{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XIVFC5QLWDHE7QWRP3AG3TESMB","short_pith_number":"pith:XIVFC5QL","canonical_record":{"source":{"id":"1110.3962","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2011-10-18T12:56:56Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"46b62e4991953befd5fbda413f7cf33b6b99e8ae107287c4e54afee1ac34a24d","abstract_canon_sha256":"a5e667fb3b95a6e1a289e8f90bcfd0191b7377b934d1bfbcfb602a35e736e1d2"},"schema_version":"1.0"},"canonical_sha256":"ba2a51760bb0ce4fc2d17ec06dcc9260504428bbd44bea114ff0825f6372988f","source":{"kind":"arxiv","id":"1110.3962","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3962","created_at":"2026-05-18T02:00:09Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3962v2","created_at":"2026-05-18T02:00:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3962","created_at":"2026-05-18T02:00:09Z"},{"alias_kind":"pith_short_12","alias_value":"XIVFC5QLWDHE","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XIVFC5QLWDHE7QWR","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XIVFC5QL","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XIVFC5QLWDHE7QWRP3AG3TESMB","target":"record","payload":{"canonical_record":{"source":{"id":"1110.3962","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2011-10-18T12:56:56Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"46b62e4991953befd5fbda413f7cf33b6b99e8ae107287c4e54afee1ac34a24d","abstract_canon_sha256":"a5e667fb3b95a6e1a289e8f90bcfd0191b7377b934d1bfbcfb602a35e736e1d2"},"schema_version":"1.0"},"canonical_sha256":"ba2a51760bb0ce4fc2d17ec06dcc9260504428bbd44bea114ff0825f6372988f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:09.357697Z","signature_b64":"UzSn03llxPBcZbBqwKTvXHQtDXLlk4fRkz2ox/lY0jeSg5UkyJv+p7r3SKCjgOjylRieSsuZ9GEtlWqBvTREBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba2a51760bb0ce4fc2d17ec06dcc9260504428bbd44bea114ff0825f6372988f","last_reissued_at":"2026-05-18T02:00:09.356972Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:09.356972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.3962","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":"2026-05-18T02:00:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5escj5FiTAEbwSWgETXuAnrJA8k3icfGgko7QBBzI6sHh10p6W1JW6cSFwkyycPR17276dsQJCzIFTYnv8roBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:08:15.006552Z"},"content_sha256":"8c820f8e7e0b2e149624fda55167a8376b110460fec6e64f81a9b290ecaf2b9e","schema_version":"1.0","event_id":"sha256:8c820f8e7e0b2e149624fda55167a8376b110460fec6e64f81a9b290ecaf2b9e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XIVFC5QLWDHE7QWRP3AG3TESMB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Power-law solutions in $f(T)$ gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"physics.gen-ph","authors_text":"F. Darabi, M. R. Setare","submitted_at":"2011-10-18T12:56:56Z","abstract_excerpt":"We have considered an action of the form $T+f(T)+L_m$ describing Einstein's gravity plus a function of the torsion scalar. By considering an exact power-law solution we have obtained the Friedmann equation as a differential equation for the function $f(T)$ in spatially flat universe and obtained the real valued solutions of this equation for some power-law solutions. We have also studied the power-law solutions when the universe enters a Phantom phase and shown that such solutions may exist for some f(T) solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3962","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":"2026-05-18T02:00:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fRIpQuHymuybrYDfvn+8ZSjp8cDdmZIHGAnFsfmGdwHhKfN46Wy+pdO2qsVWzrAVWi4qEwVz62jdguXHmuRxBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:08:15.007440Z"},"content_sha256":"cb6335972d07a0af9a273624cc7baed5fa386eb788cf92ec29c7866e22ca0294","schema_version":"1.0","event_id":"sha256:cb6335972d07a0af9a273624cc7baed5fa386eb788cf92ec29c7866e22ca0294"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XIVFC5QLWDHE7QWRP3AG3TESMB/bundle.json","state_url":"https://pith.science/pith/XIVFC5QLWDHE7QWRP3AG3TESMB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XIVFC5QLWDHE7QWRP3AG3TESMB/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":"2026-05-30T22:08:15Z","links":{"resolver":"https://pith.science/pith/XIVFC5QLWDHE7QWRP3AG3TESMB","bundle":"https://pith.science/pith/XIVFC5QLWDHE7QWRP3AG3TESMB/bundle.json","state":"https://pith.science/pith/XIVFC5QLWDHE7QWRP3AG3TESMB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XIVFC5QLWDHE7QWRP3AG3TESMB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XIVFC5QLWDHE7QWRP3AG3TESMB","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":"a5e667fb3b95a6e1a289e8f90bcfd0191b7377b934d1bfbcfb602a35e736e1d2","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2011-10-18T12:56:56Z","title_canon_sha256":"46b62e4991953befd5fbda413f7cf33b6b99e8ae107287c4e54afee1ac34a24d"},"schema_version":"1.0","source":{"id":"1110.3962","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3962","created_at":"2026-05-18T02:00:09Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3962v2","created_at":"2026-05-18T02:00:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3962","created_at":"2026-05-18T02:00:09Z"},{"alias_kind":"pith_short_12","alias_value":"XIVFC5QLWDHE","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XIVFC5QLWDHE7QWR","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XIVFC5QL","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:cb6335972d07a0af9a273624cc7baed5fa386eb788cf92ec29c7866e22ca0294","target":"graph","created_at":"2026-05-18T02:00:09Z","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":"We have considered an action of the form $T+f(T)+L_m$ describing Einstein's gravity plus a function of the torsion scalar. By considering an exact power-law solution we have obtained the Friedmann equation as a differential equation for the function $f(T)$ in spatially flat universe and obtained the real valued solutions of this equation for some power-law solutions. We have also studied the power-law solutions when the universe enters a Phantom phase and shown that such solutions may exist for some f(T) solutions.","authors_text":"F. Darabi, M. R. Setare","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2011-10-18T12:56:56Z","title":"Power-law solutions in $f(T)$ gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3962","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":"sha256:8c820f8e7e0b2e149624fda55167a8376b110460fec6e64f81a9b290ecaf2b9e","target":"record","created_at":"2026-05-18T02:00:09Z","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":"a5e667fb3b95a6e1a289e8f90bcfd0191b7377b934d1bfbcfb602a35e736e1d2","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2011-10-18T12:56:56Z","title_canon_sha256":"46b62e4991953befd5fbda413f7cf33b6b99e8ae107287c4e54afee1ac34a24d"},"schema_version":"1.0","source":{"id":"1110.3962","kind":"arxiv","version":2}},"canonical_sha256":"ba2a51760bb0ce4fc2d17ec06dcc9260504428bbd44bea114ff0825f6372988f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba2a51760bb0ce4fc2d17ec06dcc9260504428bbd44bea114ff0825f6372988f","first_computed_at":"2026-05-18T02:00:09.356972Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:09.356972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UzSn03llxPBcZbBqwKTvXHQtDXLlk4fRkz2ox/lY0jeSg5UkyJv+p7r3SKCjgOjylRieSsuZ9GEtlWqBvTREBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:09.357697Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3962","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c820f8e7e0b2e149624fda55167a8376b110460fec6e64f81a9b290ecaf2b9e","sha256:cb6335972d07a0af9a273624cc7baed5fa386eb788cf92ec29c7866e22ca0294"],"state_sha256":"37aa7adede6cfd49331234d82d1b7110dcdac57abd06235382fa31be85c0d275"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CZeBXRVPZNVBlGIIADDGnfLMPNW411IZagK3q9qhNOfkAmnN1AX3rxH4r5WKrQwC7dtlJlcJnSQ6DO803bv0BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T22:08:15.011460Z","bundle_sha256":"641ecf284d7cbdde92e7ce692924ed1bfa0fb4be0cd754fba53934bcf2030df0"}}