{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:U26VUAMBWBCR4VPGDY3DX3PEIA","short_pith_number":"pith:U26VUAMB","canonical_record":{"source":{"id":"1507.05216","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-07-18T18:55:44Z","cross_cats_sorted":[],"title_canon_sha256":"69bdf963ded35c2483eea61e7d96d6c69f0c38af0a7155898c6383977be05b01","abstract_canon_sha256":"b3f46bf4ca69f8d01dfcffbe5380c4e0bb0c2870c7b8f095a2873cdc9ab30517"},"schema_version":"1.0"},"canonical_sha256":"a6bd5a0181b0451e55e61e363bede4401fc56f3ff317692d4895160e9ab54963","source":{"kind":"arxiv","id":"1507.05216","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05216","created_at":"2026-05-18T01:35:06Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05216v1","created_at":"2026-05-18T01:35:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05216","created_at":"2026-05-18T01:35:06Z"},{"alias_kind":"pith_short_12","alias_value":"U26VUAMBWBCR","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"U26VUAMBWBCR4VPG","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"U26VUAMB","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:U26VUAMBWBCR4VPGDY3DX3PEIA","target":"record","payload":{"canonical_record":{"source":{"id":"1507.05216","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-07-18T18:55:44Z","cross_cats_sorted":[],"title_canon_sha256":"69bdf963ded35c2483eea61e7d96d6c69f0c38af0a7155898c6383977be05b01","abstract_canon_sha256":"b3f46bf4ca69f8d01dfcffbe5380c4e0bb0c2870c7b8f095a2873cdc9ab30517"},"schema_version":"1.0"},"canonical_sha256":"a6bd5a0181b0451e55e61e363bede4401fc56f3ff317692d4895160e9ab54963","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:06.772861Z","signature_b64":"ifRZ9pmWtbpA/cN1WpwgSwjHIlWW4Y8SAI8HCRqotmDmT+o09SPL9bn7mN+OKxopNrakmWQwANBnjFU4hsx1CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6bd5a0181b0451e55e61e363bede4401fc56f3ff317692d4895160e9ab54963","last_reissued_at":"2026-05-18T01:35:06.772356Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:06.772356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.05216","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":"2026-05-18T01:35:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dasAG/8iZ9dvd+lP7C+51pIeOc4SVHnxB20SPNDmH7oYipBQC+v1BLLQ19bOw3JDNqDUYaohkVRNw7NDluAEAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:27:50.203441Z"},"content_sha256":"c32f4b4ca4732e8ee40850df3aa79aa4473f3cd5a3cc11da60d29276cdb9299d","schema_version":"1.0","event_id":"sha256:c32f4b4ca4732e8ee40850df3aa79aa4473f3cd5a3cc11da60d29276cdb9299d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:U26VUAMBWBCR4VPGDY3DX3PEIA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cosmological Models Coupled with Dark Matter in a Dissipative Universe","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"A. V. Timoshkin, I. Brevik, V. V. Obukhov","submitted_at":"2015-07-18T18:55:44Z","abstract_excerpt":"We consider the cosmological system with two interacting fluids: dark energy and dark matter, in a homogeneous and isotropic universe with dissipation. The modified gravitational equation for dark matter is solved. The analytic representations for the Little Rip, the Pseudo Rip, and the bounce cosmology models with dissipation are obtained in terms of the thermodynamic parameters in the equation of state. We analyze the corrections in the energy density for dark matter, in view of the dissipative processes and the coupling with dark energy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05216","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":"2026-05-18T01:35:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qHcLYIxyZd60ULKDGu6pPOGkIo7Br62yKomidXaoy+0pokLidWNKlusoEKHQ4oEb+UCTyr2REXCt4q/1OK4kDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:27:50.204116Z"},"content_sha256":"1c1cd45b80f718fc45a61d4330e300e7bb6dd3f537b20fc0ccbe2febb92be975","schema_version":"1.0","event_id":"sha256:1c1cd45b80f718fc45a61d4330e300e7bb6dd3f537b20fc0ccbe2febb92be975"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U26VUAMBWBCR4VPGDY3DX3PEIA/bundle.json","state_url":"https://pith.science/pith/U26VUAMBWBCR4VPGDY3DX3PEIA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U26VUAMBWBCR4VPGDY3DX3PEIA/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":"2026-05-25T09:27:50Z","links":{"resolver":"https://pith.science/pith/U26VUAMBWBCR4VPGDY3DX3PEIA","bundle":"https://pith.science/pith/U26VUAMBWBCR4VPGDY3DX3PEIA/bundle.json","state":"https://pith.science/pith/U26VUAMBWBCR4VPGDY3DX3PEIA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U26VUAMBWBCR4VPGDY3DX3PEIA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:U26VUAMBWBCR4VPGDY3DX3PEIA","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":"b3f46bf4ca69f8d01dfcffbe5380c4e0bb0c2870c7b8f095a2873cdc9ab30517","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-07-18T18:55:44Z","title_canon_sha256":"69bdf963ded35c2483eea61e7d96d6c69f0c38af0a7155898c6383977be05b01"},"schema_version":"1.0","source":{"id":"1507.05216","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05216","created_at":"2026-05-18T01:35:06Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05216v1","created_at":"2026-05-18T01:35:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05216","created_at":"2026-05-18T01:35:06Z"},{"alias_kind":"pith_short_12","alias_value":"U26VUAMBWBCR","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"U26VUAMBWBCR4VPG","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"U26VUAMB","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:1c1cd45b80f718fc45a61d4330e300e7bb6dd3f537b20fc0ccbe2febb92be975","target":"graph","created_at":"2026-05-18T01:35:06Z","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 consider the cosmological system with two interacting fluids: dark energy and dark matter, in a homogeneous and isotropic universe with dissipation. The modified gravitational equation for dark matter is solved. The analytic representations for the Little Rip, the Pseudo Rip, and the bounce cosmology models with dissipation are obtained in terms of the thermodynamic parameters in the equation of state. We analyze the corrections in the energy density for dark matter, in view of the dissipative processes and the coupling with dark energy.","authors_text":"A. V. Timoshkin, I. Brevik, V. V. Obukhov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-07-18T18:55:44Z","title":"Cosmological Models Coupled with Dark Matter in a Dissipative Universe"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05216","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:c32f4b4ca4732e8ee40850df3aa79aa4473f3cd5a3cc11da60d29276cdb9299d","target":"record","created_at":"2026-05-18T01:35:06Z","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":"b3f46bf4ca69f8d01dfcffbe5380c4e0bb0c2870c7b8f095a2873cdc9ab30517","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-07-18T18:55:44Z","title_canon_sha256":"69bdf963ded35c2483eea61e7d96d6c69f0c38af0a7155898c6383977be05b01"},"schema_version":"1.0","source":{"id":"1507.05216","kind":"arxiv","version":1}},"canonical_sha256":"a6bd5a0181b0451e55e61e363bede4401fc56f3ff317692d4895160e9ab54963","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6bd5a0181b0451e55e61e363bede4401fc56f3ff317692d4895160e9ab54963","first_computed_at":"2026-05-18T01:35:06.772356Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:06.772356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ifRZ9pmWtbpA/cN1WpwgSwjHIlWW4Y8SAI8HCRqotmDmT+o09SPL9bn7mN+OKxopNrakmWQwANBnjFU4hsx1CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:06.772861Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.05216","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c32f4b4ca4732e8ee40850df3aa79aa4473f3cd5a3cc11da60d29276cdb9299d","sha256:1c1cd45b80f718fc45a61d4330e300e7bb6dd3f537b20fc0ccbe2febb92be975"],"state_sha256":"230d6c0ebdf12032f08d1c769913ed349f977a09024fa01a25b5ffe7170ed5b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gwDU8hwomJPS4GgsMjv9Hn+df4bbKw/eWZryIxutSnPdBLCdUWd6ZtgP+l2o+h1JhL5uMHsJWCB6LFO/ADnfDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T09:27:50.207655Z","bundle_sha256":"a7711e3bce2dd47fd00d1b11b1773d6e14082d0a281066ed6b6cbeabd656a9b5"}}