Z","cross_cats_sorted":[],"title_canon_sha256":"35f41d91fda18d462b05b8bc8170fc97f8eb654c5441fcf9bcbc54c318048594","abstract_canon_sha256":"8444cfe8d86771318e7245c7d7c5cdd7c27b7998f5e542023cfe51b2b9ad4db2"},"schema_version":"1.0"},"canonical_sha256":"eb3e1318a1e33ab3492330a5452a658cc9d2c91e1c6e582b053dd3df134b0e23","source":{"kind":"arxiv","id":"1902.00209","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00209","created_at":"2026-05-17T23:54:58Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00209v1","created_at":"2026-05-17T23:54:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00209","created_at":"2026-05-17T23:54:58Z"},{"alias_kind":"pith_short_12","alias_value":"5M7BGGFB4M5L","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"5M7BGGFB4M5LGSJD","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"5M7BGGFB","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:5M7BGGFB4M5LGSJDGCSUKKTFRT","target":"record","payload":{"canonical_record":{"source":{"id":"1902.00209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2019-02-01T07:44:43Z","cross_cats_sorted":[],"title_canon_sha256":"35f41d91fda18d462b05b8bc8170fc97f8eb654c5441fcf9bcbc54c318048594","abstract_canon_sha256":"8444cfe8d86771318e7245c7d7c5cdd7c27b7998f5e542023cfe51b2b9ad4db2"},"schema_version":"1.0"},"canonical_sha256":"eb3e1318a1e33ab3492330a5452a658cc9d2c91e1c6e582b053dd3df134b0e23","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:58.034797Z","signature_b64":"YL1P2YnAdUS81oDqQYR7ZCLoTJPhNHmgOqzdwCDPA83aUFPZepKGSXeZXZcdxxJlxPM19MHJ/IjNTFWcLGWjCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb3e1318a1e33ab3492330a5452a658cc9d2c91e1c6e582b053dd3df134b0e23","last_reissued_at":"2026-05-17T23:54:58.034332Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:58.034332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.00209","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":"2026-05-17T23:54:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zo532y429Nfda8bYqdvTckkB5pGOQIljB3zwhK1mfODuKlYuaDmk49Q9wT8V/WVdkFn+h+YDBacPNf1Z8xPHAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:15:25.854962Z"},"content_sha256":"02d5d6dfd60c56e7e8ed97eaa66632ec3a211de597de5863c350094af8190106","schema_version":"1.0","event_id":"sha256:02d5d6dfd60c56e7e8ed97eaa66632ec3a211de597de5863c350094af8190106"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:5M7BGGFB4M5LGSJDGCSUKKTFRT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A first approach to the Galois group of chaotic chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Stefan Groote","submitted_at":"2019-02-01T07:44:43Z","abstract_excerpt":"We explain in detail the definition, construction and generalisation of the Galois group of Chebyshev polynomials of high degree to the Galois group of chaotic chains. The calculations in this paper are performed for Chebyshev polynomials and chaotic chains of degree $N=2$. Insides into possible further steps are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00209","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":"2026-05-17T23:54:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TCf52PjsOVOQUT8auLQ/qoGqQVS0AERShXdB37QWH+xA5q5nnAw4EXgMZYAeasZFI12GIqWZuNKam+KQpXM9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:15:25.855616Z"},"content_sha256":"5b7e19160e9fa8c3eca971aad55cce916b7adbdbd8b081126d84b3b0a258a41c","schema_version":"1.0","event_id":"sha256:5b7e19160e9fa8c3eca971aad55cce916b7adbdbd8b081126d84b3b0a258a41c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5M7BGGFB4M5LGSJDGCSUKKTFRT/bundle.json","state_url":"https://pith.science/pith/5M7BGGFB4M5LGSJDGCSUKKTFRT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5M7BGGFB4M5LGSJDGCSUKKTFRT/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":"2026-05-27T19:15:25Z","links":{"resolver":"https://pith.science/pith/5M7BGGFB4M5LGSJDGCSUKKTFRT","bundle":"https://pith.science/pith/5M7BGGFB4M5LGSJDGCSUKKTFRT/bundle.json","state":"https://pith.science/pith/5M7BGGFB4M5LGSJDGCSUKKTFRT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5M7BGGFB4M5LGSJDGCSUKKTFRT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5M7BGGFB4M5LGSJDGCSUKKTFRT","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":"8444cfe8d86771318e7245c7d7c5cdd7c27b7998f5e542023cfe51b2b9ad4db2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2019-02-01T07:44:43Z","title_canon_sha256":"35f41d91fda18d462b05b8bc8170fc97f8eb654c5441fcf9bcbc54c318048594"},"schema_version":"1.0","source":{"id":"1902.00209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00209","created_at":"2026-05-17T23:54:58Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00209v1","created_at":"2026-05-17T23:54:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00209","created_at":"2026-05-17T23:54:58Z"},{"alias_kind":"pith_short_12","alias_value":"5M7BGGFB4M5L","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"5M7BGGFB4M5LGSJD","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"5M7BGGFB","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:5b7e19160e9fa8c3eca971aad55cce916b7adbdbd8b081126d84b3b0a258a41c","target":"graph","created_at":"2026-05-17T23:54:58Z","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 explain in detail the definition, construction and generalisation of the Galois group of Chebyshev polynomials of high degree to the Galois group of chaotic chains. The calculations in this paper are performed for Chebyshev polynomials and chaotic chains of degree $N=2$. Insides into possible further steps are given.","authors_text":"Stefan Groote","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2019-02-01T07:44:43Z","title":"A first approach to the Galois group of chaotic chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00209","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":"sha256:02d5d6dfd60c56e7e8ed97eaa66632ec3a211de597de5863c350094af8190106","target":"record","created_at":"2026-05-17T23:54:58Z","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":"8444cfe8d86771318e7245c7d7c5cdd7c27b7998f5e542023cfe51b2b9ad4db2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2019-02-01T07:44:43Z","title_canon_sha256":"35f41d91fda18d462b05b8bc8170fc97f8eb654c5441fcf9bcbc54c318048594"},"schema_version":"1.0","source":{"id":"1902.00209","kind":"arxiv","version":1}},"canonical_sha256":"eb3e1318a1e33ab3492330a5452a658cc9d2c91e1c6e582b053dd3df134b0e23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb3e1318a1e33ab3492330a5452a658cc9d2c91e1c6e582b053dd3df134b0e23","first_computed_at":"2026-05-17T23:54:58.034332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:58.034332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YL1P2YnAdUS81oDqQYR7ZCLoTJPhNHmgOqzdwCDPA83aUFPZepKGSXeZXZcdxxJlxPM19MHJ/IjNTFWcLGWjCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:58.034797Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.00209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02d5d6dfd60c56e7e8ed97eaa66632ec3a211de597de5863c350094af8190106","sha256:5b7e19160e9fa8c3eca971aad55cce916b7adbdbd8b081126d84b3b0a258a41c"],"state_sha256":"1b1743fd7f2ef50c8b8c97f4fca1fd24f2e242c970ae95cc4f0c9bfa1818f0a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k8s2KUc1FzxIrM9ZH97DnbULnduqbdNr7+UDBldebH3YqJAct15ymgbxy13aQHMYW/GqHIWGrmyAXxtygSRrBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T19:15:25.859013Z","bundle_sha256":"a203f51c212fb7c812a94723b8838678be9fc6ff64b87352ca5bcfb6b40deb54"}}