{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:SMSDGKOF2OH2JOJCHMCVGUG2R7","short_pith_number":"pith:SMSDGKOF","canonical_record":{"source":{"id":"2106.06432","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-06-11T14:42:08Z","cross_cats_sorted":[],"title_canon_sha256":"1bfc155ee76bbf9d8ac5ed9780a31f5ef19891868e3af83b2072e25a17c44fbc","abstract_canon_sha256":"e132fa49f435203c6bd21fb297b20bc3177119cb20fbd6c4f1d4a67656a96824"},"schema_version":"1.0"},"canonical_sha256":"93243329c5d38fa4b9223b055350da8fc30c2a117db65b1ba29713b60b518c33","source":{"kind":"arxiv","id":"2106.06432","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.06432","created_at":"2026-07-05T03:10:40Z"},{"alias_kind":"arxiv_version","alias_value":"2106.06432v2","created_at":"2026-07-05T03:10:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.06432","created_at":"2026-07-05T03:10:40Z"},{"alias_kind":"pith_short_12","alias_value":"SMSDGKOF2OH2","created_at":"2026-07-05T03:10:40Z"},{"alias_kind":"pith_short_16","alias_value":"SMSDGKOF2OH2JOJC","created_at":"2026-07-05T03:10:40Z"},{"alias_kind":"pith_short_8","alias_value":"SMSDGKOF","created_at":"2026-07-05T03:10:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:SMSDGKOF2OH2JOJCHMCVGUG2R7","target":"record","payload":{"canonical_record":{"source":{"id":"2106.06432","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-06-11T14:42:08Z","cross_cats_sorted":[],"title_canon_sha256":"1bfc155ee76bbf9d8ac5ed9780a31f5ef19891868e3af83b2072e25a17c44fbc","abstract_canon_sha256":"e132fa49f435203c6bd21fb297b20bc3177119cb20fbd6c4f1d4a67656a96824"},"schema_version":"1.0"},"canonical_sha256":"93243329c5d38fa4b9223b055350da8fc30c2a117db65b1ba29713b60b518c33","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:10:40.323505Z","signature_b64":"JDoM/JcwSdTXDT8Xq8KLvB0AvJBAits/bDhP8WL9auduvJ1jG/ARH7U57Sa4qs9hLPfHGYwJi4A8eaoaE6BKBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93243329c5d38fa4b9223b055350da8fc30c2a117db65b1ba29713b60b518c33","last_reissued_at":"2026-07-05T03:10:40.323050Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:10:40.323050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2106.06432","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":"2026-07-05T03:10:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b1fwqxuB/py0SXkCrggynbbN+PDfndYXiDx4l67kwzo86idtVWSCM1QuJgTKBFAqKWT12Lzo6bznIxFonsDiCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T15:09:22.389428Z"},"content_sha256":"11dd3a311c1063100341384db7036d6b69182be1c37ac59ea5624293b8e60732","schema_version":"1.0","event_id":"sha256:11dd3a311c1063100341384db7036d6b69182be1c37ac59ea5624293b8e60732"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:SMSDGKOF2OH2JOJCHMCVGUG2R7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Anisotropic $k$-essence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"C\\'esar A. Valenzuela-Toledo, J. Bayron Orjuela-Quintana","submitted_at":"2021-06-11T14:42:08Z","abstract_excerpt":"In this paper, we study the late time cosmology of a non-canonical scalar field ($k$-essence) coupled to a vector field in a Bianchi-I background. Specifically, we study three cases: canonical scalar field (quintessence) with exponential potential as a warm up, the dilatonic ghost condensate, and the Dirac Born Infeld field with exponentials throat and potential. By using a dynamical system approach, we show that anisotropic dark energy fixed points can be attractors for a suitable set of parameters of each model. We also numerically integrate the associated autonomous systems for particular i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.06432","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.06432/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:10:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MxDHeNYAzfdzkW2dhFjwTLWhn+1+RuUMuoqKItiY7ZgFVMTI8D25AN524F89QPr806HZohtfl2EPQVRJhdxMAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T15:09:22.390235Z"},"content_sha256":"e9cd0444be1251e4bbfc8afd1c8aac02e490cec438b562943715b3852aeb4fad","schema_version":"1.0","event_id":"sha256:e9cd0444be1251e4bbfc8afd1c8aac02e490cec438b562943715b3852aeb4fad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SMSDGKOF2OH2JOJCHMCVGUG2R7/bundle.json","state_url":"https://pith.science/pith/SMSDGKOF2OH2JOJCHMCVGUG2R7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SMSDGKOF2OH2JOJCHMCVGUG2R7/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":"2026-08-12T15:09:22Z","links":{"resolver":"https://pith.science/pith/SMSDGKOF2OH2JOJCHMCVGUG2R7","bundle":"https://pith.science/pith/SMSDGKOF2OH2JOJCHMCVGUG2R7/bundle.json","state":"https://pith.science/pith/SMSDGKOF2OH2JOJCHMCVGUG2R7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SMSDGKOF2OH2JOJCHMCVGUG2R7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:SMSDGKOF2OH2JOJCHMCVGUG2R7","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":"e132fa49f435203c6bd21fb297b20bc3177119cb20fbd6c4f1d4a67656a96824","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-06-11T14:42:08Z","title_canon_sha256":"1bfc155ee76bbf9d8ac5ed9780a31f5ef19891868e3af83b2072e25a17c44fbc"},"schema_version":"1.0","source":{"id":"2106.06432","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.06432","created_at":"2026-07-05T03:10:40Z"},{"alias_kind":"arxiv_version","alias_value":"2106.06432v2","created_at":"2026-07-05T03:10:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.06432","created_at":"2026-07-05T03:10:40Z"},{"alias_kind":"pith_short_12","alias_value":"SMSDGKOF2OH2","created_at":"2026-07-05T03:10:40Z"},{"alias_kind":"pith_short_16","alias_value":"SMSDGKOF2OH2JOJC","created_at":"2026-07-05T03:10:40Z"},{"alias_kind":"pith_short_8","alias_value":"SMSDGKOF","created_at":"2026-07-05T03:10:40Z"}],"graph_snapshots":[{"event_id":"sha256:e9cd0444be1251e4bbfc8afd1c8aac02e490cec438b562943715b3852aeb4fad","target":"graph","created_at":"2026-07-05T03:10:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2106.06432/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the late time cosmology of a non-canonical scalar field ($k$-essence) coupled to a vector field in a Bianchi-I background. Specifically, we study three cases: canonical scalar field (quintessence) with exponential potential as a warm up, the dilatonic ghost condensate, and the Dirac Born Infeld field with exponentials throat and potential. By using a dynamical system approach, we show that anisotropic dark energy fixed points can be attractors for a suitable set of parameters of each model. We also numerically integrate the associated autonomous systems for particular i","authors_text":"C\\'esar A. Valenzuela-Toledo, J. Bayron Orjuela-Quintana","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-06-11T14:42:08Z","title":"Anisotropic $k$-essence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.06432","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":"sha256:11dd3a311c1063100341384db7036d6b69182be1c37ac59ea5624293b8e60732","target":"record","created_at":"2026-07-05T03:10:40Z","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":"e132fa49f435203c6bd21fb297b20bc3177119cb20fbd6c4f1d4a67656a96824","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-06-11T14:42:08Z","title_canon_sha256":"1bfc155ee76bbf9d8ac5ed9780a31f5ef19891868e3af83b2072e25a17c44fbc"},"schema_version":"1.0","source":{"id":"2106.06432","kind":"arxiv","version":2}},"canonical_sha256":"93243329c5d38fa4b9223b055350da8fc30c2a117db65b1ba29713b60b518c33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93243329c5d38fa4b9223b055350da8fc30c2a117db65b1ba29713b60b518c33","first_computed_at":"2026-07-05T03:10:40.323050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:10:40.323050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JDoM/JcwSdTXDT8Xq8KLvB0AvJBAits/bDhP8WL9auduvJ1jG/ARH7U57Sa4qs9hLPfHGYwJi4A8eaoaE6BKBg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:10:40.323505Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.06432","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11dd3a311c1063100341384db7036d6b69182be1c37ac59ea5624293b8e60732","sha256:e9cd0444be1251e4bbfc8afd1c8aac02e490cec438b562943715b3852aeb4fad"],"state_sha256":"b62b6c418645a62734f9cbdaccc7a03945e5c30782817b5c76cb754cf4eddbcc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4v3jyRTQYdU4p82WVkdYIjamP6yeVo/fSwQefM9i46ZTJ6QjH3lRB9KtZtYiKDk3gFkljBWWWUDFPNmVcur8AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T15:09:22.396617Z","bundle_sha256":"fba78169f09853a78940facd264b0cc5ec7d36b545fc26eb11c3fabe951a7598"}}