{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:Y4MUPVJRTWHNR5NMQTQK5IY7LV","short_pith_number":"pith:Y4MUPVJR","canonical_record":{"source":{"id":"2608.00519","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-08-01T08:30:50Z","cross_cats_sorted":[],"title_canon_sha256":"2fb178900bf697200adaacfa822509071591a872d93a753f1b488ebcc898a002","abstract_canon_sha256":"355c713d59ed7dafb1d08c1b68b342c375e6ce7dc8e2bef16b0c9f3f60bb478c"},"schema_version":"1.0"},"canonical_sha256":"c71947d5319d8ed8f5ac84e0aea31f5d46e51f4e6e44dcd8ec6826d61fbca79b","source":{"kind":"arxiv","id":"2608.00519","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.00519","created_at":"2026-08-04T00:37:06Z"},{"alias_kind":"arxiv_version","alias_value":"2608.00519v1","created_at":"2026-08-04T00:37:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.00519","created_at":"2026-08-04T00:37:06Z"},{"alias_kind":"pith_short_12","alias_value":"Y4MUPVJRTWHN","created_at":"2026-08-04T00:37:06Z"},{"alias_kind":"pith_short_16","alias_value":"Y4MUPVJRTWHNR5NM","created_at":"2026-08-04T00:37:06Z"},{"alias_kind":"pith_short_8","alias_value":"Y4MUPVJR","created_at":"2026-08-04T00:37:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:Y4MUPVJRTWHNR5NMQTQK5IY7LV","target":"record","payload":{"canonical_record":{"source":{"id":"2608.00519","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-08-01T08:30:50Z","cross_cats_sorted":[],"title_canon_sha256":"2fb178900bf697200adaacfa822509071591a872d93a753f1b488ebcc898a002","abstract_canon_sha256":"355c713d59ed7dafb1d08c1b68b342c375e6ce7dc8e2bef16b0c9f3f60bb478c"},"schema_version":"1.0"},"canonical_sha256":"c71947d5319d8ed8f5ac84e0aea31f5d46e51f4e6e44dcd8ec6826d61fbca79b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T00:37:06.361083Z","signature_b64":"enYEVD0wMMvjTDGN2iVDH537H06KMd16wSMZ5WB+OTAP7saBKcTS5qgs3rBlliFjcMKlLnZnjG/fJ0sYsxa+DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c71947d5319d8ed8f5ac84e0aea31f5d46e51f4e6e44dcd8ec6826d61fbca79b","last_reissued_at":"2026-08-04T00:37:06.359430Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T00:37:06.359430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.00519","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":"2026-08-04T00:37:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IaFt258u8yzF5ng4Pqu+gi58M9Ol8/QG34hHj1P9SFlwdsnfuqrl4FRmwD2z7pajhJ+RgfqOLBmo8/0Y41ltBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T14:37:58.828459Z"},"content_sha256":"3e80ad955b08bfed2d515c82507d8f50b7ccfd187ab484c5cec58cee00bb22bc","schema_version":"1.0","event_id":"sha256:3e80ad955b08bfed2d515c82507d8f50b7ccfd187ab484c5cec58cee00bb22bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:Y4MUPVJRTWHNR5NMQTQK5IY7LV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convexity criterion and radial-profile response for off-shell Kerr geometries: a fuzzy-dark-matter profile as an analytic benchmark","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Jie Shi, Jingxu Wu, Liangyu Luo","submitted_at":"2026-08-01T08:30:50Z","abstract_excerpt":"We establish a sufficient one-minimum criterion for the off-shell Kerr family $\\Delta(r) = r^2 - 2rm(r) + a^2$ with a positive, nondecreasing mass profile $m(r)$, showing that $1 - 2m'(r) - rm''(r) > 0$ ensures strict convexity and determines root counts for $\\Delta$. Using a fuzzy-dark-matter-inspired benchmark satisfying this bound, we derive first-order responses for the outer horizon, extremal branch, photon sphere, and shadow functional under general deformations $m/M_{\\text{ADM}} = 1 + \\varepsilon h$. We demonstrate that static horizon and photon responses are profile-controlled, spin-od"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00519","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/2608.00519/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":"2026-08-04T00:37:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"22aJR4beqz5LocaAZPbBvTONlRze8GxJRr3yS6DcPUYbFShuEnQhFkSpzs86j7p2KDjLXNuEfRvA9u08dNt0Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T14:37:58.829058Z"},"content_sha256":"4b0aafb8d453756bd0c8177891827316ddca4c01e96ec4446430cdaf7b0988dd","schema_version":"1.0","event_id":"sha256:4b0aafb8d453756bd0c8177891827316ddca4c01e96ec4446430cdaf7b0988dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y4MUPVJRTWHNR5NMQTQK5IY7LV/bundle.json","state_url":"https://pith.science/pith/Y4MUPVJRTWHNR5NMQTQK5IY7LV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y4MUPVJRTWHNR5NMQTQK5IY7LV/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":"2026-08-19T14:37:58Z","links":{"resolver":"https://pith.science/pith/Y4MUPVJRTWHNR5NMQTQK5IY7LV","bundle":"https://pith.science/pith/Y4MUPVJRTWHNR5NMQTQK5IY7LV/bundle.json","state":"https://pith.science/pith/Y4MUPVJRTWHNR5NMQTQK5IY7LV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y4MUPVJRTWHNR5NMQTQK5IY7LV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:Y4MUPVJRTWHNR5NMQTQK5IY7LV","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":"355c713d59ed7dafb1d08c1b68b342c375e6ce7dc8e2bef16b0c9f3f60bb478c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-08-01T08:30:50Z","title_canon_sha256":"2fb178900bf697200adaacfa822509071591a872d93a753f1b488ebcc898a002"},"schema_version":"1.0","source":{"id":"2608.00519","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.00519","created_at":"2026-08-04T00:37:06Z"},{"alias_kind":"arxiv_version","alias_value":"2608.00519v1","created_at":"2026-08-04T00:37:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.00519","created_at":"2026-08-04T00:37:06Z"},{"alias_kind":"pith_short_12","alias_value":"Y4MUPVJRTWHN","created_at":"2026-08-04T00:37:06Z"},{"alias_kind":"pith_short_16","alias_value":"Y4MUPVJRTWHNR5NM","created_at":"2026-08-04T00:37:06Z"},{"alias_kind":"pith_short_8","alias_value":"Y4MUPVJR","created_at":"2026-08-04T00:37:06Z"}],"graph_snapshots":[{"event_id":"sha256:4b0aafb8d453756bd0c8177891827316ddca4c01e96ec4446430cdaf7b0988dd","target":"graph","created_at":"2026-08-04T00:37:06Z","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/2608.00519/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish a sufficient one-minimum criterion for the off-shell Kerr family $\\Delta(r) = r^2 - 2rm(r) + a^2$ with a positive, nondecreasing mass profile $m(r)$, showing that $1 - 2m'(r) - rm''(r) > 0$ ensures strict convexity and determines root counts for $\\Delta$. Using a fuzzy-dark-matter-inspired benchmark satisfying this bound, we derive first-order responses for the outer horizon, extremal branch, photon sphere, and shadow functional under general deformations $m/M_{\\text{ADM}} = 1 + \\varepsilon h$. We demonstrate that static horizon and photon responses are profile-controlled, spin-od","authors_text":"Jie Shi, Jingxu Wu, Liangyu Luo","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-08-01T08:30:50Z","title":"Convexity criterion and radial-profile response for off-shell Kerr geometries: a fuzzy-dark-matter profile as an analytic benchmark"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00519","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":"sha256:3e80ad955b08bfed2d515c82507d8f50b7ccfd187ab484c5cec58cee00bb22bc","target":"record","created_at":"2026-08-04T00:37:06Z","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":"355c713d59ed7dafb1d08c1b68b342c375e6ce7dc8e2bef16b0c9f3f60bb478c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-08-01T08:30:50Z","title_canon_sha256":"2fb178900bf697200adaacfa822509071591a872d93a753f1b488ebcc898a002"},"schema_version":"1.0","source":{"id":"2608.00519","kind":"arxiv","version":1}},"canonical_sha256":"c71947d5319d8ed8f5ac84e0aea31f5d46e51f4e6e44dcd8ec6826d61fbca79b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c71947d5319d8ed8f5ac84e0aea31f5d46e51f4e6e44dcd8ec6826d61fbca79b","first_computed_at":"2026-08-04T00:37:06.359430Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-04T00:37:06.359430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"enYEVD0wMMvjTDGN2iVDH537H06KMd16wSMZ5WB+OTAP7saBKcTS5qgs3rBlliFjcMKlLnZnjG/fJ0sYsxa+DA==","signature_status":"signed_v1","signed_at":"2026-08-04T00:37:06.361083Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.00519","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e80ad955b08bfed2d515c82507d8f50b7ccfd187ab484c5cec58cee00bb22bc","sha256:4b0aafb8d453756bd0c8177891827316ddca4c01e96ec4446430cdaf7b0988dd"],"state_sha256":"3c2e1a1dfe9b021553aa00d15e3833fd53bf2c560b799cfdcb6a9f362d0d57d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e0x7O9MsQJMrx1VSjdiJKJekxbkjQRePmirR4yQBn+LCDED2JioJLSm27z2a5qaU8RC0mj8gWmEDmj7UWL3lDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T14:37:58.835531Z","bundle_sha256":"72074e408597de7c75992a0db128422451136729edd078edda6d042dcdde61e0"}}