{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:KH3ACJLBKF2CH4OVZXWUHTNVEJ","short_pith_number":"pith:KH3ACJLB","canonical_record":{"source":{"id":"2105.10521","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-05-21T18:07:48Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"af9d38bc0219f6b3c994b4354ccd692d6cac0d5ea3abd160551c28225f7e1037","abstract_canon_sha256":"92a95471a15c6f33d7c9a66f5358bf2730ff862be023fb2e4432e7e33a7f6b24"},"schema_version":"1.0"},"canonical_sha256":"51f6012561517423f1d5cded43cdb52242cb0a206068a933e13550b4e2966659","source":{"kind":"arxiv","id":"2105.10521","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.10521","created_at":"2026-07-05T03:39:00Z"},{"alias_kind":"arxiv_version","alias_value":"2105.10521v3","created_at":"2026-07-05T03:39:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.10521","created_at":"2026-07-05T03:39:00Z"},{"alias_kind":"pith_short_12","alias_value":"KH3ACJLBKF2C","created_at":"2026-07-05T03:39:00Z"},{"alias_kind":"pith_short_16","alias_value":"KH3ACJLBKF2CH4OV","created_at":"2026-07-05T03:39:00Z"},{"alias_kind":"pith_short_8","alias_value":"KH3ACJLB","created_at":"2026-07-05T03:39:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:KH3ACJLBKF2CH4OVZXWUHTNVEJ","target":"record","payload":{"canonical_record":{"source":{"id":"2105.10521","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-05-21T18:07:48Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"af9d38bc0219f6b3c994b4354ccd692d6cac0d5ea3abd160551c28225f7e1037","abstract_canon_sha256":"92a95471a15c6f33d7c9a66f5358bf2730ff862be023fb2e4432e7e33a7f6b24"},"schema_version":"1.0"},"canonical_sha256":"51f6012561517423f1d5cded43cdb52242cb0a206068a933e13550b4e2966659","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:39:00.029550Z","signature_b64":"PYyRIssQRQQOM6p1KrFE12fqK1I63nCu0WBdrqFyaKPja0ilvZbIyUdSzNNFQarV0LcoImb6BU664pizGoq/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51f6012561517423f1d5cded43cdb52242cb0a206068a933e13550b4e2966659","last_reissued_at":"2026-07-05T03:39:00.029109Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:39:00.029109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2105.10521","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:39:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n1jvwyhcIZ+xetvSVQBUoEpUFTxq7FU5+SNfXdtWoObfm/k2+wktQZuzN4zChxUnNitq+MIybhdowHi61yG7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T04:19:01.977062Z"},"content_sha256":"a04587496039c93d4b9c3300f01759c0b79b2902de42ce334e972d51b0bb4d26","schema_version":"1.0","event_id":"sha256:a04587496039c93d4b9c3300f01759c0b79b2902de42ce334e972d51b0bb4d26"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:KH3ACJLBKF2CH4OVZXWUHTNVEJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$f(R)$ Dual Theories of Quintessence : Expansion-Collapse Duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-th"],"primary_cat":"gr-qc","authors_text":"Dipayan Mukherjee, H. K. Jassal, Kinjalk Lochan","submitted_at":"2021-05-21T18:07:48Z","abstract_excerpt":"The accelerated expansion of the universe demands presence of an exotic matter, namely the dark energy. Though the cosmological constant fits this role very well, a scalar field minimally coupled to gravity, or quintessence, can also be considered as a viable alternative for the cosmological constant. We study $f(R)$ gravity models which can lead to an effective description of dark energy implemented by quintessence fields in Einstein gravity, using the Einstein frame-Jordan frame duality. For a family of viable quintessence models, the reconstruction of the $f(R)$ function in the Jordan frame"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.10521","kind":"arxiv","version":3},"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/2105.10521/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":"2026-07-05T03:39:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6LhBAsE+Hd3hGnmJVmJrL/JB7zOp+hhyL2hYLFsVfhConRbm+G9Y+4C/NcYQzkXtKFL5cCUgsPNY42bMGhIeAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T04:19:01.977510Z"},"content_sha256":"e46f2621a52f622a86a695914dcf0e2dd498acc285966850025bc6f9658cc99e","schema_version":"1.0","event_id":"sha256:e46f2621a52f622a86a695914dcf0e2dd498acc285966850025bc6f9658cc99e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KH3ACJLBKF2CH4OVZXWUHTNVEJ/bundle.json","state_url":"https://pith.science/pith/KH3ACJLBKF2CH4OVZXWUHTNVEJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KH3ACJLBKF2CH4OVZXWUHTNVEJ/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":"2026-07-11T04:19:01Z","links":{"resolver":"https://pith.science/pith/KH3ACJLBKF2CH4OVZXWUHTNVEJ","bundle":"https://pith.science/pith/KH3ACJLBKF2CH4OVZXWUHTNVEJ/bundle.json","state":"https://pith.science/pith/KH3ACJLBKF2CH4OVZXWUHTNVEJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KH3ACJLBKF2CH4OVZXWUHTNVEJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:KH3ACJLBKF2CH4OVZXWUHTNVEJ","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":"92a95471a15c6f33d7c9a66f5358bf2730ff862be023fb2e4432e7e33a7f6b24","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-05-21T18:07:48Z","title_canon_sha256":"af9d38bc0219f6b3c994b4354ccd692d6cac0d5ea3abd160551c28225f7e1037"},"schema_version":"1.0","source":{"id":"2105.10521","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.10521","created_at":"2026-07-05T03:39:00Z"},{"alias_kind":"arxiv_version","alias_value":"2105.10521v3","created_at":"2026-07-05T03:39:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.10521","created_at":"2026-07-05T03:39:00Z"},{"alias_kind":"pith_short_12","alias_value":"KH3ACJLBKF2C","created_at":"2026-07-05T03:39:00Z"},{"alias_kind":"pith_short_16","alias_value":"KH3ACJLBKF2CH4OV","created_at":"2026-07-05T03:39:00Z"},{"alias_kind":"pith_short_8","alias_value":"KH3ACJLB","created_at":"2026-07-05T03:39:00Z"}],"graph_snapshots":[{"event_id":"sha256:e46f2621a52f622a86a695914dcf0e2dd498acc285966850025bc6f9658cc99e","target":"graph","created_at":"2026-07-05T03:39:00Z","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/2105.10521/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The accelerated expansion of the universe demands presence of an exotic matter, namely the dark energy. Though the cosmological constant fits this role very well, a scalar field minimally coupled to gravity, or quintessence, can also be considered as a viable alternative for the cosmological constant. We study $f(R)$ gravity models which can lead to an effective description of dark energy implemented by quintessence fields in Einstein gravity, using the Einstein frame-Jordan frame duality. For a family of viable quintessence models, the reconstruction of the $f(R)$ function in the Jordan frame","authors_text":"Dipayan Mukherjee, H. K. Jassal, Kinjalk Lochan","cross_cats":["astro-ph.CO","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-05-21T18:07:48Z","title":"$f(R)$ Dual Theories of Quintessence : Expansion-Collapse Duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.10521","kind":"arxiv","version":3},"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:a04587496039c93d4b9c3300f01759c0b79b2902de42ce334e972d51b0bb4d26","target":"record","created_at":"2026-07-05T03:39:00Z","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":"92a95471a15c6f33d7c9a66f5358bf2730ff862be023fb2e4432e7e33a7f6b24","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-05-21T18:07:48Z","title_canon_sha256":"af9d38bc0219f6b3c994b4354ccd692d6cac0d5ea3abd160551c28225f7e1037"},"schema_version":"1.0","source":{"id":"2105.10521","kind":"arxiv","version":3}},"canonical_sha256":"51f6012561517423f1d5cded43cdb52242cb0a206068a933e13550b4e2966659","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51f6012561517423f1d5cded43cdb52242cb0a206068a933e13550b4e2966659","first_computed_at":"2026-07-05T03:39:00.029109Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:39:00.029109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PYyRIssQRQQOM6p1KrFE12fqK1I63nCu0WBdrqFyaKPja0ilvZbIyUdSzNNFQarV0LcoImb6BU664pizGoq/Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:39:00.029550Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.10521","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a04587496039c93d4b9c3300f01759c0b79b2902de42ce334e972d51b0bb4d26","sha256:e46f2621a52f622a86a695914dcf0e2dd498acc285966850025bc6f9658cc99e"],"state_sha256":"4485a9daa91a4f308bfa792009fe6f46176b20c1489a03a5bc262fd881faf573"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vea4UtsXbUdfKf08ZRqPIangeDz8j9IGymr8yQBeqmWERMXtyx/cvldn+MJsZPU9IAvdnnkqqZ6Yw843SOBYAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-11T04:19:01.980807Z","bundle_sha256":"0f5606651ffae9881482d50aba0f6c7671dda5ec02ecc1d59a51288cbee0d44b"}}