{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:SHBRAEVKVN4IZ56TMPZV7AHKLO","short_pith_number":"pith:SHBRAEVK","canonical_record":{"source":{"id":"1409.5585","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-09-19T10:31:26Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"6dc989ef502308bfb7647c002f48917ce2245b77e3469cf5d103398c0970c764","abstract_canon_sha256":"e022a79e56427ec6a0d2dda911161e55d28f1a02bd40647efcb9f41e2e5f5dfd"},"schema_version":"1.0"},"canonical_sha256":"91c31012aaab788cf7d363f35f80ea5ba9932a4e24853dce97f3e15e2a23c78c","source":{"kind":"arxiv","id":"1409.5585","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5585","created_at":"2026-05-18T00:12:41Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5585v2","created_at":"2026-05-18T00:12:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5585","created_at":"2026-05-18T00:12:41Z"},{"alias_kind":"pith_short_12","alias_value":"SHBRAEVKVN4I","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SHBRAEVKVN4IZ56T","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SHBRAEVK","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:SHBRAEVKVN4IZ56TMPZV7AHKLO","target":"record","payload":{"canonical_record":{"source":{"id":"1409.5585","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-09-19T10:31:26Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"6dc989ef502308bfb7647c002f48917ce2245b77e3469cf5d103398c0970c764","abstract_canon_sha256":"e022a79e56427ec6a0d2dda911161e55d28f1a02bd40647efcb9f41e2e5f5dfd"},"schema_version":"1.0"},"canonical_sha256":"91c31012aaab788cf7d363f35f80ea5ba9932a4e24853dce97f3e15e2a23c78c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:41.096119Z","signature_b64":"0FtXCbsqlNC9p2gEDC2c5h58N9hu75X5x9XTSRowps1uNmLmGNq1uDR/Roo3Pr/pug+sRIOgOT2uNk38LB00Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91c31012aaab788cf7d363f35f80ea5ba9932a4e24853dce97f3e15e2a23c78c","last_reissued_at":"2026-05-18T00:12:41.095590Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:41.095590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.5585","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":"2026-05-18T00:12:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2tRD9Ql3zpPITviGn2f1hKRsI7xgcEOUtxQTjL58pKBSpJfsLwjd3Sgi1aqXf48KDveTkD+4WLGJXMIxkR+jBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:41:33.011363Z"},"content_sha256":"7aa3d39480e0f9152f7ef80ab1ae3c12f6984771d90b5c314a3205d89931a490","schema_version":"1.0","event_id":"sha256:7aa3d39480e0f9152f7ef80ab1ae3c12f6984771d90b5c314a3205d89931a490"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:SHBRAEVKVN4IZ56TMPZV7AHKLO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamical systems in cosmology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"gr-qc","authors_text":"Christian G. Boehmer, Nyein Chan","submitted_at":"2014-09-19T10:31:26Z","abstract_excerpt":"Cosmology is a well established research area in physics while dynamical systems are well established in mathematics. It turns out that dynamical system techniques are very well suited to study many aspects of cosmology. The aim of this book chapter is to provide the reader with a concise introduction to both cosmology and dynamical system. The material is self-contained with references to more detailed work. It is aimed at applied mathematics and theoretical physics graduate level students who have an interest in this exciting topic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5585","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":"2026-05-18T00:12:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kqcAPJnfU9eAX1H+60ALEmGSRPKVytZoaBew0O4saXsa/qsBSDw+3YL53eimuEbI6MBVcyjD7HaGFfRwLYMeAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:41:33.011977Z"},"content_sha256":"009ba9f52a2eb73a1ac64d37859dd0cba9e8f014df7e0a493991b0980d60e39e","schema_version":"1.0","event_id":"sha256:009ba9f52a2eb73a1ac64d37859dd0cba9e8f014df7e0a493991b0980d60e39e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SHBRAEVKVN4IZ56TMPZV7AHKLO/bundle.json","state_url":"https://pith.science/pith/SHBRAEVKVN4IZ56TMPZV7AHKLO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SHBRAEVKVN4IZ56TMPZV7AHKLO/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":"2026-05-25T17:41:33Z","links":{"resolver":"https://pith.science/pith/SHBRAEVKVN4IZ56TMPZV7AHKLO","bundle":"https://pith.science/pith/SHBRAEVKVN4IZ56TMPZV7AHKLO/bundle.json","state":"https://pith.science/pith/SHBRAEVKVN4IZ56TMPZV7AHKLO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SHBRAEVKVN4IZ56TMPZV7AHKLO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SHBRAEVKVN4IZ56TMPZV7AHKLO","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":"e022a79e56427ec6a0d2dda911161e55d28f1a02bd40647efcb9f41e2e5f5dfd","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-09-19T10:31:26Z","title_canon_sha256":"6dc989ef502308bfb7647c002f48917ce2245b77e3469cf5d103398c0970c764"},"schema_version":"1.0","source":{"id":"1409.5585","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5585","created_at":"2026-05-18T00:12:41Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5585v2","created_at":"2026-05-18T00:12:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5585","created_at":"2026-05-18T00:12:41Z"},{"alias_kind":"pith_short_12","alias_value":"SHBRAEVKVN4I","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SHBRAEVKVN4IZ56T","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SHBRAEVK","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:009ba9f52a2eb73a1ac64d37859dd0cba9e8f014df7e0a493991b0980d60e39e","target":"graph","created_at":"2026-05-18T00:12:41Z","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":"Cosmology is a well established research area in physics while dynamical systems are well established in mathematics. It turns out that dynamical system techniques are very well suited to study many aspects of cosmology. The aim of this book chapter is to provide the reader with a concise introduction to both cosmology and dynamical system. The material is self-contained with references to more detailed work. It is aimed at applied mathematics and theoretical physics graduate level students who have an interest in this exciting topic.","authors_text":"Christian G. Boehmer, Nyein Chan","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-09-19T10:31:26Z","title":"Dynamical systems in cosmology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5585","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":"sha256:7aa3d39480e0f9152f7ef80ab1ae3c12f6984771d90b5c314a3205d89931a490","target":"record","created_at":"2026-05-18T00:12:41Z","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":"e022a79e56427ec6a0d2dda911161e55d28f1a02bd40647efcb9f41e2e5f5dfd","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-09-19T10:31:26Z","title_canon_sha256":"6dc989ef502308bfb7647c002f48917ce2245b77e3469cf5d103398c0970c764"},"schema_version":"1.0","source":{"id":"1409.5585","kind":"arxiv","version":2}},"canonical_sha256":"91c31012aaab788cf7d363f35f80ea5ba9932a4e24853dce97f3e15e2a23c78c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91c31012aaab788cf7d363f35f80ea5ba9932a4e24853dce97f3e15e2a23c78c","first_computed_at":"2026-05-18T00:12:41.095590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:41.095590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0FtXCbsqlNC9p2gEDC2c5h58N9hu75X5x9XTSRowps1uNmLmGNq1uDR/Roo3Pr/pug+sRIOgOT2uNk38LB00Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:41.096119Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.5585","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7aa3d39480e0f9152f7ef80ab1ae3c12f6984771d90b5c314a3205d89931a490","sha256:009ba9f52a2eb73a1ac64d37859dd0cba9e8f014df7e0a493991b0980d60e39e"],"state_sha256":"3489dde19a8012041898e7aa824506ca9e13f40b508731dc9ba57aa5a6fee386"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wuq3ys7aCLDhkGlMM3hqbz4xZPPCPzevi55xaxDqVEdbqyIobj06LKNympWbDtPQlvRPwwYl4cain5gB+NyBAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T17:41:33.015425Z","bundle_sha256":"90cefb843067f3542586d2a267a9eaa116269073b2320173039684ae76c990d2"}}