{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:2E2B2KEYOFAGBU4H2JRGM6Q36O","short_pith_number":"pith:2E2B2KEY","canonical_record":{"source":{"id":"2508.11600","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-08-15T17:10:15Z","cross_cats_sorted":["math.AP","math.DG","math.FA"],"title_canon_sha256":"57dcfb19cda7b52e702a5dc1c34a87c05fd5ab29f2ec936a31a3880835399eaf","abstract_canon_sha256":"5468d9c2dad91c11f6903e9e7efb3e2bfcadd696dba777a2f9b455477c27038f"},"schema_version":"1.0"},"canonical_sha256":"d1341d2898714060d387d262667a1bf38a7e082fe1786fc3dfe55c0743bafb02","source":{"kind":"arxiv","id":"2508.11600","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.11600","created_at":"2026-05-21T01:05:07Z"},{"alias_kind":"arxiv_version","alias_value":"2508.11600v2","created_at":"2026-05-21T01:05:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.11600","created_at":"2026-05-21T01:05:07Z"},{"alias_kind":"pith_short_12","alias_value":"2E2B2KEYOFAG","created_at":"2026-05-21T01:05:07Z"},{"alias_kind":"pith_short_16","alias_value":"2E2B2KEYOFAGBU4H","created_at":"2026-05-21T01:05:07Z"},{"alias_kind":"pith_short_8","alias_value":"2E2B2KEY","created_at":"2026-05-21T01:05:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:2E2B2KEYOFAGBU4H2JRGM6Q36O","target":"record","payload":{"canonical_record":{"source":{"id":"2508.11600","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-08-15T17:10:15Z","cross_cats_sorted":["math.AP","math.DG","math.FA"],"title_canon_sha256":"57dcfb19cda7b52e702a5dc1c34a87c05fd5ab29f2ec936a31a3880835399eaf","abstract_canon_sha256":"5468d9c2dad91c11f6903e9e7efb3e2bfcadd696dba777a2f9b455477c27038f"},"schema_version":"1.0"},"canonical_sha256":"d1341d2898714060d387d262667a1bf38a7e082fe1786fc3dfe55c0743bafb02","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:05:07.911298Z","signature_b64":"n3LIkMGHgPj/wfKVTjlvpll3/RrktO7PBTZCcTLP4KHq5NE7F+Znb17wuE31xeKnKZ9JzBax+hx6YPlmjFTWDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1341d2898714060d387d262667a1bf38a7e082fe1786fc3dfe55c0743bafb02","last_reissued_at":"2026-05-21T01:05:07.910258Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:05:07.910258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.11600","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-21T01:05:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cR0ce3flqPWbnANc+9/fwQUuyt8friIFruUaSJ1mBZmQ316Jotu4CTT2b+DQaPaSeL9f7Rs11HPF84/lSLnGBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:24:04.820803Z"},"content_sha256":"0caca4f99f31b7e8a0a59d000a2fadba3352528c0935b9cc1fc157c3407cebd4","schema_version":"1.0","event_id":"sha256:0caca4f99f31b7e8a0a59d000a2fadba3352528c0935b9cc1fc157c3407cebd4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:2E2B2KEYOFAGBU4H2JRGM6Q36O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Explicit solutions to Christoffel-Minkowski problems and Hessian equations under rotational symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG","math.FA"],"primary_cat":"math.MG","authors_text":"Fabian Mussnig, Jacopo Ulivelli","submitted_at":"2025-08-15T17:10:15Z","abstract_excerpt":"An explicit solution to the Christoffel-Minkowski problem for convex bodies of revolution is presented. The conditions on the prescribed measure involve only first moments over spherical caps, and the support function of the resulting convex body is given by an explicit representation formula in terms of the measure. More generally, existence problems for mixed area measures are addressed. The approach relies on constructing explicit convex solutions to mixed Monge-Amp\\`ere equations on $\\mathbb{R}^n$ under the assumption of radial symmetry, with the conditions on the measure being expressed t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.11600","kind":"arxiv","version":2},"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/2508.11600/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":"2026-05-21T01:05:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NxDJgre3ztK1tZYXmyyiP2LOaPt2HG7DTnvPJkE+OJbDkW15gy7tsCOFoBNhaGHENBpw5XElSS/agAqCFT9vAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:24:04.821598Z"},"content_sha256":"b6131af337efafc49358845707c3552413e0d548875480e716318d86f1081c03","schema_version":"1.0","event_id":"sha256:b6131af337efafc49358845707c3552413e0d548875480e716318d86f1081c03"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2E2B2KEYOFAGBU4H2JRGM6Q36O/bundle.json","state_url":"https://pith.science/pith/2E2B2KEYOFAGBU4H2JRGM6Q36O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2E2B2KEYOFAGBU4H2JRGM6Q36O/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":"2026-06-10T23:24:04Z","links":{"resolver":"https://pith.science/pith/2E2B2KEYOFAGBU4H2JRGM6Q36O","bundle":"https://pith.science/pith/2E2B2KEYOFAGBU4H2JRGM6Q36O/bundle.json","state":"https://pith.science/pith/2E2B2KEYOFAGBU4H2JRGM6Q36O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2E2B2KEYOFAGBU4H2JRGM6Q36O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2E2B2KEYOFAGBU4H2JRGM6Q36O","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":"5468d9c2dad91c11f6903e9e7efb3e2bfcadd696dba777a2f9b455477c27038f","cross_cats_sorted":["math.AP","math.DG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-08-15T17:10:15Z","title_canon_sha256":"57dcfb19cda7b52e702a5dc1c34a87c05fd5ab29f2ec936a31a3880835399eaf"},"schema_version":"1.0","source":{"id":"2508.11600","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.11600","created_at":"2026-05-21T01:05:07Z"},{"alias_kind":"arxiv_version","alias_value":"2508.11600v2","created_at":"2026-05-21T01:05:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.11600","created_at":"2026-05-21T01:05:07Z"},{"alias_kind":"pith_short_12","alias_value":"2E2B2KEYOFAG","created_at":"2026-05-21T01:05:07Z"},{"alias_kind":"pith_short_16","alias_value":"2E2B2KEYOFAGBU4H","created_at":"2026-05-21T01:05:07Z"},{"alias_kind":"pith_short_8","alias_value":"2E2B2KEY","created_at":"2026-05-21T01:05:07Z"}],"graph_snapshots":[{"event_id":"sha256:b6131af337efafc49358845707c3552413e0d548875480e716318d86f1081c03","target":"graph","created_at":"2026-05-21T01:05:07Z","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/2508.11600/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An explicit solution to the Christoffel-Minkowski problem for convex bodies of revolution is presented. The conditions on the prescribed measure involve only first moments over spherical caps, and the support function of the resulting convex body is given by an explicit representation formula in terms of the measure. More generally, existence problems for mixed area measures are addressed. The approach relies on constructing explicit convex solutions to mixed Monge-Amp\\`ere equations on $\\mathbb{R}^n$ under the assumption of radial symmetry, with the conditions on the measure being expressed t","authors_text":"Fabian Mussnig, Jacopo Ulivelli","cross_cats":["math.AP","math.DG","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-08-15T17:10:15Z","title":"Explicit solutions to Christoffel-Minkowski problems and Hessian equations under rotational symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.11600","kind":"arxiv","version":2},"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":"sha256:0caca4f99f31b7e8a0a59d000a2fadba3352528c0935b9cc1fc157c3407cebd4","target":"record","created_at":"2026-05-21T01:05:07Z","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":"5468d9c2dad91c11f6903e9e7efb3e2bfcadd696dba777a2f9b455477c27038f","cross_cats_sorted":["math.AP","math.DG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-08-15T17:10:15Z","title_canon_sha256":"57dcfb19cda7b52e702a5dc1c34a87c05fd5ab29f2ec936a31a3880835399eaf"},"schema_version":"1.0","source":{"id":"2508.11600","kind":"arxiv","version":2}},"canonical_sha256":"d1341d2898714060d387d262667a1bf38a7e082fe1786fc3dfe55c0743bafb02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1341d2898714060d387d262667a1bf38a7e082fe1786fc3dfe55c0743bafb02","first_computed_at":"2026-05-21T01:05:07.910258Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:05:07.910258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n3LIkMGHgPj/wfKVTjlvpll3/RrktO7PBTZCcTLP4KHq5NE7F+Znb17wuE31xeKnKZ9JzBax+hx6YPlmjFTWDw==","signature_status":"signed_v1","signed_at":"2026-05-21T01:05:07.911298Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.11600","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0caca4f99f31b7e8a0a59d000a2fadba3352528c0935b9cc1fc157c3407cebd4","sha256:b6131af337efafc49358845707c3552413e0d548875480e716318d86f1081c03"],"state_sha256":"3f7c8f3f435515eb91f82626114a6d50e987253f2d04cee6b758a7447ca6b6e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EudMPqMXkpqle7DoYRMdfy8snDBncYnxi/FzsR7kH4lVU0RypP+O5htj3kQOpIRx6x7cNT+vPO/aKg0SAk4QDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T23:24:04.826022Z","bundle_sha256":"ac77d72b5d956139d913a5dd0dba11b70e437888ae3c462c83888f5ed61c9e88"}}