{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:2THCWDBET3OTURTIWRKY4MT24Y","short_pith_number":"pith:2THCWDBE","canonical_record":{"source":{"id":"2605.26504","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-26T03:37:39Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"8e2a771e7ea95250109e718d5b852bd47d07570c838857e38021b9afa8c755a4","abstract_canon_sha256":"6b312f477de46eeade2df4e75a7655da3fcb02c86438d55fa5c13b5654e7b930"},"schema_version":"1.0"},"canonical_sha256":"d4ce2b0c249edd3a4668b4558e327ae6023c217baab21d902ec5c42b068ee79e","source":{"kind":"arxiv","id":"2605.26504","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.26504","created_at":"2026-05-27T01:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"2605.26504v1","created_at":"2026-05-27T01:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.26504","created_at":"2026-05-27T01:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"2THCWDBET3OT","created_at":"2026-05-27T01:05:23Z"},{"alias_kind":"pith_short_16","alias_value":"2THCWDBET3OTURTI","created_at":"2026-05-27T01:05:23Z"},{"alias_kind":"pith_short_8","alias_value":"2THCWDBE","created_at":"2026-05-27T01:05:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:2THCWDBET3OTURTIWRKY4MT24Y","target":"record","payload":{"canonical_record":{"source":{"id":"2605.26504","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-26T03:37:39Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"8e2a771e7ea95250109e718d5b852bd47d07570c838857e38021b9afa8c755a4","abstract_canon_sha256":"6b312f477de46eeade2df4e75a7655da3fcb02c86438d55fa5c13b5654e7b930"},"schema_version":"1.0"},"canonical_sha256":"d4ce2b0c249edd3a4668b4558e327ae6023c217baab21d902ec5c42b068ee79e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T01:05:23.424725Z","signature_b64":"A/l3SLxxwoVrzd9kKia/uQKObwBM58rP4iwgrV5Jnu38ffhETkzxDItp4+uiUDi1EqYCUFqFRpXvuAa0h6a9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4ce2b0c249edd3a4668b4558e327ae6023c217baab21d902ec5c42b068ee79e","last_reissued_at":"2026-05-27T01:05:23.423906Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T01:05:23.423906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.26504","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":"2026-05-27T01:05:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CuwpbdfQ/qn8BXchCH3xDTILkLm07fN2Pgwa2i0Mk2TD8JaxFDeFJhl1dxDszEYxXBxEF2Ui85G966gDtpg5DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T04:17:55.681777Z"},"content_sha256":"45aed05e18e9a6310688ce59e30f7ce05df9f69deaf2ccee7ccfef9c5a2b570d","schema_version":"1.0","event_id":"sha256:45aed05e18e9a6310688ce59e30f7ce05df9f69deaf2ccee7ccfef9c5a2b570d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:2THCWDBET3OTURTIWRKY4MT24Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The $\\sigma$-inverse mean curvature flow and the generalized Penrose conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.DG","authors_text":"Conghan Dong","submitted_at":"2026-05-26T03:37:39Z","abstract_excerpt":"Let $(M^3, g, \\mathbf{k})$ be a complete asymptotically flat initial data set satisfying the dominant energy condition, and let $m$ denote its ADM mass. The generalized Penrose conjecture asserts that the area of an outermost generalized apparent horizon $N\\subset M$ satisfies $|N| \\leq 16 \\pi m^2$. In this paper, we establish this inequality for each connected component of $N$ in the special case where $\\mathbf{k}$ is proportional to the metric $g$. Our approach is based on a new geometric evolution, which we call the $\\sigma $-inverse mean curvature flow, together with a novel monotonicity f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26504","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/2605.26504/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":"2026-05-27T01:05:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3FKMzYK9h16qEm04sdhFbQ5vIS6hVZWghtXN89u0yqLsBUI4fa7yHP12+CDCi9Rr23ZZS2G+EFaSACWOcYcZAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T04:17:55.682141Z"},"content_sha256":"cd1a2ba1430523ad0651d94617160640b77f56a55d85b553020da1bda1b51ec2","schema_version":"1.0","event_id":"sha256:cd1a2ba1430523ad0651d94617160640b77f56a55d85b553020da1bda1b51ec2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2THCWDBET3OTURTIWRKY4MT24Y/bundle.json","state_url":"https://pith.science/pith/2THCWDBET3OTURTIWRKY4MT24Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2THCWDBET3OTURTIWRKY4MT24Y/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":"2026-06-28T04:17:55Z","links":{"resolver":"https://pith.science/pith/2THCWDBET3OTURTIWRKY4MT24Y","bundle":"https://pith.science/pith/2THCWDBET3OTURTIWRKY4MT24Y/bundle.json","state":"https://pith.science/pith/2THCWDBET3OTURTIWRKY4MT24Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2THCWDBET3OTURTIWRKY4MT24Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:2THCWDBET3OTURTIWRKY4MT24Y","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":"6b312f477de46eeade2df4e75a7655da3fcb02c86438d55fa5c13b5654e7b930","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-26T03:37:39Z","title_canon_sha256":"8e2a771e7ea95250109e718d5b852bd47d07570c838857e38021b9afa8c755a4"},"schema_version":"1.0","source":{"id":"2605.26504","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.26504","created_at":"2026-05-27T01:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"2605.26504v1","created_at":"2026-05-27T01:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.26504","created_at":"2026-05-27T01:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"2THCWDBET3OT","created_at":"2026-05-27T01:05:23Z"},{"alias_kind":"pith_short_16","alias_value":"2THCWDBET3OTURTI","created_at":"2026-05-27T01:05:23Z"},{"alias_kind":"pith_short_8","alias_value":"2THCWDBE","created_at":"2026-05-27T01:05:23Z"}],"graph_snapshots":[{"event_id":"sha256:cd1a2ba1430523ad0651d94617160640b77f56a55d85b553020da1bda1b51ec2","target":"graph","created_at":"2026-05-27T01:05:23Z","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/2605.26504/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $(M^3, g, \\mathbf{k})$ be a complete asymptotically flat initial data set satisfying the dominant energy condition, and let $m$ denote its ADM mass. The generalized Penrose conjecture asserts that the area of an outermost generalized apparent horizon $N\\subset M$ satisfies $|N| \\leq 16 \\pi m^2$. In this paper, we establish this inequality for each connected component of $N$ in the special case where $\\mathbf{k}$ is proportional to the metric $g$. Our approach is based on a new geometric evolution, which we call the $\\sigma $-inverse mean curvature flow, together with a novel monotonicity f","authors_text":"Conghan Dong","cross_cats":["gr-qc"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-26T03:37:39Z","title":"The $\\sigma$-inverse mean curvature flow and the generalized Penrose conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26504","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":"sha256:45aed05e18e9a6310688ce59e30f7ce05df9f69deaf2ccee7ccfef9c5a2b570d","target":"record","created_at":"2026-05-27T01:05:23Z","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":"6b312f477de46eeade2df4e75a7655da3fcb02c86438d55fa5c13b5654e7b930","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-26T03:37:39Z","title_canon_sha256":"8e2a771e7ea95250109e718d5b852bd47d07570c838857e38021b9afa8c755a4"},"schema_version":"1.0","source":{"id":"2605.26504","kind":"arxiv","version":1}},"canonical_sha256":"d4ce2b0c249edd3a4668b4558e327ae6023c217baab21d902ec5c42b068ee79e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4ce2b0c249edd3a4668b4558e327ae6023c217baab21d902ec5c42b068ee79e","first_computed_at":"2026-05-27T01:05:23.423906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T01:05:23.423906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A/l3SLxxwoVrzd9kKia/uQKObwBM58rP4iwgrV5Jnu38ffhETkzxDItp4+uiUDi1EqYCUFqFRpXvuAa0h6a9DQ==","signature_status":"signed_v1","signed_at":"2026-05-27T01:05:23.424725Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.26504","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45aed05e18e9a6310688ce59e30f7ce05df9f69deaf2ccee7ccfef9c5a2b570d","sha256:cd1a2ba1430523ad0651d94617160640b77f56a55d85b553020da1bda1b51ec2"],"state_sha256":"403cd75130308818efe5b093f67e4354d0f86c005e9a66f662b02468e28d6f98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DuTaWYCz0SYv0hiUtSr/ygqzoTR6cMZQqubPexoRz8zWLEroo7nsyncJejTFbwOG2upFGtwdD3e0y0bRX9XQAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T04:17:55.684087Z","bundle_sha256":"1d4309be923ef9cf40886275def227290d569caf794c21862a9d7a2f455ff18c"}}