{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:URFADLQWG5CWIHJ67T4XH6GRYM","short_pith_number":"pith:URFADLQW","canonical_record":{"source":{"id":"1109.1694","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-09-08T11:52:45Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"1987ed601f9bf8985a1f2a72b9ded439bd4a3571331ba4f15820819edd73d435","abstract_canon_sha256":"cb7bfeb985f4b99fada6e51222b55a622e25d0bee2673c56de256ccc3ba3962e"},"schema_version":"1.0"},"canonical_sha256":"a44a01ae163745641d3efcf973f8d1c3330c8c0196b1aeca71e0fb535aa608bf","source":{"kind":"arxiv","id":"1109.1694","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1694","created_at":"2026-05-18T02:00:37Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1694v2","created_at":"2026-05-18T02:00:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1694","created_at":"2026-05-18T02:00:37Z"},{"alias_kind":"pith_short_12","alias_value":"URFADLQWG5CW","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"URFADLQWG5CWIHJ6","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"URFADLQW","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:URFADLQWG5CWIHJ67T4XH6GRYM","target":"record","payload":{"canonical_record":{"source":{"id":"1109.1694","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-09-08T11:52:45Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"1987ed601f9bf8985a1f2a72b9ded439bd4a3571331ba4f15820819edd73d435","abstract_canon_sha256":"cb7bfeb985f4b99fada6e51222b55a622e25d0bee2673c56de256ccc3ba3962e"},"schema_version":"1.0"},"canonical_sha256":"a44a01ae163745641d3efcf973f8d1c3330c8c0196b1aeca71e0fb535aa608bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:37.935169Z","signature_b64":"8tuFqrmsa592TS5bJCNmY0mWt0iCX8Yxu9xeTdTojG9v5xGbZMi3o5uvchSeQ3t9hCqtDwUwUVjRFKVwazNqBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a44a01ae163745641d3efcf973f8d1c3330c8c0196b1aeca71e0fb535aa608bf","last_reissued_at":"2026-05-18T02:00:37.934352Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:37.934352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.1694","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":"2026-05-18T02:00:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aZyetelMYJk4rWm3hHmWoi8Pk44KM9V5cFrvYY7/msD6q8RIobMoNWAbitSLeRsplIeWyoWA+5WHHnTDKQABAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:30:00.136385Z"},"content_sha256":"fd2c4107cba3b36c2916018f727e72deb985aeb296720b48351364f2603ced71","schema_version":"1.0","event_id":"sha256:fd2c4107cba3b36c2916018f727e72deb985aeb296720b48351364f2603ced71"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:URFADLQWG5CWIHJ67T4XH6GRYM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Thermodynamics of cosmological horizons in $f(T)$ gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-th"],"primary_cat":"gr-qc","authors_text":"Chao-Qiang Geng, Kazuharu Bamba","submitted_at":"2011-09-08T11:52:45Z","abstract_excerpt":"We explore thermodynamics of the apparent horizon in $f(T)$ gravity with both equilibrium and non-equilibrium descriptions. We find the same dual equilibrium/non-equilibrium formulation for $f(T)$ as for $f(R)$ gravity. In particular, we show that the second law of thermodynamics can be satisfied for the universe with the same temperature of the outside and inside the apparent horizon."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1694","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":"2026-05-18T02:00:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9avjFZvgUk5xng5MGPAUIFhKGwDcYKEhObuyaGyDQFq3WpKj1wlStTek+p3lxKKwD5Z+/f2gHxoB7F/WJWBbDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:30:00.137067Z"},"content_sha256":"319353a0a7c3272559f0e3027d9f80355c01995f01dad200c1108ffb47dc5335","schema_version":"1.0","event_id":"sha256:319353a0a7c3272559f0e3027d9f80355c01995f01dad200c1108ffb47dc5335"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/URFADLQWG5CWIHJ67T4XH6GRYM/bundle.json","state_url":"https://pith.science/pith/URFADLQWG5CWIHJ67T4XH6GRYM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/URFADLQWG5CWIHJ67T4XH6GRYM/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":"2026-05-27T23:30:00Z","links":{"resolver":"https://pith.science/pith/URFADLQWG5CWIHJ67T4XH6GRYM","bundle":"https://pith.science/pith/URFADLQWG5CWIHJ67T4XH6GRYM/bundle.json","state":"https://pith.science/pith/URFADLQWG5CWIHJ67T4XH6GRYM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/URFADLQWG5CWIHJ67T4XH6GRYM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:URFADLQWG5CWIHJ67T4XH6GRYM","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":"cb7bfeb985f4b99fada6e51222b55a622e25d0bee2673c56de256ccc3ba3962e","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-09-08T11:52:45Z","title_canon_sha256":"1987ed601f9bf8985a1f2a72b9ded439bd4a3571331ba4f15820819edd73d435"},"schema_version":"1.0","source":{"id":"1109.1694","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1694","created_at":"2026-05-18T02:00:37Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1694v2","created_at":"2026-05-18T02:00:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1694","created_at":"2026-05-18T02:00:37Z"},{"alias_kind":"pith_short_12","alias_value":"URFADLQWG5CW","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"URFADLQWG5CWIHJ6","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"URFADLQW","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:319353a0a7c3272559f0e3027d9f80355c01995f01dad200c1108ffb47dc5335","target":"graph","created_at":"2026-05-18T02:00:37Z","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 explore thermodynamics of the apparent horizon in $f(T)$ gravity with both equilibrium and non-equilibrium descriptions. We find the same dual equilibrium/non-equilibrium formulation for $f(T)$ as for $f(R)$ gravity. In particular, we show that the second law of thermodynamics can be satisfied for the universe with the same temperature of the outside and inside the apparent horizon.","authors_text":"Chao-Qiang Geng, Kazuharu Bamba","cross_cats":["astro-ph.CO","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-09-08T11:52:45Z","title":"Thermodynamics of cosmological horizons in $f(T)$ gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1694","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:fd2c4107cba3b36c2916018f727e72deb985aeb296720b48351364f2603ced71","target":"record","created_at":"2026-05-18T02:00:37Z","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":"cb7bfeb985f4b99fada6e51222b55a622e25d0bee2673c56de256ccc3ba3962e","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-09-08T11:52:45Z","title_canon_sha256":"1987ed601f9bf8985a1f2a72b9ded439bd4a3571331ba4f15820819edd73d435"},"schema_version":"1.0","source":{"id":"1109.1694","kind":"arxiv","version":2}},"canonical_sha256":"a44a01ae163745641d3efcf973f8d1c3330c8c0196b1aeca71e0fb535aa608bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a44a01ae163745641d3efcf973f8d1c3330c8c0196b1aeca71e0fb535aa608bf","first_computed_at":"2026-05-18T02:00:37.934352Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:37.934352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8tuFqrmsa592TS5bJCNmY0mWt0iCX8Yxu9xeTdTojG9v5xGbZMi3o5uvchSeQ3t9hCqtDwUwUVjRFKVwazNqBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:37.935169Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.1694","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd2c4107cba3b36c2916018f727e72deb985aeb296720b48351364f2603ced71","sha256:319353a0a7c3272559f0e3027d9f80355c01995f01dad200c1108ffb47dc5335"],"state_sha256":"5430b8050c926918c6d1d905a6295014c4b2266e61de47cb5abd84d7c719ea49"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"12HRTgXqyMbg4XovcOAzMYF9FFvqhLER3SJCWwFVAZpmxIlWwyoNNx96BGTY4o9fXTs8CbCXON7ykztdYkveBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T23:30:00.140944Z","bundle_sha256":"efea16c17bd2f41cf28b76f31ceb2047cac268876abb33ca9e5f9211088e306c"}}