{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:GBVGUN36G5UHVJNGSYLXPZ2W7G","short_pith_number":"pith:GBVGUN36","canonical_record":{"source":{"id":"1210.4417","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-16T14:08:55Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"903a096b3052dd0da6bb14e93e68437733ef8e37c6467612cbfbb182d3af8fa3","abstract_canon_sha256":"402d898fa4309b403cca839aaaedc07aa82fc3c313708e9083066cafe9a9cccd"},"schema_version":"1.0"},"canonical_sha256":"306a6a377e37687aa5a6961777e756f98e20236f2337de48695d5c3add2f8cca","source":{"kind":"arxiv","id":"1210.4417","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4417","created_at":"2026-05-18T03:43:06Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4417v1","created_at":"2026-05-18T03:43:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4417","created_at":"2026-05-18T03:43:06Z"},{"alias_kind":"pith_short_12","alias_value":"GBVGUN36G5UH","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GBVGUN36G5UHVJNG","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GBVGUN36","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:GBVGUN36G5UHVJNGSYLXPZ2W7G","target":"record","payload":{"canonical_record":{"source":{"id":"1210.4417","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-16T14:08:55Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"903a096b3052dd0da6bb14e93e68437733ef8e37c6467612cbfbb182d3af8fa3","abstract_canon_sha256":"402d898fa4309b403cca839aaaedc07aa82fc3c313708e9083066cafe9a9cccd"},"schema_version":"1.0"},"canonical_sha256":"306a6a377e37687aa5a6961777e756f98e20236f2337de48695d5c3add2f8cca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:06.043119Z","signature_b64":"eNUoIRtIipYhbWczdja470EF8U1HSNn2fefXzZRjEDLMeghHNFtC9P2Aw8/1I50LSPDlog4nV2VbPAxcq+vcAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"306a6a377e37687aa5a6961777e756f98e20236f2337de48695d5c3add2f8cca","last_reissued_at":"2026-05-18T03:43:06.042547Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:06.042547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.4417","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":"2026-05-18T03:43:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G9aZ2QX3E57VCp8hYShOFF+f6lW9ICmjmx9ePFS81VwO6KSoT1jNCiMzK505hMYf1QYjQWbt7zOOvaal2pfeDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:58:26.723144Z"},"content_sha256":"d8249d981a2220766e367dbff39690adfe08a94b952ef564fa7f8a19c3031bdc","schema_version":"1.0","event_id":"sha256:d8249d981a2220766e367dbff39690adfe08a94b952ef564fa7f8a19c3031bdc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:GBVGUN36G5UHVJNGSYLXPZ2W7G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A monotonicity property of variances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.PR","authors_text":"J. M. Aldaz","submitted_at":"2012-10-16T14:08:55Z","abstract_excerpt":"We prove that variances of non-negative random variables have the following monotonicity property: For all $0 < r < s \\le 1$, and all $0 \\le X \\in L^2$, we have $\\operatorname{Var}(X^r)^{1/r} \\le \\operatorname{Var}(X^s)^{1/s}$. We also discuss the real valued case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4417","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":"2026-05-18T03:43:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B2d4Hxu1DXQ7rIcUB+pQqulVAZHI1qSdvN3ZCHQ+cFFZdFlu9TqWt4JvM7dpA3tQZ25JEDM8xx3MAk5emGxmDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:58:26.723494Z"},"content_sha256":"b24fd6cc3d306a7629778bbe4a740e6017fb86edaf265f5b9da19c97c136b685","schema_version":"1.0","event_id":"sha256:b24fd6cc3d306a7629778bbe4a740e6017fb86edaf265f5b9da19c97c136b685"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GBVGUN36G5UHVJNGSYLXPZ2W7G/bundle.json","state_url":"https://pith.science/pith/GBVGUN36G5UHVJNGSYLXPZ2W7G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GBVGUN36G5UHVJNGSYLXPZ2W7G/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":"2026-06-27T02:58:26Z","links":{"resolver":"https://pith.science/pith/GBVGUN36G5UHVJNGSYLXPZ2W7G","bundle":"https://pith.science/pith/GBVGUN36G5UHVJNGSYLXPZ2W7G/bundle.json","state":"https://pith.science/pith/GBVGUN36G5UHVJNGSYLXPZ2W7G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GBVGUN36G5UHVJNGSYLXPZ2W7G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GBVGUN36G5UHVJNGSYLXPZ2W7G","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":"402d898fa4309b403cca839aaaedc07aa82fc3c313708e9083066cafe9a9cccd","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-16T14:08:55Z","title_canon_sha256":"903a096b3052dd0da6bb14e93e68437733ef8e37c6467612cbfbb182d3af8fa3"},"schema_version":"1.0","source":{"id":"1210.4417","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4417","created_at":"2026-05-18T03:43:06Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4417v1","created_at":"2026-05-18T03:43:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4417","created_at":"2026-05-18T03:43:06Z"},{"alias_kind":"pith_short_12","alias_value":"GBVGUN36G5UH","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GBVGUN36G5UHVJNG","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GBVGUN36","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:b24fd6cc3d306a7629778bbe4a740e6017fb86edaf265f5b9da19c97c136b685","target":"graph","created_at":"2026-05-18T03:43:06Z","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"},"paper":{"abstract_excerpt":"We prove that variances of non-negative random variables have the following monotonicity property: For all $0 < r < s \\le 1$, and all $0 \\le X \\in L^2$, we have $\\operatorname{Var}(X^r)^{1/r} \\le \\operatorname{Var}(X^s)^{1/s}$. We also discuss the real valued case.","authors_text":"J. M. Aldaz","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-16T14:08:55Z","title":"A monotonicity property of variances"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4417","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:d8249d981a2220766e367dbff39690adfe08a94b952ef564fa7f8a19c3031bdc","target":"record","created_at":"2026-05-18T03:43:06Z","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":"402d898fa4309b403cca839aaaedc07aa82fc3c313708e9083066cafe9a9cccd","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-16T14:08:55Z","title_canon_sha256":"903a096b3052dd0da6bb14e93e68437733ef8e37c6467612cbfbb182d3af8fa3"},"schema_version":"1.0","source":{"id":"1210.4417","kind":"arxiv","version":1}},"canonical_sha256":"306a6a377e37687aa5a6961777e756f98e20236f2337de48695d5c3add2f8cca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"306a6a377e37687aa5a6961777e756f98e20236f2337de48695d5c3add2f8cca","first_computed_at":"2026-05-18T03:43:06.042547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:06.042547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eNUoIRtIipYhbWczdja470EF8U1HSNn2fefXzZRjEDLMeghHNFtC9P2Aw8/1I50LSPDlog4nV2VbPAxcq+vcAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:06.043119Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.4417","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8249d981a2220766e367dbff39690adfe08a94b952ef564fa7f8a19c3031bdc","sha256:b24fd6cc3d306a7629778bbe4a740e6017fb86edaf265f5b9da19c97c136b685"],"state_sha256":"bd8e814acc6b3497050ada52f8553280e9ff9df33a6a6394e3fc24b89d4fc57a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h8r9yodIfPiqwqkELVY4+Tp5gXk9vb/1pK4JGJ4ARtEeu+ybzCI4dOOS9P91okl3hNlFwp2lnJjb9f4tRxoXDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T02:58:26.725250Z","bundle_sha256":"d0b0e3eb81c7cd99d0753a5e71bed312258c55724de5b01a19663ed5ae451ba2"}}