{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:EAMFN5YFRKJUDOR3HKX65CNDUZ","short_pith_number":"pith:EAMFN5YF","schema_version":"1.0","canonical_sha256":"201856f7058a9341ba3b3aafee89a3a6573c67414d67084a1ffbb75617efa8a7","source":{"kind":"arxiv","id":"1809.03579","version":1},"attestation_state":"computed","paper":{"title":"Thermodynamics and phase transitions of galactic clustering in higher-order Modified Gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Behnam Pourhassan, Salvatore Capozziello, Sudhaker Upadhyay","submitted_at":"2018-09-11T06:04:57Z","abstract_excerpt":"We study the thermodynamics of galactic clustering under the higher-order corrected Newtonian dynamics. The clustering of galaxies is considered as a gravitational phase transition. In order to study the effects of higher-order correction to the thermodynamics of gravitational system, we compute more exact equations of state. Moreover, we investigate the corrected probability distribution function for such gravitating system. A relation between order parameter and the critical temperature is also established."},"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":"1809.03579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-09-11T06:04:57Z","cross_cats_sorted":[],"title_canon_sha256":"469afe4253ceffcfecbdfbc024f7d73b6657042d2e373a874ad86c38e6a1d294","abstract_canon_sha256":"8c4271324f28d142396fb0cb81249734b1aaa7652a88cd4b624befcea50f9125"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:55.222087Z","signature_b64":"2RaB1R33XsD/40mgF/YCeArRcl9xXfeK4HW9JyMlnHUQ3/DZeerJ1HWuXK9SuR/3+6DffIlH6i3JUdKL1qi9BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"201856f7058a9341ba3b3aafee89a3a6573c67414d67084a1ffbb75617efa8a7","last_reissued_at":"2026-05-17T23:55:55.221559Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:55.221559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Thermodynamics and phase transitions of galactic clustering in higher-order Modified Gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Behnam Pourhassan, Salvatore Capozziello, Sudhaker Upadhyay","submitted_at":"2018-09-11T06:04:57Z","abstract_excerpt":"We study the thermodynamics of galactic clustering under the higher-order corrected Newtonian dynamics. The clustering of galaxies is considered as a gravitational phase transition. In order to study the effects of higher-order correction to the thermodynamics of gravitational system, we compute more exact equations of state. Moreover, we investigate the corrected probability distribution function for such gravitating system. A relation between order parameter and the critical temperature is also established."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03579","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1809.03579","created_at":"2026-05-17T23:55:55.221662+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.03579v1","created_at":"2026-05-17T23:55:55.221662+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03579","created_at":"2026-05-17T23:55:55.221662+00:00"},{"alias_kind":"pith_short_12","alias_value":"EAMFN5YFRKJU","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"EAMFN5YFRKJUDOR3","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"EAMFN5YF","created_at":"2026-05-18T12:32:22.470017+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/EAMFN5YFRKJUDOR3HKX65CNDUZ","json":"https://pith.science/pith/EAMFN5YFRKJUDOR3HKX65CNDUZ.json","graph_json":"https://pith.science/api/pith-number/EAMFN5YFRKJUDOR3HKX65CNDUZ/graph.json","events_json":"https://pith.science/api/pith-number/EAMFN5YFRKJUDOR3HKX65CNDUZ/events.json","paper":"https://pith.science/paper/EAMFN5YF"},"agent_actions":{"view_html":"https://pith.science/pith/EAMFN5YFRKJUDOR3HKX65CNDUZ","download_json":"https://pith.science/pith/EAMFN5YFRKJUDOR3HKX65CNDUZ.json","view_paper":"https://pith.science/paper/EAMFN5YF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.03579&json=true","fetch_graph":"https://pith.science/api/pith-number/EAMFN5YFRKJUDOR3HKX65CNDUZ/graph.json","fetch_events":"https://pith.science/api/pith-number/EAMFN5YFRKJUDOR3HKX65CNDUZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EAMFN5YFRKJUDOR3HKX65CNDUZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EAMFN5YFRKJUDOR3HKX65CNDUZ/action/storage_attestation","attest_author":"https://pith.science/pith/EAMFN5YFRKJUDOR3HKX65CNDUZ/action/author_attestation","sign_citation":"https://pith.science/pith/EAMFN5YFRKJUDOR3HKX65CNDUZ/action/citation_signature","submit_replication":"https://pith.science/pith/EAMFN5YFRKJUDOR3HKX65CNDUZ/action/replication_record"}},"created_at":"2026-05-17T23:55:55.221662+00:00","updated_at":"2026-05-17T23:55:55.221662+00:00"}