{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:SDYIYF2J3O7TOCJBCSKSONYWJE","short_pith_number":"pith:SDYIYF2J","canonical_record":{"source":{"id":"2504.10641","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-14T18:50:23Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"790ce8c54abe975b1637fb4203b2c610d62c68b1059b997619e9c23a4170bb46","abstract_canon_sha256":"021c874c68263bde6e2c6257873d1877dcc554538cf382c08bd435f0b9a2a2c2"},"schema_version":"1.0"},"canonical_sha256":"90f08c1749dbbf370921149527371649030d401aea0bef8adf372eddd90b2630","source":{"kind":"arxiv","id":"2504.10641","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.10641","created_at":"2026-07-05T10:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"2504.10641v1","created_at":"2026-07-05T10:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.10641","created_at":"2026-07-05T10:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"SDYIYF2J3O7T","created_at":"2026-07-05T10:49:20Z"},{"alias_kind":"pith_short_16","alias_value":"SDYIYF2J3O7TOCJB","created_at":"2026-07-05T10:49:20Z"},{"alias_kind":"pith_short_8","alias_value":"SDYIYF2J","created_at":"2026-07-05T10:49:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:SDYIYF2J3O7TOCJBCSKSONYWJE","target":"record","payload":{"canonical_record":{"source":{"id":"2504.10641","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-14T18:50:23Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"790ce8c54abe975b1637fb4203b2c610d62c68b1059b997619e9c23a4170bb46","abstract_canon_sha256":"021c874c68263bde6e2c6257873d1877dcc554538cf382c08bd435f0b9a2a2c2"},"schema_version":"1.0"},"canonical_sha256":"90f08c1749dbbf370921149527371649030d401aea0bef8adf372eddd90b2630","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:49:20.902166Z","signature_b64":"eZ/HNxBoglGEbPxJBSzIlfRNqWoUnWcrqDZ+x1PW6uWX37Yv5hy0h/HwWM0gE5rjFDCLbqvIURznC7xxj8fnCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90f08c1749dbbf370921149527371649030d401aea0bef8adf372eddd90b2630","last_reissued_at":"2026-07-05T10:49:20.901725Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:49:20.901725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.10641","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":"2026-07-05T10:49:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oKTYFNpHkCzCTHIsfOQ73LabrWncT5j2Jgysp0j34b6eeGRiXf7KaLeYtZmsMSIL4NGHfTNf4SiYKkO9Rb7jAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:53:13.872899Z"},"content_sha256":"2bc03a1714cd66a95db9b74e7cb1460d7481842f74f5726772fee0e161ae2393","schema_version":"1.0","event_id":"sha256:2bc03a1714cd66a95db9b74e7cb1460d7481842f74f5726772fee0e161ae2393"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:SDYIYF2J3O7TOCJBCSKSONYWJE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Proof of the Spacetime Penrose Inequality With Suboptimal Constant in the Asymptotically Flat and Asymptotically Hyperboloidal Regimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.DG","authors_text":"Brian Allen, Demetre Kazaras, Edward Bryden, Marcus Khuri","submitted_at":"2025-04-14T18:50:23Z","abstract_excerpt":"We establish mass lower bounds of Penrose-type in the setting of $3$-dimensional initial data sets for the Einstein equations satisfying the dominant energy condition, which are either asymptotically flat or asymptotically hyperboloidal. More precisely, the lower bound consists of a universal constant multiplied by the square root of the minimal area required to enclose the outermost apparent horizon. Here the outermost apparent horizon may contain both marginally outer trapped (MOTS) and marginally inner trapped (MITS) components. The proof is based on the harmonic level set approach to the p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.10641","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/2504.10641/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":"2026-07-05T10:49:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/CfkwmicjjC3zd4v6+vfItlqiQAkznZGmW+hknRoFaLbwYTdRFj3mNK9jE4VjwJiP/puO+I/2/4YID6/XZ2NAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:53:13.873270Z"},"content_sha256":"becc41c8ccf736df7d5386ea1ba8b89522a95517c3e2fcde77efbef05597a144","schema_version":"1.0","event_id":"sha256:becc41c8ccf736df7d5386ea1ba8b89522a95517c3e2fcde77efbef05597a144"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SDYIYF2J3O7TOCJBCSKSONYWJE/bundle.json","state_url":"https://pith.science/pith/SDYIYF2J3O7TOCJBCSKSONYWJE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SDYIYF2J3O7TOCJBCSKSONYWJE/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":"2026-07-07T13:53:13Z","links":{"resolver":"https://pith.science/pith/SDYIYF2J3O7TOCJBCSKSONYWJE","bundle":"https://pith.science/pith/SDYIYF2J3O7TOCJBCSKSONYWJE/bundle.json","state":"https://pith.science/pith/SDYIYF2J3O7TOCJBCSKSONYWJE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SDYIYF2J3O7TOCJBCSKSONYWJE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SDYIYF2J3O7TOCJBCSKSONYWJE","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":"021c874c68263bde6e2c6257873d1877dcc554538cf382c08bd435f0b9a2a2c2","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-14T18:50:23Z","title_canon_sha256":"790ce8c54abe975b1637fb4203b2c610d62c68b1059b997619e9c23a4170bb46"},"schema_version":"1.0","source":{"id":"2504.10641","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.10641","created_at":"2026-07-05T10:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"2504.10641v1","created_at":"2026-07-05T10:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.10641","created_at":"2026-07-05T10:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"SDYIYF2J3O7T","created_at":"2026-07-05T10:49:20Z"},{"alias_kind":"pith_short_16","alias_value":"SDYIYF2J3O7TOCJB","created_at":"2026-07-05T10:49:20Z"},{"alias_kind":"pith_short_8","alias_value":"SDYIYF2J","created_at":"2026-07-05T10:49:20Z"}],"graph_snapshots":[{"event_id":"sha256:becc41c8ccf736df7d5386ea1ba8b89522a95517c3e2fcde77efbef05597a144","target":"graph","created_at":"2026-07-05T10:49:20Z","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/2504.10641/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish mass lower bounds of Penrose-type in the setting of $3$-dimensional initial data sets for the Einstein equations satisfying the dominant energy condition, which are either asymptotically flat or asymptotically hyperboloidal. More precisely, the lower bound consists of a universal constant multiplied by the square root of the minimal area required to enclose the outermost apparent horizon. Here the outermost apparent horizon may contain both marginally outer trapped (MOTS) and marginally inner trapped (MITS) components. The proof is based on the harmonic level set approach to the p","authors_text":"Brian Allen, Demetre Kazaras, Edward Bryden, Marcus Khuri","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-14T18:50:23Z","title":"Proof of the Spacetime Penrose Inequality With Suboptimal Constant in the Asymptotically Flat and Asymptotically Hyperboloidal Regimes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.10641","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":"sha256:2bc03a1714cd66a95db9b74e7cb1460d7481842f74f5726772fee0e161ae2393","target":"record","created_at":"2026-07-05T10:49:20Z","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":"021c874c68263bde6e2c6257873d1877dcc554538cf382c08bd435f0b9a2a2c2","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-14T18:50:23Z","title_canon_sha256":"790ce8c54abe975b1637fb4203b2c610d62c68b1059b997619e9c23a4170bb46"},"schema_version":"1.0","source":{"id":"2504.10641","kind":"arxiv","version":1}},"canonical_sha256":"90f08c1749dbbf370921149527371649030d401aea0bef8adf372eddd90b2630","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90f08c1749dbbf370921149527371649030d401aea0bef8adf372eddd90b2630","first_computed_at":"2026-07-05T10:49:20.901725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:49:20.901725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eZ/HNxBoglGEbPxJBSzIlfRNqWoUnWcrqDZ+x1PW6uWX37Yv5hy0h/HwWM0gE5rjFDCLbqvIURznC7xxj8fnCg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:49:20.902166Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.10641","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2bc03a1714cd66a95db9b74e7cb1460d7481842f74f5726772fee0e161ae2393","sha256:becc41c8ccf736df7d5386ea1ba8b89522a95517c3e2fcde77efbef05597a144"],"state_sha256":"e9880b237dc4e6164a58aeb6b8bc8d0b265ca847f9eae38c19baab80f996d8af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M6raBSve4pGDTBmiU3AtbbmgV3KI5wyFm7IVGOiNIwpkYVCFoTRHwY2ZVxbMrHB+OFDwknqG9kG+gzJuf0q3BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T13:53:13.875158Z","bundle_sha256":"bb168a7defde4030f3779c395523ac7f3f46e4b6bb7f57f1131948f9c0122302"}}