{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:YDCQSQEW4HLRS4VTXKS26CWDMM","short_pith_number":"pith:YDCQSQEW","canonical_record":{"source":{"id":"2401.08427","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2024-01-16T15:11:49Z","cross_cats_sorted":[],"title_canon_sha256":"371c058feec41a94edcd562b2f84cecebafd57483c1870e29fae386152bbe88a","abstract_canon_sha256":"1cd9c40ad43a073ec4e10ccc45a5e8b756672414af00179394e23a4028e93a32"},"schema_version":"1.0"},"canonical_sha256":"c0c5094096e1d71972b3baa5af0ac36327ee2cc87b655341df60913fd4a1b971","source":{"kind":"arxiv","id":"2401.08427","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.08427","created_at":"2026-07-05T08:58:42Z"},{"alias_kind":"arxiv_version","alias_value":"2401.08427v5","created_at":"2026-07-05T08:58:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.08427","created_at":"2026-07-05T08:58:42Z"},{"alias_kind":"pith_short_12","alias_value":"YDCQSQEW4HLR","created_at":"2026-07-05T08:58:42Z"},{"alias_kind":"pith_short_16","alias_value":"YDCQSQEW4HLRS4VT","created_at":"2026-07-05T08:58:42Z"},{"alias_kind":"pith_short_8","alias_value":"YDCQSQEW","created_at":"2026-07-05T08:58:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:YDCQSQEW4HLRS4VTXKS26CWDMM","target":"record","payload":{"canonical_record":{"source":{"id":"2401.08427","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2024-01-16T15:11:49Z","cross_cats_sorted":[],"title_canon_sha256":"371c058feec41a94edcd562b2f84cecebafd57483c1870e29fae386152bbe88a","abstract_canon_sha256":"1cd9c40ad43a073ec4e10ccc45a5e8b756672414af00179394e23a4028e93a32"},"schema_version":"1.0"},"canonical_sha256":"c0c5094096e1d71972b3baa5af0ac36327ee2cc87b655341df60913fd4a1b971","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:58:42.090440Z","signature_b64":"jEOZIISTRW1fr3mcr7gP7Nden00WFsAcCrPtTqUupzWgRdZthosxO/qy1uWm+M1NMM5lT3fnESn0tpzjWehrAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0c5094096e1d71972b3baa5af0ac36327ee2cc87b655341df60913fd4a1b971","last_reissued_at":"2026-07-05T08:58:42.090025Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:58:42.090025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.08427","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:58:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kWF0XghZoNz5qyql60AVlOUFw4nDWEOF6goutXYS9R9jNz2r+MCu0IKIOLmaD0mqJ9+EygF1OMgpoZYXQSH5CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T20:10:09.727757Z"},"content_sha256":"cf11a409539df54eff44e2a5293a6b84db00c5a821faa0b4545b4301a9a05aa5","schema_version":"1.0","event_id":"sha256:cf11a409539df54eff44e2a5293a6b84db00c5a821faa0b4545b4301a9a05aa5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:YDCQSQEW4HLRS4VTXKS26CWDMM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The generalized Gaussian log-Minkowski problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Jinrong Hu","submitted_at":"2024-01-16T15:11:49Z","abstract_excerpt":"The generalized Gaussian distribution that stems from information theory is studied. The log-Minkowski problem associated with generalized Gaussian distribution shall be introduced and solved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.08427","kind":"arxiv","version":5},"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/2401.08427/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":"2026-07-05T08:58:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ufbz8EXegyJpogYJt3Q6m23mRO9rW6hCFbGWD+WGDEpNq2LLI4//Tulp3sLLxI969A+Qc0pvm/VW1UfvMCYeCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T20:10:09.728832Z"},"content_sha256":"87598fc5ccd2746afd8d8bfdc2f6e4fdc73e5f9a0ed683aec68f99f0e3214268","schema_version":"1.0","event_id":"sha256:87598fc5ccd2746afd8d8bfdc2f6e4fdc73e5f9a0ed683aec68f99f0e3214268"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YDCQSQEW4HLRS4VTXKS26CWDMM/bundle.json","state_url":"https://pith.science/pith/YDCQSQEW4HLRS4VTXKS26CWDMM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YDCQSQEW4HLRS4VTXKS26CWDMM/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":"2026-08-18T20:10:09Z","links":{"resolver":"https://pith.science/pith/YDCQSQEW4HLRS4VTXKS26CWDMM","bundle":"https://pith.science/pith/YDCQSQEW4HLRS4VTXKS26CWDMM/bundle.json","state":"https://pith.science/pith/YDCQSQEW4HLRS4VTXKS26CWDMM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YDCQSQEW4HLRS4VTXKS26CWDMM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:YDCQSQEW4HLRS4VTXKS26CWDMM","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":"1cd9c40ad43a073ec4e10ccc45a5e8b756672414af00179394e23a4028e93a32","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2024-01-16T15:11:49Z","title_canon_sha256":"371c058feec41a94edcd562b2f84cecebafd57483c1870e29fae386152bbe88a"},"schema_version":"1.0","source":{"id":"2401.08427","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.08427","created_at":"2026-07-05T08:58:42Z"},{"alias_kind":"arxiv_version","alias_value":"2401.08427v5","created_at":"2026-07-05T08:58:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.08427","created_at":"2026-07-05T08:58:42Z"},{"alias_kind":"pith_short_12","alias_value":"YDCQSQEW4HLR","created_at":"2026-07-05T08:58:42Z"},{"alias_kind":"pith_short_16","alias_value":"YDCQSQEW4HLRS4VT","created_at":"2026-07-05T08:58:42Z"},{"alias_kind":"pith_short_8","alias_value":"YDCQSQEW","created_at":"2026-07-05T08:58:42Z"}],"graph_snapshots":[{"event_id":"sha256:87598fc5ccd2746afd8d8bfdc2f6e4fdc73e5f9a0ed683aec68f99f0e3214268","target":"graph","created_at":"2026-07-05T08:58:42Z","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/2401.08427/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The generalized Gaussian distribution that stems from information theory is studied. The log-Minkowski problem associated with generalized Gaussian distribution shall be introduced and solved.","authors_text":"Jinrong Hu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2024-01-16T15:11:49Z","title":"The generalized Gaussian log-Minkowski problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.08427","kind":"arxiv","version":5},"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:cf11a409539df54eff44e2a5293a6b84db00c5a821faa0b4545b4301a9a05aa5","target":"record","created_at":"2026-07-05T08:58:42Z","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":"1cd9c40ad43a073ec4e10ccc45a5e8b756672414af00179394e23a4028e93a32","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2024-01-16T15:11:49Z","title_canon_sha256":"371c058feec41a94edcd562b2f84cecebafd57483c1870e29fae386152bbe88a"},"schema_version":"1.0","source":{"id":"2401.08427","kind":"arxiv","version":5}},"canonical_sha256":"c0c5094096e1d71972b3baa5af0ac36327ee2cc87b655341df60913fd4a1b971","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0c5094096e1d71972b3baa5af0ac36327ee2cc87b655341df60913fd4a1b971","first_computed_at":"2026-07-05T08:58:42.090025Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:58:42.090025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jEOZIISTRW1fr3mcr7gP7Nden00WFsAcCrPtTqUupzWgRdZthosxO/qy1uWm+M1NMM5lT3fnESn0tpzjWehrAg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:58:42.090440Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.08427","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf11a409539df54eff44e2a5293a6b84db00c5a821faa0b4545b4301a9a05aa5","sha256:87598fc5ccd2746afd8d8bfdc2f6e4fdc73e5f9a0ed683aec68f99f0e3214268"],"state_sha256":"1a2e52659c26833a0461efb248d64efb145912625fb253eea8b8726933936d52"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GrcXqTrRW86yiu02BznnqQ+jRCVT7+ozcqQVdacbjAUXKuBqINboggeYPsFrMEDW4hmJbtvXXLWC7xj+uyN9DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T20:10:09.734145Z","bundle_sha256":"7b7bb33612d6d37859edab24f603acf3e206b26d909c0f65c828eceb0b165b35"}}