{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FH4YT7FT7NSXAJJ3QIBENR7YLA","short_pith_number":"pith:FH4YT7FT","canonical_record":{"source":{"id":"1506.06400","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-06-21T18:52:47Z","cross_cats_sorted":["math.AP","math.DG"],"title_canon_sha256":"9a26608022262cca03b409f1075c1ea2f68a1c854f694bcfc737f8a83ad443b1","abstract_canon_sha256":"14f411213df311f82ede9ff0ea8bb33690d20adbf0398609df0ca796e6233987"},"schema_version":"1.0"},"canonical_sha256":"29f989fcb3fb6570253b820246c7f858287d7de553fefe3ed29524b4caa8aff7","source":{"kind":"arxiv","id":"1506.06400","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06400","created_at":"2026-05-18T01:41:45Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06400v1","created_at":"2026-05-18T01:41:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06400","created_at":"2026-05-18T01:41:45Z"},{"alias_kind":"pith_short_12","alias_value":"FH4YT7FT7NSX","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FH4YT7FT7NSXAJJ3","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FH4YT7FT","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FH4YT7FT7NSXAJJ3QIBENR7YLA","target":"record","payload":{"canonical_record":{"source":{"id":"1506.06400","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-06-21T18:52:47Z","cross_cats_sorted":["math.AP","math.DG"],"title_canon_sha256":"9a26608022262cca03b409f1075c1ea2f68a1c854f694bcfc737f8a83ad443b1","abstract_canon_sha256":"14f411213df311f82ede9ff0ea8bb33690d20adbf0398609df0ca796e6233987"},"schema_version":"1.0"},"canonical_sha256":"29f989fcb3fb6570253b820246c7f858287d7de553fefe3ed29524b4caa8aff7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:45.318219Z","signature_b64":"+e4sCIzix85ocwtKSKZYNoh8TBdIhjzxxDYHN3MliyQ/AbiLg6lQPu93APG5tWrHZ/aokLPe8ONfJU2BA+HnAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29f989fcb3fb6570253b820246c7f858287d7de553fefe3ed29524b4caa8aff7","last_reissued_at":"2026-05-18T01:41:45.317663Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:45.317663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.06400","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":"2026-05-18T01:41:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A4FZHGDbNrx4OdsmBS7JSmW2CM1IK3bEoBwUrM86AAkkF/KKGRTn8Ck2Ei2D22LlQxh5+g618fxcIOKtKHJfAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T16:24:39.944286Z"},"content_sha256":"ce2ea95334374a7991f9a5858a15dbc900d7e814952e430f7b52ee5d9e7f986e","schema_version":"1.0","event_id":"sha256:ce2ea95334374a7991f9a5858a15dbc900d7e814952e430f7b52ee5d9e7f986e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FH4YT7FT7NSXAJJ3QIBENR7YLA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Penrose inequality on perturbations of the Schwarzschild exterior","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG"],"primary_cat":"gr-qc","authors_text":"Spyros Alexakis","submitted_at":"2015-06-21T18:52:47Z","abstract_excerpt":"We prove a version the Penrose inequality for black hole space-times which are perturbations of the Schwarzschild exterior in a slab around a null hypersurface $\\underline{\\mathcal{N}}_0$. $\\underline{\\mathcal{N}}_0$ terminates at past null infinity $\\mathcal{I}^-$ and $\\mathcal{S}_0:=\\partial\\underline{\\mathcal{N}}_0$ is chosen to be a marginally outer trapped sphere. We show that the area of $\\mathcal{S}_0$ yields a lower bound for the Bondi energy of sections of past null infinity, thus also for the total ADM energy. Our argument is perturbative, and rests on suitably deforming the initial "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06400","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":""},"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":"2026-05-18T01:41:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IhjGhW6lib9zxDpXkVE8LkLAzKSZAouo4PBeutLZ+e6IRfgsAt7nTVFpoW/9LPh1cR0Wiv+SclTWM/JNK4DmDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T16:24:39.944996Z"},"content_sha256":"dd365b1ff36047edc31d12524b467f53845ba2a5c55bbff9a09c9efdcfe2a668","schema_version":"1.0","event_id":"sha256:dd365b1ff36047edc31d12524b467f53845ba2a5c55bbff9a09c9efdcfe2a668"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FH4YT7FT7NSXAJJ3QIBENR7YLA/bundle.json","state_url":"https://pith.science/pith/FH4YT7FT7NSXAJJ3QIBENR7YLA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FH4YT7FT7NSXAJJ3QIBENR7YLA/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":"2026-05-23T16:24:39Z","links":{"resolver":"https://pith.science/pith/FH4YT7FT7NSXAJJ3QIBENR7YLA","bundle":"https://pith.science/pith/FH4YT7FT7NSXAJJ3QIBENR7YLA/bundle.json","state":"https://pith.science/pith/FH4YT7FT7NSXAJJ3QIBENR7YLA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FH4YT7FT7NSXAJJ3QIBENR7YLA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FH4YT7FT7NSXAJJ3QIBENR7YLA","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":"14f411213df311f82ede9ff0ea8bb33690d20adbf0398609df0ca796e6233987","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-06-21T18:52:47Z","title_canon_sha256":"9a26608022262cca03b409f1075c1ea2f68a1c854f694bcfc737f8a83ad443b1"},"schema_version":"1.0","source":{"id":"1506.06400","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06400","created_at":"2026-05-18T01:41:45Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06400v1","created_at":"2026-05-18T01:41:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06400","created_at":"2026-05-18T01:41:45Z"},{"alias_kind":"pith_short_12","alias_value":"FH4YT7FT7NSX","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FH4YT7FT7NSXAJJ3","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FH4YT7FT","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:dd365b1ff36047edc31d12524b467f53845ba2a5c55bbff9a09c9efdcfe2a668","target":"graph","created_at":"2026-05-18T01:41:45Z","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 prove a version the Penrose inequality for black hole space-times which are perturbations of the Schwarzschild exterior in a slab around a null hypersurface $\\underline{\\mathcal{N}}_0$. $\\underline{\\mathcal{N}}_0$ terminates at past null infinity $\\mathcal{I}^-$ and $\\mathcal{S}_0:=\\partial\\underline{\\mathcal{N}}_0$ is chosen to be a marginally outer trapped sphere. We show that the area of $\\mathcal{S}_0$ yields a lower bound for the Bondi energy of sections of past null infinity, thus also for the total ADM energy. Our argument is perturbative, and rests on suitably deforming the initial ","authors_text":"Spyros Alexakis","cross_cats":["math.AP","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-06-21T18:52:47Z","title":"The Penrose inequality on perturbations of the Schwarzschild exterior"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06400","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:ce2ea95334374a7991f9a5858a15dbc900d7e814952e430f7b52ee5d9e7f986e","target":"record","created_at":"2026-05-18T01:41:45Z","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":"14f411213df311f82ede9ff0ea8bb33690d20adbf0398609df0ca796e6233987","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-06-21T18:52:47Z","title_canon_sha256":"9a26608022262cca03b409f1075c1ea2f68a1c854f694bcfc737f8a83ad443b1"},"schema_version":"1.0","source":{"id":"1506.06400","kind":"arxiv","version":1}},"canonical_sha256":"29f989fcb3fb6570253b820246c7f858287d7de553fefe3ed29524b4caa8aff7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29f989fcb3fb6570253b820246c7f858287d7de553fefe3ed29524b4caa8aff7","first_computed_at":"2026-05-18T01:41:45.317663Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:45.317663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+e4sCIzix85ocwtKSKZYNoh8TBdIhjzxxDYHN3MliyQ/AbiLg6lQPu93APG5tWrHZ/aokLPe8ONfJU2BA+HnAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:45.318219Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06400","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce2ea95334374a7991f9a5858a15dbc900d7e814952e430f7b52ee5d9e7f986e","sha256:dd365b1ff36047edc31d12524b467f53845ba2a5c55bbff9a09c9efdcfe2a668"],"state_sha256":"b3b1354afa9ec274032e758fd5ad3a6edd58d1babc95868675f2912d69af9362"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nfdmpeg2m9HXSXXJ5a1jhhWX+o46PcqbpvZfk2P+CjHU1oEHQkSFPTYKg4opHhARkePPSNUAErTaC1nWO6i/Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T16:24:39.949272Z","bundle_sha256":"a9962b87de31313a6047f63951741976965cead327934d80335b8f0c8450e124"}}