{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:JLB75PIW7I57ILQ6O7UQN3BVCK","short_pith_number":"pith:JLB75PIW","canonical_record":{"source":{"id":"2604.16545","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-04-17T06:08:58Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"e89b86e7157d2454c26f351e785e9954b52e4796573bdffaea8213d4e74117bd","abstract_canon_sha256":"698d58871b768cd3606d61a2a22b856ec74244ed581df9b89b540003aff8f2b9"},"schema_version":"1.0"},"canonical_sha256":"4ac3febd16fa3bf42e1e77e906ec3512adebc69862ed4fd1dae0c895b9460ff4","source":{"kind":"arxiv","id":"2604.16545","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.16545","created_at":"2026-06-19T16:10:37Z"},{"alias_kind":"arxiv_version","alias_value":"2604.16545v3","created_at":"2026-06-19T16:10:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.16545","created_at":"2026-06-19T16:10:37Z"},{"alias_kind":"pith_short_12","alias_value":"JLB75PIW7I57","created_at":"2026-06-19T16:10:37Z"},{"alias_kind":"pith_short_16","alias_value":"JLB75PIW7I57ILQ6","created_at":"2026-06-19T16:10:37Z"},{"alias_kind":"pith_short_8","alias_value":"JLB75PIW","created_at":"2026-06-19T16:10:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:JLB75PIW7I57ILQ6O7UQN3BVCK","target":"record","payload":{"canonical_record":{"source":{"id":"2604.16545","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-04-17T06:08:58Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"e89b86e7157d2454c26f351e785e9954b52e4796573bdffaea8213d4e74117bd","abstract_canon_sha256":"698d58871b768cd3606d61a2a22b856ec74244ed581df9b89b540003aff8f2b9"},"schema_version":"1.0"},"canonical_sha256":"4ac3febd16fa3bf42e1e77e906ec3512adebc69862ed4fd1dae0c895b9460ff4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:37.483338Z","signature_b64":"YdBgT8EjaxJ0fFofBM+edBVEZKN10CeGqvIvZC4aV+ITl4U5+2t1+/fKFqVhsb/SaLHZaYDfimUFgESTqH0KBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ac3febd16fa3bf42e1e77e906ec3512adebc69862ed4fd1dae0c895b9460ff4","last_reissued_at":"2026-06-19T16:10:37.482979Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:37.482979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2604.16545","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":"2026-06-19T16:10:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7LtrXJO0p4gQCnrTnMBZ8aVZfe1HdEGyLtDJL+20I0vesU1KYfmAg37R/wr4KEy/6CvgFZAAkvYBr6uk2o9gAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T03:46:11.832796Z"},"content_sha256":"ef1f13e8bfd73fa5f193ba7391f7178e3d19335388620406419d8fd13f40d71e","schema_version":"1.0","event_id":"sha256:ef1f13e8bfd73fa5f193ba7391f7178e3d19335388620406419d8fd13f40d71e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:JLB75PIW7I57ILQ6O7UQN3BVCK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Energy conditions in static, spherically symmetric spacetimes and effective geometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A logarithmic correction to Schwarzschild in static spherical symmetry obeys all classical energy conditions and serves as an effective exterior for horizon-bearing and horizonless compact objects.","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Emmanuele Battista, Zi-Liang Wang","submitted_at":"2026-04-17T06:08:58Z","abstract_excerpt":"Classical energy conditions are investigated in generic static and spherically symmetric spacetimes. In setups with nonconstant $g_{tt} g_{rr}$, the appearance of horizons can signal the violation of the null energy condition and the breakdown of some standard near-horizon properties. For configurations satisfying $g_{tt}g_{rr}=-1$, we devise a systematic algorithm to generate solutions of the Einstein field equations that automatically obey the null energy condition. Within this family, we select a particularly significant metric that incorporates a logarithmic correction to the Schwarzschild"},"claims":{"count":3,"items":[{"kind":"strongest_claim","text":"Within this family, we select a particularly significant metric that incorporates a logarithmic correction to the Schwarzschild model and fulfills all standard energy criteria. Our analysis shows that this geometry can be interpreted as an effective exterior description for both horizon-bearing and horizonless compact objects, and suggests that it can potentially act, in certain regimes, as a black hole mimicker.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that g_tt g_rr = -1 enables a systematic algorithm to generate solutions obeying the null energy condition; the paper states that non-constant products can signal null energy condition violation at horizons.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A logarithmic correction to Schwarzschild in static spherical symmetry obeys all classical energy conditions and serves as an effective exterior for horizon-bearing and horizonless compact objects.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"}],"snapshot_sha256":"ec01095630c12e4790e8dd1adf2be6843ad5af95335cc27ff7cd25f59061b0d9"},"source":{"id":"2604.16545","kind":"arxiv","version":3},"verdict":{"id":"1f869827-2440-4b87-8bd0-5d4e12c4a8a9","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T08:30:41.704028Z","strongest_claim":"Within this family, we select a particularly significant metric that incorporates a logarithmic correction to the Schwarzschild model and fulfills all standard energy criteria. Our analysis shows that this geometry can be interpreted as an effective exterior description for both horizon-bearing and horizonless compact objects, and suggests that it can potentially act, in certain regimes, as a black hole mimicker.","one_line_summary":"A logarithmic correction to Schwarzschild in static spherical symmetry obeys all classical energy conditions and serves as an effective exterior for horizon-bearing and horizonless compact objects.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that g_tt g_rr = -1 enables a systematic algorithm to generate solutions obeying the null energy condition; the paper states that non-constant products can signal null energy condition violation at horizons.","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.16545/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":"1f869827-2440-4b87-8bd0-5d4e12c4a8a9"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:10:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uajcg0er2IjJPxCHqlQIBD2ZYnQHhmILRK+zU6anqFe5eF25c5EtrTiBf7Q1MgmTf82j1WSKgsWIpFthDquIBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T03:46:11.833304Z"},"content_sha256":"82ae21664e474857c7685a3ab0a624d95a6192df48f37e89acd116c3e48331f2","schema_version":"1.0","event_id":"sha256:82ae21664e474857c7685a3ab0a624d95a6192df48f37e89acd116c3e48331f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JLB75PIW7I57ILQ6O7UQN3BVCK/bundle.json","state_url":"https://pith.science/pith/JLB75PIW7I57ILQ6O7UQN3BVCK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JLB75PIW7I57ILQ6O7UQN3BVCK/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":"2026-06-28T03:46:11Z","links":{"resolver":"https://pith.science/pith/JLB75PIW7I57ILQ6O7UQN3BVCK","bundle":"https://pith.science/pith/JLB75PIW7I57ILQ6O7UQN3BVCK/bundle.json","state":"https://pith.science/pith/JLB75PIW7I57ILQ6O7UQN3BVCK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JLB75PIW7I57ILQ6O7UQN3BVCK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:JLB75PIW7I57ILQ6O7UQN3BVCK","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":"698d58871b768cd3606d61a2a22b856ec74244ed581df9b89b540003aff8f2b9","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-04-17T06:08:58Z","title_canon_sha256":"e89b86e7157d2454c26f351e785e9954b52e4796573bdffaea8213d4e74117bd"},"schema_version":"1.0","source":{"id":"2604.16545","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.16545","created_at":"2026-06-19T16:10:37Z"},{"alias_kind":"arxiv_version","alias_value":"2604.16545v3","created_at":"2026-06-19T16:10:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.16545","created_at":"2026-06-19T16:10:37Z"},{"alias_kind":"pith_short_12","alias_value":"JLB75PIW7I57","created_at":"2026-06-19T16:10:37Z"},{"alias_kind":"pith_short_16","alias_value":"JLB75PIW7I57ILQ6","created_at":"2026-06-19T16:10:37Z"},{"alias_kind":"pith_short_8","alias_value":"JLB75PIW","created_at":"2026-06-19T16:10:37Z"}],"graph_snapshots":[{"event_id":"sha256:82ae21664e474857c7685a3ab0a624d95a6192df48f37e89acd116c3e48331f2","target":"graph","created_at":"2026-06-19T16:10:37Z","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":3,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"Within this family, we select a particularly significant metric that incorporates a logarithmic correction to the Schwarzschild model and fulfills all standard energy criteria. Our analysis shows that this geometry can be interpreted as an effective exterior description for both horizon-bearing and horizonless compact objects, and suggests that it can potentially act, in certain regimes, as a black hole mimicker."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The assumption that g_tt g_rr = -1 enables a systematic algorithm to generate solutions obeying the null energy condition; the paper states that non-constant products can signal null energy condition violation at horizons."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"A logarithmic correction to Schwarzschild in static spherical symmetry obeys all classical energy conditions and serves as an effective exterior for horizon-bearing and horizonless compact objects."}],"snapshot_sha256":"ec01095630c12e4790e8dd1adf2be6843ad5af95335cc27ff7cd25f59061b0d9"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2604.16545/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Classical energy conditions are investigated in generic static and spherically symmetric spacetimes. In setups with nonconstant $g_{tt} g_{rr}$, the appearance of horizons can signal the violation of the null energy condition and the breakdown of some standard near-horizon properties. For configurations satisfying $g_{tt}g_{rr}=-1$, we devise a systematic algorithm to generate solutions of the Einstein field equations that automatically obey the null energy condition. Within this family, we select a particularly significant metric that incorporates a logarithmic correction to the Schwarzschild","authors_text":"Emmanuele Battista, Zi-Liang Wang","cross_cats":["hep-th"],"headline":"A logarithmic correction to Schwarzschild in static spherical symmetry obeys all classical energy conditions and serves as an effective exterior for horizon-bearing and horizonless compact objects.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-04-17T06:08:58Z","title":"Energy conditions in static, spherically symmetric spacetimes and effective geometries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.16545","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-10T08:30:41.704028Z","id":"1f869827-2440-4b87-8bd0-5d4e12c4a8a9","model_set":{"reader":"grok-4.3"},"one_line_summary":"A logarithmic correction to Schwarzschild in static spherical symmetry obeys all classical energy conditions and serves as an effective exterior for horizon-bearing and horizonless compact objects.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"","strongest_claim":"Within this family, we select a particularly significant metric that incorporates a logarithmic correction to the Schwarzschild model and fulfills all standard energy criteria. Our analysis shows that this geometry can be interpreted as an effective exterior description for both horizon-bearing and horizonless compact objects, and suggests that it can potentially act, in certain regimes, as a black hole mimicker.","weakest_assumption":"The assumption that g_tt g_rr = -1 enables a systematic algorithm to generate solutions obeying the null energy condition; the paper states that non-constant products can signal null energy condition violation at horizons."}},"verdict_id":"1f869827-2440-4b87-8bd0-5d4e12c4a8a9"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ef1f13e8bfd73fa5f193ba7391f7178e3d19335388620406419d8fd13f40d71e","target":"record","created_at":"2026-06-19T16:10:37Z","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":"698d58871b768cd3606d61a2a22b856ec74244ed581df9b89b540003aff8f2b9","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-04-17T06:08:58Z","title_canon_sha256":"e89b86e7157d2454c26f351e785e9954b52e4796573bdffaea8213d4e74117bd"},"schema_version":"1.0","source":{"id":"2604.16545","kind":"arxiv","version":3}},"canonical_sha256":"4ac3febd16fa3bf42e1e77e906ec3512adebc69862ed4fd1dae0c895b9460ff4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ac3febd16fa3bf42e1e77e906ec3512adebc69862ed4fd1dae0c895b9460ff4","first_computed_at":"2026-06-19T16:10:37.482979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:37.482979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YdBgT8EjaxJ0fFofBM+edBVEZKN10CeGqvIvZC4aV+ITl4U5+2t1+/fKFqVhsb/SaLHZaYDfimUFgESTqH0KBA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:37.483338Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.16545","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef1f13e8bfd73fa5f193ba7391f7178e3d19335388620406419d8fd13f40d71e","sha256:82ae21664e474857c7685a3ab0a624d95a6192df48f37e89acd116c3e48331f2"],"state_sha256":"f4a4b7551a775a073d5c6fe70f602f679af827fb125118b5784aaf409c18561a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4arSINlgVJ9PaI8p0Tt1wT5AfrrOX0iwtg54hFXIc4q9YCTUnORaxSrBFSIZglkzc6RrawvWJrcgW3DdZ3j9BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T03:46:11.835859Z","bundle_sha256":"b7f0cdd77664ea361726c2a22383169f30ddf279008e0eeb694b66440a4e9b59"}}