{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:HUPPUJ53XDYPTPWBTHBGS2HINB","short_pith_number":"pith:HUPPUJ53","canonical_record":{"source":{"id":"2411.18469","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2024-11-27T16:04:43Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"144ae8c69193993321727e68662689a5f6a9454140ef56b482a55fb3e14443fd","abstract_canon_sha256":"2d017e751ecc497a984cbfe2ce5b6def1a195932f7809efee0d2fe2161324b46"},"schema_version":"1.0"},"canonical_sha256":"3d1efa27bbb8f0f9bec199c26968e8685adf4c75a5cbbe88be95e2cd9eda19ed","source":{"kind":"arxiv","id":"2411.18469","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.18469","created_at":"2026-07-05T09:41:16Z"},{"alias_kind":"arxiv_version","alias_value":"2411.18469v1","created_at":"2026-07-05T09:41:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.18469","created_at":"2026-07-05T09:41:16Z"},{"alias_kind":"pith_short_12","alias_value":"HUPPUJ53XDYP","created_at":"2026-07-05T09:41:16Z"},{"alias_kind":"pith_short_16","alias_value":"HUPPUJ53XDYPTPWB","created_at":"2026-07-05T09:41:16Z"},{"alias_kind":"pith_short_8","alias_value":"HUPPUJ53","created_at":"2026-07-05T09:41:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:HUPPUJ53XDYPTPWBTHBGS2HINB","target":"record","payload":{"canonical_record":{"source":{"id":"2411.18469","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2024-11-27T16:04:43Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"144ae8c69193993321727e68662689a5f6a9454140ef56b482a55fb3e14443fd","abstract_canon_sha256":"2d017e751ecc497a984cbfe2ce5b6def1a195932f7809efee0d2fe2161324b46"},"schema_version":"1.0"},"canonical_sha256":"3d1efa27bbb8f0f9bec199c26968e8685adf4c75a5cbbe88be95e2cd9eda19ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:41:16.820276Z","signature_b64":"qQQKOvovhHDt7Z+NsmFre3l082DWGH6foXbiWonM1N7xojUU8PRTSRJ7/sn7D9opSTAfpJ1XPwK+mYpvJs9JAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d1efa27bbb8f0f9bec199c26968e8685adf4c75a5cbbe88be95e2cd9eda19ed","last_reissued_at":"2026-07-05T09:41:16.819852Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:41:16.819852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.18469","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:41:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0BT6564D9Z6RqtZxmuxEl735G022OeWQ874P7l+NSEDYuAcTe8EAGaWmX4ZTis9VtaBg4cKsZQRUiIgC1qshAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T00:24:22.587128Z"},"content_sha256":"abcdc292499589c6a5a0cafce5660e8cb0a53cbfb29663726d5fae64ed0d8b59","schema_version":"1.0","event_id":"sha256:abcdc292499589c6a5a0cafce5660e8cb0a53cbfb29663726d5fae64ed0d8b59"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:HUPPUJ53XDYPTPWBTHBGS2HINB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Thermodynamics of $f(R)$ Theories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Sergio E. Jor\\'as","submitted_at":"2024-11-27T16:04:43Z","abstract_excerpt":"This series of three lectures was presented at ``Escola de Cosmologia e Gravita\\c{c}\\~ao\" \\url{https://cosmosecontexto.org.br/ecg-inscricoes} and webcast at \\url{https://shorturl.at/2ZSI7} -- in Portuguese, but slides in English.\n  We will go through a brief review on $f(R)$ theories (in the metric approach) and the usual requirements for successful modifications of General Relativity. Then we will open a large parenthesis to talk about a non-standard approach to Phase Transitions: the Catastrophe Theory. Finally, we will connect the previous lectures to introduce a new Thermodynamic interpret"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18469","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.18469/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":"2026-07-05T09:41:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U5AhbFh9dGNTxuddJdkaty2h/1vGmwvSVS151Q6SPE9HjB5ghscVyhMLJ4NKM50HolsOUGpHCIdxsKE5fFfXAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T00:24:22.587558Z"},"content_sha256":"7341f3e80699506d40d0fb1154b66b83cd372a01622965b42a4238bcffa23e93","schema_version":"1.0","event_id":"sha256:7341f3e80699506d40d0fb1154b66b83cd372a01622965b42a4238bcffa23e93"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HUPPUJ53XDYPTPWBTHBGS2HINB/bundle.json","state_url":"https://pith.science/pith/HUPPUJ53XDYPTPWBTHBGS2HINB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HUPPUJ53XDYPTPWBTHBGS2HINB/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":"2026-08-13T00:24:22Z","links":{"resolver":"https://pith.science/pith/HUPPUJ53XDYPTPWBTHBGS2HINB","bundle":"https://pith.science/pith/HUPPUJ53XDYPTPWBTHBGS2HINB/bundle.json","state":"https://pith.science/pith/HUPPUJ53XDYPTPWBTHBGS2HINB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HUPPUJ53XDYPTPWBTHBGS2HINB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:HUPPUJ53XDYPTPWBTHBGS2HINB","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":"2d017e751ecc497a984cbfe2ce5b6def1a195932f7809efee0d2fe2161324b46","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2024-11-27T16:04:43Z","title_canon_sha256":"144ae8c69193993321727e68662689a5f6a9454140ef56b482a55fb3e14443fd"},"schema_version":"1.0","source":{"id":"2411.18469","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.18469","created_at":"2026-07-05T09:41:16Z"},{"alias_kind":"arxiv_version","alias_value":"2411.18469v1","created_at":"2026-07-05T09:41:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.18469","created_at":"2026-07-05T09:41:16Z"},{"alias_kind":"pith_short_12","alias_value":"HUPPUJ53XDYP","created_at":"2026-07-05T09:41:16Z"},{"alias_kind":"pith_short_16","alias_value":"HUPPUJ53XDYPTPWB","created_at":"2026-07-05T09:41:16Z"},{"alias_kind":"pith_short_8","alias_value":"HUPPUJ53","created_at":"2026-07-05T09:41:16Z"}],"graph_snapshots":[{"event_id":"sha256:7341f3e80699506d40d0fb1154b66b83cd372a01622965b42a4238bcffa23e93","target":"graph","created_at":"2026-07-05T09:41:16Z","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/2411.18469/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This series of three lectures was presented at ``Escola de Cosmologia e Gravita\\c{c}\\~ao\" \\url{https://cosmosecontexto.org.br/ecg-inscricoes} and webcast at \\url{https://shorturl.at/2ZSI7} -- in Portuguese, but slides in English.\n  We will go through a brief review on $f(R)$ theories (in the metric approach) and the usual requirements for successful modifications of General Relativity. Then we will open a large parenthesis to talk about a non-standard approach to Phase Transitions: the Catastrophe Theory. Finally, we will connect the previous lectures to introduce a new Thermodynamic interpret","authors_text":"Sergio E. Jor\\'as","cross_cats":["hep-th"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2024-11-27T16:04:43Z","title":"Thermodynamics of $f(R)$ Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18469","kind":"arxiv","version":1},"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:abcdc292499589c6a5a0cafce5660e8cb0a53cbfb29663726d5fae64ed0d8b59","target":"record","created_at":"2026-07-05T09:41:16Z","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":"2d017e751ecc497a984cbfe2ce5b6def1a195932f7809efee0d2fe2161324b46","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2024-11-27T16:04:43Z","title_canon_sha256":"144ae8c69193993321727e68662689a5f6a9454140ef56b482a55fb3e14443fd"},"schema_version":"1.0","source":{"id":"2411.18469","kind":"arxiv","version":1}},"canonical_sha256":"3d1efa27bbb8f0f9bec199c26968e8685adf4c75a5cbbe88be95e2cd9eda19ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d1efa27bbb8f0f9bec199c26968e8685adf4c75a5cbbe88be95e2cd9eda19ed","first_computed_at":"2026-07-05T09:41:16.819852Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:41:16.819852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qQQKOvovhHDt7Z+NsmFre3l082DWGH6foXbiWonM1N7xojUU8PRTSRJ7/sn7D9opSTAfpJ1XPwK+mYpvJs9JAw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:41:16.820276Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.18469","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:abcdc292499589c6a5a0cafce5660e8cb0a53cbfb29663726d5fae64ed0d8b59","sha256:7341f3e80699506d40d0fb1154b66b83cd372a01622965b42a4238bcffa23e93"],"state_sha256":"47f0e6e4c2539f86e28c7495adc5ccbf15513820cfd06467d7598a6fad0f567d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BVvfFX/4Phiy2V9oTb+cbAOCSspr7LP3NnPVFf4qosMr4fnTnKYLWHxOEylwzCj+pbv4p3Wur6zVamy5weMwBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T00:24:22.589981Z","bundle_sha256":"85e9a5af6ebad706149400ec5b29a24c5a7fdda05d2758f7dbd77df27645bec8"}}