{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4SR4F34E7KDDD44DAZ4GEGRI6K","short_pith_number":"pith:4SR4F34E","canonical_record":{"source":{"id":"1608.05732","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-19T20:33:56Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"93ff5b6f9d905dc8180291d519115f18b000897758bcbb0bdde4bf29ae533803","abstract_canon_sha256":"474d24c3e513970073c58e3a540f9c4b115a21e3049718a53c02ba000a0db757"},"schema_version":"1.0"},"canonical_sha256":"e4a3c2ef84fa8631f3830678621a28f2824c3df7f0ae57fcba820ce0b95184aa","source":{"kind":"arxiv","id":"1608.05732","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05732","created_at":"2026-05-18T00:01:19Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05732v2","created_at":"2026-05-18T00:01:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05732","created_at":"2026-05-18T00:01:19Z"},{"alias_kind":"pith_short_12","alias_value":"4SR4F34E7KDD","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4SR4F34E7KDDD44D","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4SR4F34E","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4SR4F34E7KDDD44DAZ4GEGRI6K","target":"record","payload":{"canonical_record":{"source":{"id":"1608.05732","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-19T20:33:56Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"93ff5b6f9d905dc8180291d519115f18b000897758bcbb0bdde4bf29ae533803","abstract_canon_sha256":"474d24c3e513970073c58e3a540f9c4b115a21e3049718a53c02ba000a0db757"},"schema_version":"1.0"},"canonical_sha256":"e4a3c2ef84fa8631f3830678621a28f2824c3df7f0ae57fcba820ce0b95184aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:19.874878Z","signature_b64":"nT6LvvdhXszEwJbG7Txam/f7MOgDw3tV2s3FY2t/ryNVQzzFOzTC3pWI/ZHqjJPZkAr06DGS8fLBn7WURE4PDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4a3c2ef84fa8631f3830678621a28f2824c3df7f0ae57fcba820ce0b95184aa","last_reissued_at":"2026-05-18T00:01:19.874430Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:19.874430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.05732","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":"2026-05-18T00:01:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZRN575OPa1N0Uha/NS9EE3Au42oF1cMB7Zs3nBjfcTL4U0fAZBKCPGourOmUdJ+4pSYA1HhX5S9avVhh2z6NDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:47:40.573051Z"},"content_sha256":"aeeffe283decadf0fca7062b7d25435569a99b2f237fadd7a6fbfa76d5f5c1ff","schema_version":"1.0","event_id":"sha256:aeeffe283decadf0fca7062b7d25435569a99b2f237fadd7a6fbfa76d5f5c1ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4SR4F34E7KDDD44DAZ4GEGRI6K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hamiltonian Dynamics of Cosmological Quintessence Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Emil M. Prodanov, Rossen I. Ivanov","submitted_at":"2016-08-19T20:33:56Z","abstract_excerpt":"The time-evolution dynamics of two nonlinear cosmological real gas models has been reexamined in detail with methods from the theory of Hamiltonian dynamical systems. These examples are FRWL cosmologies, one based on a gas, satisfying the van der Waals equation and another one based on the virial expansion gas equation. The cosmological variables used are the expansion rate, given by the Hubble parameter, and the energy density. The analysis is aided by the existence of global first integral as well as several special (second) integrals in each case. In addition, the global first integral can "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05732","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":"2026-05-18T00:01:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8UjPiNWEcGB4EEdRi3376LSs1qjihkD89ofi/ci98+AZflPrFggTZmBgIw9ywzVJ89d8mlzxWnX2blcZVI8mCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:47:40.573712Z"},"content_sha256":"568c001fe734b9bf20dc7d1db0dd69bd25f377ef9b342d6059a7e4e0e49192a8","schema_version":"1.0","event_id":"sha256:568c001fe734b9bf20dc7d1db0dd69bd25f377ef9b342d6059a7e4e0e49192a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4SR4F34E7KDDD44DAZ4GEGRI6K/bundle.json","state_url":"https://pith.science/pith/4SR4F34E7KDDD44DAZ4GEGRI6K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4SR4F34E7KDDD44DAZ4GEGRI6K/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":"2026-06-04T02:47:40Z","links":{"resolver":"https://pith.science/pith/4SR4F34E7KDDD44DAZ4GEGRI6K","bundle":"https://pith.science/pith/4SR4F34E7KDDD44DAZ4GEGRI6K/bundle.json","state":"https://pith.science/pith/4SR4F34E7KDDD44DAZ4GEGRI6K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4SR4F34E7KDDD44DAZ4GEGRI6K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4SR4F34E7KDDD44DAZ4GEGRI6K","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":"474d24c3e513970073c58e3a540f9c4b115a21e3049718a53c02ba000a0db757","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-19T20:33:56Z","title_canon_sha256":"93ff5b6f9d905dc8180291d519115f18b000897758bcbb0bdde4bf29ae533803"},"schema_version":"1.0","source":{"id":"1608.05732","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05732","created_at":"2026-05-18T00:01:19Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05732v2","created_at":"2026-05-18T00:01:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05732","created_at":"2026-05-18T00:01:19Z"},{"alias_kind":"pith_short_12","alias_value":"4SR4F34E7KDD","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4SR4F34E7KDDD44D","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4SR4F34E","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:568c001fe734b9bf20dc7d1db0dd69bd25f377ef9b342d6059a7e4e0e49192a8","target":"graph","created_at":"2026-05-18T00:01:19Z","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":"The time-evolution dynamics of two nonlinear cosmological real gas models has been reexamined in detail with methods from the theory of Hamiltonian dynamical systems. These examples are FRWL cosmologies, one based on a gas, satisfying the van der Waals equation and another one based on the virial expansion gas equation. The cosmological variables used are the expansion rate, given by the Hubble parameter, and the energy density. The analysis is aided by the existence of global first integral as well as several special (second) integrals in each case. In addition, the global first integral can ","authors_text":"Emil M. Prodanov, Rossen I. Ivanov","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-19T20:33:56Z","title":"Hamiltonian Dynamics of Cosmological Quintessence Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05732","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:aeeffe283decadf0fca7062b7d25435569a99b2f237fadd7a6fbfa76d5f5c1ff","target":"record","created_at":"2026-05-18T00:01:19Z","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":"474d24c3e513970073c58e3a540f9c4b115a21e3049718a53c02ba000a0db757","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-19T20:33:56Z","title_canon_sha256":"93ff5b6f9d905dc8180291d519115f18b000897758bcbb0bdde4bf29ae533803"},"schema_version":"1.0","source":{"id":"1608.05732","kind":"arxiv","version":2}},"canonical_sha256":"e4a3c2ef84fa8631f3830678621a28f2824c3df7f0ae57fcba820ce0b95184aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4a3c2ef84fa8631f3830678621a28f2824c3df7f0ae57fcba820ce0b95184aa","first_computed_at":"2026-05-18T00:01:19.874430Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:19.874430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nT6LvvdhXszEwJbG7Txam/f7MOgDw3tV2s3FY2t/ryNVQzzFOzTC3pWI/ZHqjJPZkAr06DGS8fLBn7WURE4PDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:19.874878Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.05732","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aeeffe283decadf0fca7062b7d25435569a99b2f237fadd7a6fbfa76d5f5c1ff","sha256:568c001fe734b9bf20dc7d1db0dd69bd25f377ef9b342d6059a7e4e0e49192a8"],"state_sha256":"446cd6d791c253f82a77e9da9d0df446cae20cae67463af407fb04faa8d07cbe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EBiDBw7fxrO8C1Nc8GWDURy3mVzCdnahqKtpzIKQP24z1x91zAl+faFNTWIDmColdRjF29svfPuC6OxntwzFBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T02:47:40.576802Z","bundle_sha256":"cdbbfeb346ec9bb943fca91e913591e123941f4795c467274b04ec448d5e5427"}}