{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:BJ6XUUUZLEI2CKZN7AN2BKL2L3","short_pith_number":"pith:BJ6XUUUZ","schema_version":"1.0","canonical_sha256":"0a7d7a52995911a12b2df81ba0a97a5ed029d86cd43c0e2e988d9ad196d0c542","source":{"kind":"arxiv","id":"1509.00163","version":4},"attestation_state":"computed","paper":{"title":"Thermodynamical aspects of running vacuum models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-ph","hep-th"],"primary_cat":"gr-qc","authors_text":"J. A. S. Lima, Joan Sol\\`a, Spyros Basilakos","submitted_at":"2015-09-01T07:30:11Z","abstract_excerpt":"The thermal history of a large class of running vacuum models in which the effective cosmological term is described by a truncated power series of the Hubble rate, whose dominant term is $\\Lambda (H) \\propto H^{n+2}$, is discussed in detail. Specifically, by assuming that the ultra-relativistic particles produced by the vacuum decay emerge into space-time in such a way that its energy density $\\rho_r \\propto T^{4}$, the temperature evolution law and the increasing entropy function are analytically calculated. For the whole class of vacuum models explored here we findthat the primeval value of "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1509.00163","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-09-01T07:30:11Z","cross_cats_sorted":["astro-ph.CO","hep-ph","hep-th"],"title_canon_sha256":"958f3c92277770b11dba994d3d609b3cdaacb7e8979bbb11b1d9312773bbdbe1","abstract_canon_sha256":"d13ba2c8a78d6aae067229eceb49a58f39cd22b6a62e9d98205109b248109d40"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:07.100351Z","signature_b64":"0LmDPBkp6BmiOcZ8hhGPYr5R2B1PfHQkeLCcG7AU5InbHkkWrle8K+gwbDcFPjvtVwKFKoz/j5MEg5mbv22KCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a7d7a52995911a12b2df81ba0a97a5ed029d86cd43c0e2e988d9ad196d0c542","last_reissued_at":"2026-05-18T01:16:07.099799Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:07.099799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Thermodynamical aspects of running vacuum models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-ph","hep-th"],"primary_cat":"gr-qc","authors_text":"J. A. S. Lima, Joan Sol\\`a, Spyros Basilakos","submitted_at":"2015-09-01T07:30:11Z","abstract_excerpt":"The thermal history of a large class of running vacuum models in which the effective cosmological term is described by a truncated power series of the Hubble rate, whose dominant term is $\\Lambda (H) \\propto H^{n+2}$, is discussed in detail. Specifically, by assuming that the ultra-relativistic particles produced by the vacuum decay emerge into space-time in such a way that its energy density $\\rho_r \\propto T^{4}$, the temperature evolution law and the increasing entropy function are analytically calculated. For the whole class of vacuum models explored here we findthat the primeval value of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00163","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1509.00163","created_at":"2026-05-18T01:16:07.099879+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.00163v4","created_at":"2026-05-18T01:16:07.099879+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00163","created_at":"2026-05-18T01:16:07.099879+00:00"},{"alias_kind":"pith_short_12","alias_value":"BJ6XUUUZLEI2","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BJ6XUUUZLEI2CKZN","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BJ6XUUUZ","created_at":"2026-05-18T12:29:14.074870+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BJ6XUUUZLEI2CKZN7AN2BKL2L3","json":"https://pith.science/pith/BJ6XUUUZLEI2CKZN7AN2BKL2L3.json","graph_json":"https://pith.science/api/pith-number/BJ6XUUUZLEI2CKZN7AN2BKL2L3/graph.json","events_json":"https://pith.science/api/pith-number/BJ6XUUUZLEI2CKZN7AN2BKL2L3/events.json","paper":"https://pith.science/paper/BJ6XUUUZ"},"agent_actions":{"view_html":"https://pith.science/pith/BJ6XUUUZLEI2CKZN7AN2BKL2L3","download_json":"https://pith.science/pith/BJ6XUUUZLEI2CKZN7AN2BKL2L3.json","view_paper":"https://pith.science/paper/BJ6XUUUZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.00163&json=true","fetch_graph":"https://pith.science/api/pith-number/BJ6XUUUZLEI2CKZN7AN2BKL2L3/graph.json","fetch_events":"https://pith.science/api/pith-number/BJ6XUUUZLEI2CKZN7AN2BKL2L3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BJ6XUUUZLEI2CKZN7AN2BKL2L3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BJ6XUUUZLEI2CKZN7AN2BKL2L3/action/storage_attestation","attest_author":"https://pith.science/pith/BJ6XUUUZLEI2CKZN7AN2BKL2L3/action/author_attestation","sign_citation":"https://pith.science/pith/BJ6XUUUZLEI2CKZN7AN2BKL2L3/action/citation_signature","submit_replication":"https://pith.science/pith/BJ6XUUUZLEI2CKZN7AN2BKL2L3/action/replication_record"}},"created_at":"2026-05-18T01:16:07.099879+00:00","updated_at":"2026-05-18T01:16:07.099879+00:00"}