{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TWMEXSNHCOSGUCMW5X4WSCXEL3","short_pith_number":"pith:TWMEXSNH","canonical_record":{"source":{"id":"1607.02401","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-07-08T15:08:44Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"d5119ed2a322bf3e4ef623372d3d5653522d4d3eeed82b2326a5b3c6bad6dc06","abstract_canon_sha256":"9f607d8a8b2259d524161ee6b79909148140075e2ecfbf9405b838c105e6bbd3"},"schema_version":"1.0"},"canonical_sha256":"9d984bc9a713a46a0996edf9690ae45efbf725ffed28739bca34e4f5d5937341","source":{"kind":"arxiv","id":"1607.02401","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.02401","created_at":"2026-05-18T00:56:45Z"},{"alias_kind":"arxiv_version","alias_value":"1607.02401v2","created_at":"2026-05-18T00:56:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02401","created_at":"2026-05-18T00:56:45Z"},{"alias_kind":"pith_short_12","alias_value":"TWMEXSNHCOSG","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TWMEXSNHCOSGUCMW","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TWMEXSNH","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TWMEXSNHCOSGUCMW5X4WSCXEL3","target":"record","payload":{"canonical_record":{"source":{"id":"1607.02401","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-07-08T15:08:44Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"d5119ed2a322bf3e4ef623372d3d5653522d4d3eeed82b2326a5b3c6bad6dc06","abstract_canon_sha256":"9f607d8a8b2259d524161ee6b79909148140075e2ecfbf9405b838c105e6bbd3"},"schema_version":"1.0"},"canonical_sha256":"9d984bc9a713a46a0996edf9690ae45efbf725ffed28739bca34e4f5d5937341","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:45.810296Z","signature_b64":"J0Q5/lzKMzK1Tf0fGewIUcq6pLyD2cTuXHkwmkpZjNQdDsiBb70cBYQ0NVIcE5KKp8ju9AA3nzOpYOZKJPd5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d984bc9a713a46a0996edf9690ae45efbf725ffed28739bca34e4f5d5937341","last_reissued_at":"2026-05-18T00:56:45.809684Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:45.809684Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.02401","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":"2026-05-18T00:56:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GY6Nmz66qnl/Kt+m+v/JBRdML+O3UdA6qkBypaBh0u7pfy2ySezG8/jdM0jxwW/rPisEcNXCo8d6JQVtTDwODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T18:37:15.167809Z"},"content_sha256":"10dd8006ab715ee1e761182d2038b4e21fdabab1eef029daa62e0835e4ce82d3","schema_version":"1.0","event_id":"sha256:10dd8006ab715ee1e761182d2038b4e21fdabab1eef029daa62e0835e4ce82d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TWMEXSNHCOSGUCMW5X4WSCXEL3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Degenerate Bogdanov-Takens Normal Form for FLRW Cosmologies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Ikjyot Singh Kohli, Michael C. Haslam","submitted_at":"2016-07-08T15:08:44Z","abstract_excerpt":"In this paper, we first show that the Einstein field equations for all perfect-fluid FLRW cosmologies can be written as a planar dynamical system with the equation of state parameter $w$ and cosmological constant $\\Lambda$ as parameters. An important equilibrium point of this dynamical system is the origin which represents Minkowski spacetime. It is shown that the Einstein field equations in a neigbourhood of this point are equivalent to a degenerate Bogdanov-Takens normal form. This normal form admits a set of equilibrium points that describes a set of solutions to the Einstein field equation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02401","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":"2026-05-18T00:56:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sYgEtWMeJTAUjVugSPzEgZ8EoqTHq6y5iiHshRBx8MoK+8pnIBEYYSwqvpuAOMSbgwXRzlVScVUjQXerAp+YDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T18:37:15.168431Z"},"content_sha256":"472b5bbed4cb70897075be91a7478e46406b86d706e401565935b148de6fcd24","schema_version":"1.0","event_id":"sha256:472b5bbed4cb70897075be91a7478e46406b86d706e401565935b148de6fcd24"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TWMEXSNHCOSGUCMW5X4WSCXEL3/bundle.json","state_url":"https://pith.science/pith/TWMEXSNHCOSGUCMW5X4WSCXEL3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TWMEXSNHCOSGUCMW5X4WSCXEL3/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":"2026-08-17T18:37:15Z","links":{"resolver":"https://pith.science/pith/TWMEXSNHCOSGUCMW5X4WSCXEL3","bundle":"https://pith.science/pith/TWMEXSNHCOSGUCMW5X4WSCXEL3/bundle.json","state":"https://pith.science/pith/TWMEXSNHCOSGUCMW5X4WSCXEL3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TWMEXSNHCOSGUCMW5X4WSCXEL3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TWMEXSNHCOSGUCMW5X4WSCXEL3","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":"9f607d8a8b2259d524161ee6b79909148140075e2ecfbf9405b838c105e6bbd3","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-07-08T15:08:44Z","title_canon_sha256":"d5119ed2a322bf3e4ef623372d3d5653522d4d3eeed82b2326a5b3c6bad6dc06"},"schema_version":"1.0","source":{"id":"1607.02401","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.02401","created_at":"2026-05-18T00:56:45Z"},{"alias_kind":"arxiv_version","alias_value":"1607.02401v2","created_at":"2026-05-18T00:56:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02401","created_at":"2026-05-18T00:56:45Z"},{"alias_kind":"pith_short_12","alias_value":"TWMEXSNHCOSG","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TWMEXSNHCOSGUCMW","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TWMEXSNH","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:472b5bbed4cb70897075be91a7478e46406b86d706e401565935b148de6fcd24","target":"graph","created_at":"2026-05-18T00:56:45Z","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":"In this paper, we first show that the Einstein field equations for all perfect-fluid FLRW cosmologies can be written as a planar dynamical system with the equation of state parameter $w$ and cosmological constant $\\Lambda$ as parameters. An important equilibrium point of this dynamical system is the origin which represents Minkowski spacetime. It is shown that the Einstein field equations in a neigbourhood of this point are equivalent to a degenerate Bogdanov-Takens normal form. This normal form admits a set of equilibrium points that describes a set of solutions to the Einstein field equation","authors_text":"Ikjyot Singh Kohli, Michael C. Haslam","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-07-08T15:08:44Z","title":"A Degenerate Bogdanov-Takens Normal Form for FLRW Cosmologies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02401","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":"sha256:10dd8006ab715ee1e761182d2038b4e21fdabab1eef029daa62e0835e4ce82d3","target":"record","created_at":"2026-05-18T00:56:45Z","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":"9f607d8a8b2259d524161ee6b79909148140075e2ecfbf9405b838c105e6bbd3","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-07-08T15:08:44Z","title_canon_sha256":"d5119ed2a322bf3e4ef623372d3d5653522d4d3eeed82b2326a5b3c6bad6dc06"},"schema_version":"1.0","source":{"id":"1607.02401","kind":"arxiv","version":2}},"canonical_sha256":"9d984bc9a713a46a0996edf9690ae45efbf725ffed28739bca34e4f5d5937341","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d984bc9a713a46a0996edf9690ae45efbf725ffed28739bca34e4f5d5937341","first_computed_at":"2026-05-18T00:56:45.809684Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:45.809684Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J0Q5/lzKMzK1Tf0fGewIUcq6pLyD2cTuXHkwmkpZjNQdDsiBb70cBYQ0NVIcE5KKp8ju9AA3nzOpYOZKJPd5Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:45.810296Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.02401","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10dd8006ab715ee1e761182d2038b4e21fdabab1eef029daa62e0835e4ce82d3","sha256:472b5bbed4cb70897075be91a7478e46406b86d706e401565935b148de6fcd24"],"state_sha256":"12f5591d1793a428613f8600ac5dd23535c56db1d025e5f8572ce3e921936d0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+56JvOmDgfD8OQKKOKnwSdID39fLnOsjgeEnILIotCyZcep+6WuIXxlj6+tKTCYkTqX+g+MajCo/qrLncT9kAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T18:37:15.172157Z","bundle_sha256":"252f636f4743f7e2e029f8283a029bd49e7b1136183f5004199dd11dcd5aa077"}}