{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:MWJZJEDAEDXFLSLHT4H65QD63Q","short_pith_number":"pith:MWJZJEDA","canonical_record":{"source":{"id":"1703.09973","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-29T11:21:34Z","cross_cats_sorted":[],"title_canon_sha256":"594bc021a9ba9dd65d16dc1ae257f5808369c094b3915c196ddb59ac67ca68a6","abstract_canon_sha256":"4b31233166d98d420ef2c3ee6381ef70a3807a29fa1d461db12081daf7ff99dd"},"schema_version":"1.0"},"canonical_sha256":"659394906020ee55c9679f0feec07edc372df954119e598fabbe7aec4e5a55e7","source":{"kind":"arxiv","id":"1703.09973","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.09973","created_at":"2026-05-18T00:47:38Z"},{"alias_kind":"arxiv_version","alias_value":"1703.09973v1","created_at":"2026-05-18T00:47:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.09973","created_at":"2026-05-18T00:47:38Z"},{"alias_kind":"pith_short_12","alias_value":"MWJZJEDAEDXF","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MWJZJEDAEDXFLSLH","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MWJZJEDA","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:MWJZJEDAEDXFLSLHT4H65QD63Q","target":"record","payload":{"canonical_record":{"source":{"id":"1703.09973","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-29T11:21:34Z","cross_cats_sorted":[],"title_canon_sha256":"594bc021a9ba9dd65d16dc1ae257f5808369c094b3915c196ddb59ac67ca68a6","abstract_canon_sha256":"4b31233166d98d420ef2c3ee6381ef70a3807a29fa1d461db12081daf7ff99dd"},"schema_version":"1.0"},"canonical_sha256":"659394906020ee55c9679f0feec07edc372df954119e598fabbe7aec4e5a55e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:38.907300Z","signature_b64":"BDhAadsOKzWZvC0ChVUyo5ntdT1zVZEMhOsqePnDQ+0IPjpEB6Om1cBqWgoj+lkQr3BnymHOF1trxXdzMoSjAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"659394906020ee55c9679f0feec07edc372df954119e598fabbe7aec4e5a55e7","last_reissued_at":"2026-05-18T00:47:38.906749Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:38.906749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.09973","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":"2026-05-18T00:47:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hGAIePVaLfpC/CLAKHxxNVgAxdHt9U3tCeP1Wg9ZiWKkUerbio42J9ySHX150X0NzebL2tNrt/gHluB+UwlvDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T03:37:33.934325Z"},"content_sha256":"b0264d7ce3338ec591d5397f6ea1b9955dc2a58ff28f6ef0fe0417466b1d716d","schema_version":"1.0","event_id":"sha256:b0264d7ce3338ec591d5397f6ea1b9955dc2a58ff28f6ef0fe0417466b1d716d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:MWJZJEDAEDXFLSLHT4H65QD63Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The variance conjecture on projections of the cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"David Alonso-Guti\\'errez, Julio Bernu\\'es","submitted_at":"2017-03-29T11:21:34Z","abstract_excerpt":"We prove that the uniform probability measure $\\mu$ on every $(n-k)$-dimensional projection of the $n$-dimensional unit cube verifies the variance conjecture with an absolute constant $C$ $$\\textrm{Var}_\\mu|x|^2\\leq C \\sup_{\\theta\\in S^{n-1}}{\\mathbb E}_\\mu\\langle x,\\theta\\rangle^2{\\mathbb E}_\\mu|x|^2, $$ provided that $1\\leq k\\leq\\sqrt n$. We also prove that if $1\\leq k\\leq n^{\\frac{2}{3}}(\\log n)^{-\\frac{1}{3}}$, the conjecture is true for the family of uniform probabilities on its projections on random $(n-k)$-dimensional subspaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09973","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":"2026-05-18T00:47:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PGdlLQ2ptxCIpSVxCrTo9ybVfaCXhlUlmsvk4Acez4EakEkzBsMz0kC760ocSGmDXAYPDa8Td/H86nlXdQFKAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T03:37:33.934675Z"},"content_sha256":"0db6a1b41178c247a21b683ea40d2fd857ee6c48e4a1075615819400b5a8c3f2","schema_version":"1.0","event_id":"sha256:0db6a1b41178c247a21b683ea40d2fd857ee6c48e4a1075615819400b5a8c3f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MWJZJEDAEDXFLSLHT4H65QD63Q/bundle.json","state_url":"https://pith.science/pith/MWJZJEDAEDXFLSLHT4H65QD63Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MWJZJEDAEDXFLSLHT4H65QD63Q/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":"2026-06-01T03:37:33Z","links":{"resolver":"https://pith.science/pith/MWJZJEDAEDXFLSLHT4H65QD63Q","bundle":"https://pith.science/pith/MWJZJEDAEDXFLSLHT4H65QD63Q/bundle.json","state":"https://pith.science/pith/MWJZJEDAEDXFLSLHT4H65QD63Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MWJZJEDAEDXFLSLHT4H65QD63Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MWJZJEDAEDXFLSLHT4H65QD63Q","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":"4b31233166d98d420ef2c3ee6381ef70a3807a29fa1d461db12081daf7ff99dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-29T11:21:34Z","title_canon_sha256":"594bc021a9ba9dd65d16dc1ae257f5808369c094b3915c196ddb59ac67ca68a6"},"schema_version":"1.0","source":{"id":"1703.09973","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.09973","created_at":"2026-05-18T00:47:38Z"},{"alias_kind":"arxiv_version","alias_value":"1703.09973v1","created_at":"2026-05-18T00:47:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.09973","created_at":"2026-05-18T00:47:38Z"},{"alias_kind":"pith_short_12","alias_value":"MWJZJEDAEDXF","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MWJZJEDAEDXFLSLH","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MWJZJEDA","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:0db6a1b41178c247a21b683ea40d2fd857ee6c48e4a1075615819400b5a8c3f2","target":"graph","created_at":"2026-05-18T00:47:38Z","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 the uniform probability measure $\\mu$ on every $(n-k)$-dimensional projection of the $n$-dimensional unit cube verifies the variance conjecture with an absolute constant $C$ $$\\textrm{Var}_\\mu|x|^2\\leq C \\sup_{\\theta\\in S^{n-1}}{\\mathbb E}_\\mu\\langle x,\\theta\\rangle^2{\\mathbb E}_\\mu|x|^2, $$ provided that $1\\leq k\\leq\\sqrt n$. We also prove that if $1\\leq k\\leq n^{\\frac{2}{3}}(\\log n)^{-\\frac{1}{3}}$, the conjecture is true for the family of uniform probabilities on its projections on random $(n-k)$-dimensional subspaces.","authors_text":"David Alonso-Guti\\'errez, Julio Bernu\\'es","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-29T11:21:34Z","title":"The variance conjecture on projections of the cube"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09973","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:b0264d7ce3338ec591d5397f6ea1b9955dc2a58ff28f6ef0fe0417466b1d716d","target":"record","created_at":"2026-05-18T00:47:38Z","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":"4b31233166d98d420ef2c3ee6381ef70a3807a29fa1d461db12081daf7ff99dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-29T11:21:34Z","title_canon_sha256":"594bc021a9ba9dd65d16dc1ae257f5808369c094b3915c196ddb59ac67ca68a6"},"schema_version":"1.0","source":{"id":"1703.09973","kind":"arxiv","version":1}},"canonical_sha256":"659394906020ee55c9679f0feec07edc372df954119e598fabbe7aec4e5a55e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"659394906020ee55c9679f0feec07edc372df954119e598fabbe7aec4e5a55e7","first_computed_at":"2026-05-18T00:47:38.906749Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:38.906749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BDhAadsOKzWZvC0ChVUyo5ntdT1zVZEMhOsqePnDQ+0IPjpEB6Om1cBqWgoj+lkQr3BnymHOF1trxXdzMoSjAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:38.907300Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.09973","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0264d7ce3338ec591d5397f6ea1b9955dc2a58ff28f6ef0fe0417466b1d716d","sha256:0db6a1b41178c247a21b683ea40d2fd857ee6c48e4a1075615819400b5a8c3f2"],"state_sha256":"77ecb13622eab81e231800225ae49dbced76027fd948ae0556c362533fd96ce8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7oZZ3+GGRnChw85ULx304OKgms4IgRiWUqzwYHNN8NFn9Gh8x/Nn10HGjBS0B6XyvcIABfn54QqV4785IVKzDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T03:37:33.936731Z","bundle_sha256":"b6f0c7f91045a7ab311cb9e0704431140c4f2c97bca4913432414c975994d780"}}