{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:LJED2MFMUIBDJ4PU2LZUTSPECE","short_pith_number":"pith:LJED2MFM","canonical_record":{"source":{"id":"1202.0046","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-31T22:51:21Z","cross_cats_sorted":[],"title_canon_sha256":"e5d207d89a0e49b5719a151177fc5f8b27d6e4f5ccc6817d8af14885cd120cf3","abstract_canon_sha256":"42d95abde352714a3519771821f08debd29f622307dc368268606f663d7cc948"},"schema_version":"1.0"},"canonical_sha256":"5a483d30aca20234f1f4d2f349c9e41109338780d32b57118549d52ed09e0aac","source":{"kind":"arxiv","id":"1202.0046","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0046","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0046v1","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0046","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"LJED2MFMUIBD","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LJED2MFMUIBDJ4PU","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LJED2MFM","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:LJED2MFMUIBDJ4PU2LZUTSPECE","target":"record","payload":{"canonical_record":{"source":{"id":"1202.0046","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-31T22:51:21Z","cross_cats_sorted":[],"title_canon_sha256":"e5d207d89a0e49b5719a151177fc5f8b27d6e4f5ccc6817d8af14885cd120cf3","abstract_canon_sha256":"42d95abde352714a3519771821f08debd29f622307dc368268606f663d7cc948"},"schema_version":"1.0"},"canonical_sha256":"5a483d30aca20234f1f4d2f349c9e41109338780d32b57118549d52ed09e0aac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:17.680165Z","signature_b64":"TV/0NhzbbJkc3aD0DthZtjmkPFZoY49IP24Pe7VygUBkUYvw3Fmql9U4bf4Olfek1eCzuXWFJyKh4RRE22L8Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a483d30aca20234f1f4d2f349c9e41109338780d32b57118549d52ed09e0aac","last_reissued_at":"2026-05-18T03:14:17.679569Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:17.679569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.0046","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":"2026-05-18T03:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kmICBsb5+MPTlLbeUQ/7cEo4hI0Q5amGZN6UK7bkzaBVJzPOQgVnsvS1FTkWLlvMFNUacZAf6AyPmkxomNdiBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:14:28.039658Z"},"content_sha256":"a1d481d669ff525fb33d6343220686588320e6c2db2cd39842e7965d1ea7ca23","schema_version":"1.0","event_id":"sha256:a1d481d669ff525fb33d6343220686588320e6c2db2cd39842e7965d1ea7ca23"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:LJED2MFMUIBDJ4PU2LZUTSPECE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Note on a Brunn-Minkowski Inequality for the Gaussian Measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Piotr Nayar, Tomasz Tkocz","submitted_at":"2012-01-31T22:51:21Z","abstract_excerpt":"We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0046","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":"2026-05-18T03:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jUfk1LaUXk5ag9en3tyYK/77IjMjoxhaRpFR3i7ByVtDDwHiHELIrt0JMRFxPBXtv7NCTnIb85h8MCYVL3IICw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:14:28.040014Z"},"content_sha256":"76043af97797e63f4096d7b865c1ac9d7d0318b7a2315a7e894cbee360839132","schema_version":"1.0","event_id":"sha256:76043af97797e63f4096d7b865c1ac9d7d0318b7a2315a7e894cbee360839132"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LJED2MFMUIBDJ4PU2LZUTSPECE/bundle.json","state_url":"https://pith.science/pith/LJED2MFMUIBDJ4PU2LZUTSPECE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LJED2MFMUIBDJ4PU2LZUTSPECE/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":"2026-06-25T09:14:28Z","links":{"resolver":"https://pith.science/pith/LJED2MFMUIBDJ4PU2LZUTSPECE","bundle":"https://pith.science/pith/LJED2MFMUIBDJ4PU2LZUTSPECE/bundle.json","state":"https://pith.science/pith/LJED2MFMUIBDJ4PU2LZUTSPECE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LJED2MFMUIBDJ4PU2LZUTSPECE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LJED2MFMUIBDJ4PU2LZUTSPECE","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":"42d95abde352714a3519771821f08debd29f622307dc368268606f663d7cc948","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-31T22:51:21Z","title_canon_sha256":"e5d207d89a0e49b5719a151177fc5f8b27d6e4f5ccc6817d8af14885cd120cf3"},"schema_version":"1.0","source":{"id":"1202.0046","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0046","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0046v1","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0046","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"LJED2MFMUIBD","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LJED2MFMUIBDJ4PU","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LJED2MFM","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:76043af97797e63f4096d7b865c1ac9d7d0318b7a2315a7e894cbee360839132","target":"graph","created_at":"2026-05-18T03:14:17Z","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 give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.","authors_text":"Piotr Nayar, Tomasz Tkocz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-31T22:51:21Z","title":"A Note on a Brunn-Minkowski Inequality for the Gaussian Measure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0046","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:a1d481d669ff525fb33d6343220686588320e6c2db2cd39842e7965d1ea7ca23","target":"record","created_at":"2026-05-18T03:14:17Z","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":"42d95abde352714a3519771821f08debd29f622307dc368268606f663d7cc948","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-31T22:51:21Z","title_canon_sha256":"e5d207d89a0e49b5719a151177fc5f8b27d6e4f5ccc6817d8af14885cd120cf3"},"schema_version":"1.0","source":{"id":"1202.0046","kind":"arxiv","version":1}},"canonical_sha256":"5a483d30aca20234f1f4d2f349c9e41109338780d32b57118549d52ed09e0aac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a483d30aca20234f1f4d2f349c9e41109338780d32b57118549d52ed09e0aac","first_computed_at":"2026-05-18T03:14:17.679569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:17.679569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TV/0NhzbbJkc3aD0DthZtjmkPFZoY49IP24Pe7VygUBkUYvw3Fmql9U4bf4Olfek1eCzuXWFJyKh4RRE22L8Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:17.680165Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.0046","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1d481d669ff525fb33d6343220686588320e6c2db2cd39842e7965d1ea7ca23","sha256:76043af97797e63f4096d7b865c1ac9d7d0318b7a2315a7e894cbee360839132"],"state_sha256":"b1ff2fdf849c8f469db165a0e2249649b984d3718270a790c4a5ad2d6ced375a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"69xHt0sSsopecYrtOTOTCxyOWIWX8g5JYaiqYaaX+vQ5HRTtPBfZC93dJwd+xTGbvf9eQt2nT5Z69DCSSoOcCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T09:14:28.042097Z","bundle_sha256":"f964a6720d96d14119c0b3944acfc990610e4f0e667cd10dd09581373d79d836"}}