{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:XDRR2CZ4LGV66T3V7WMAWWOBTZ","short_pith_number":"pith:XDRR2CZ4","canonical_record":{"source":{"id":"2502.07700","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2025-02-11T16:55:15Z","cross_cats_sorted":[],"title_canon_sha256":"def34482e2aeb16514e2cc9cdb751f02df792d9aa752ef0cad2fe79b343be701","abstract_canon_sha256":"73750c65f9c06f453cb29dd843292d738b5f1ed8bd9c03b5977c675195908495"},"schema_version":"1.0"},"canonical_sha256":"b8e31d0b3c59abef4f75fd980b59c19e645ae5d2dff94c6df13da7c8db671af5","source":{"kind":"arxiv","id":"2502.07700","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.07700","created_at":"2026-07-05T11:29:55Z"},{"alias_kind":"arxiv_version","alias_value":"2502.07700v2","created_at":"2026-07-05T11:29:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.07700","created_at":"2026-07-05T11:29:55Z"},{"alias_kind":"pith_short_12","alias_value":"XDRR2CZ4LGV6","created_at":"2026-07-05T11:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"XDRR2CZ4LGV66T3V","created_at":"2026-07-05T11:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"XDRR2CZ4","created_at":"2026-07-05T11:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:XDRR2CZ4LGV66T3V7WMAWWOBTZ","target":"record","payload":{"canonical_record":{"source":{"id":"2502.07700","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2025-02-11T16:55:15Z","cross_cats_sorted":[],"title_canon_sha256":"def34482e2aeb16514e2cc9cdb751f02df792d9aa752ef0cad2fe79b343be701","abstract_canon_sha256":"73750c65f9c06f453cb29dd843292d738b5f1ed8bd9c03b5977c675195908495"},"schema_version":"1.0"},"canonical_sha256":"b8e31d0b3c59abef4f75fd980b59c19e645ae5d2dff94c6df13da7c8db671af5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:29:55.179952Z","signature_b64":"hb/9XHnZRojR7T90qNYsHxMpRmTf1p3uplOvkV7vdJZrefpD/ZN5sZp+qA07wuvyDoOnDHCmlM4gF9YLMMDSAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8e31d0b3c59abef4f75fd980b59c19e645ae5d2dff94c6df13da7c8db671af5","last_reissued_at":"2026-07-05T11:29:55.179480Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:29:55.179480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.07700","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":"2026-07-05T11:29:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mAgmfYspLMQO2fWd42gAtpgwtSWGZIOUbLHYSametn4bpKMGhAS0AdNNyY3HsJHPU/Z1Qdc0wueGy/pywFjZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T10:34:09.271175Z"},"content_sha256":"a5e634e45b49929ee3a3472c2da57c6b19a0f19cdaf97a0b005d244067ecca91","schema_version":"1.0","event_id":"sha256:a5e634e45b49929ee3a3472c2da57c6b19a0f19cdaf97a0b005d244067ecca91"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:XDRR2CZ4LGV66T3V7WMAWWOBTZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Alternative Approach to the Exact Solution of FRW-Type Spacetime with a Generalized Chaplygin Gas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"D Panigrahi","submitted_at":"2025-02-11T16:55:15Z","abstract_excerpt":"The generalized Chaplygin gas model, characterized by the equation of state\n  $p = - \\frac{B}{\\rho^{\\alpha}}$, is investigated within the framework of a Robertson-Walker spacetime. The resulting field equations governing this model are highly non-linear in the scale factor, forming the central focus of this work. Previous studies have employed this equation to describe both a dust-dominated universe and an accelerating universe in two extreme cases. However, the time evolution of the scale factor between these two extremal cases remains unclear. To address this gap, we have employed a first-or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07700","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/2502.07700/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":"2026-07-05T11:29:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PyiMarNi+POXH8yftNUN+gFH9Mi09ilhCS3n5/7MiW9gQ6lf9gPXnMqFCqSeHwHnNMgKcIgl8pjGR2/diYZXDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T10:34:09.271672Z"},"content_sha256":"155e46e67999f2013b739889c525181bf7bbc4e13006941554db647ec1eba12b","schema_version":"1.0","event_id":"sha256:155e46e67999f2013b739889c525181bf7bbc4e13006941554db647ec1eba12b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XDRR2CZ4LGV66T3V7WMAWWOBTZ/bundle.json","state_url":"https://pith.science/pith/XDRR2CZ4LGV66T3V7WMAWWOBTZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XDRR2CZ4LGV66T3V7WMAWWOBTZ/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":"2026-08-13T10:34:09Z","links":{"resolver":"https://pith.science/pith/XDRR2CZ4LGV66T3V7WMAWWOBTZ","bundle":"https://pith.science/pith/XDRR2CZ4LGV66T3V7WMAWWOBTZ/bundle.json","state":"https://pith.science/pith/XDRR2CZ4LGV66T3V7WMAWWOBTZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XDRR2CZ4LGV66T3V7WMAWWOBTZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:XDRR2CZ4LGV66T3V7WMAWWOBTZ","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":"73750c65f9c06f453cb29dd843292d738b5f1ed8bd9c03b5977c675195908495","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2025-02-11T16:55:15Z","title_canon_sha256":"def34482e2aeb16514e2cc9cdb751f02df792d9aa752ef0cad2fe79b343be701"},"schema_version":"1.0","source":{"id":"2502.07700","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.07700","created_at":"2026-07-05T11:29:55Z"},{"alias_kind":"arxiv_version","alias_value":"2502.07700v2","created_at":"2026-07-05T11:29:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.07700","created_at":"2026-07-05T11:29:55Z"},{"alias_kind":"pith_short_12","alias_value":"XDRR2CZ4LGV6","created_at":"2026-07-05T11:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"XDRR2CZ4LGV66T3V","created_at":"2026-07-05T11:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"XDRR2CZ4","created_at":"2026-07-05T11:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:155e46e67999f2013b739889c525181bf7bbc4e13006941554db647ec1eba12b","target":"graph","created_at":"2026-07-05T11:29:55Z","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/2502.07700/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The generalized Chaplygin gas model, characterized by the equation of state\n  $p = - \\frac{B}{\\rho^{\\alpha}}$, is investigated within the framework of a Robertson-Walker spacetime. The resulting field equations governing this model are highly non-linear in the scale factor, forming the central focus of this work. Previous studies have employed this equation to describe both a dust-dominated universe and an accelerating universe in two extreme cases. However, the time evolution of the scale factor between these two extremal cases remains unclear. To address this gap, we have employed a first-or","authors_text":"D Panigrahi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2025-02-11T16:55:15Z","title":"An Alternative Approach to the Exact Solution of FRW-Type Spacetime with a Generalized Chaplygin Gas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07700","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:a5e634e45b49929ee3a3472c2da57c6b19a0f19cdaf97a0b005d244067ecca91","target":"record","created_at":"2026-07-05T11:29:55Z","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":"73750c65f9c06f453cb29dd843292d738b5f1ed8bd9c03b5977c675195908495","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2025-02-11T16:55:15Z","title_canon_sha256":"def34482e2aeb16514e2cc9cdb751f02df792d9aa752ef0cad2fe79b343be701"},"schema_version":"1.0","source":{"id":"2502.07700","kind":"arxiv","version":2}},"canonical_sha256":"b8e31d0b3c59abef4f75fd980b59c19e645ae5d2dff94c6df13da7c8db671af5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8e31d0b3c59abef4f75fd980b59c19e645ae5d2dff94c6df13da7c8db671af5","first_computed_at":"2026-07-05T11:29:55.179480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:29:55.179480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hb/9XHnZRojR7T90qNYsHxMpRmTf1p3uplOvkV7vdJZrefpD/ZN5sZp+qA07wuvyDoOnDHCmlM4gF9YLMMDSAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:29:55.179952Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.07700","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5e634e45b49929ee3a3472c2da57c6b19a0f19cdaf97a0b005d244067ecca91","sha256:155e46e67999f2013b739889c525181bf7bbc4e13006941554db647ec1eba12b"],"state_sha256":"02899ec2ef3872db5289d6698d9be25f8671aa9696c9dc53a924a899000e838f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3LuKI11TD+2q5JrC0tbbuAUdYKYfSjmN4GhFgNfxh4BnZfdzsytXR+a131SIQ3v7y/qb8cjE2a8/YNM42wOtBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T10:34:09.275064Z","bundle_sha256":"acf35416a1f3cd97075a8d4a8333ab1522a8ff2f87dc13c61dc3adbe1b3e0cb8"}}