{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:2BISACYVM3K6FBTKY5UQHYMWDF","short_pith_number":"pith:2BISACYV","canonical_record":{"source":{"id":"1712.01206","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-12-04T17:13:32Z","cross_cats_sorted":["math.CO","math.PR"],"title_canon_sha256":"f70b4a1c477bbd5e1095acae1b63cdd6b8f998bb31b3075908e5b7c81199efec","abstract_canon_sha256":"c6f78389402781824fdb9d787ee8022fda32c2adb47f1914e2746c1d465ec042"},"schema_version":"1.0"},"canonical_sha256":"d051200b1566d5e2866ac76903e196197f8e43260f2e8a825be43ad1ecc6925b","source":{"kind":"arxiv","id":"1712.01206","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.01206","created_at":"2026-05-18T00:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"1712.01206v2","created_at":"2026-05-18T00:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.01206","created_at":"2026-05-18T00:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"2BISACYVM3K6","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2BISACYVM3K6FBTK","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2BISACYV","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:2BISACYVM3K6FBTKY5UQHYMWDF","target":"record","payload":{"canonical_record":{"source":{"id":"1712.01206","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-12-04T17:13:32Z","cross_cats_sorted":["math.CO","math.PR"],"title_canon_sha256":"f70b4a1c477bbd5e1095acae1b63cdd6b8f998bb31b3075908e5b7c81199efec","abstract_canon_sha256":"c6f78389402781824fdb9d787ee8022fda32c2adb47f1914e2746c1d465ec042"},"schema_version":"1.0"},"canonical_sha256":"d051200b1566d5e2866ac76903e196197f8e43260f2e8a825be43ad1ecc6925b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:05.171974Z","signature_b64":"/Y5TL1kbQennZbdmcnlIZ43iOcerN/mEHWUc1OZE/1Gx7sqyQ6yfnvgDKBejy9Cq706NeD8bh9BpotNtIOCfDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d051200b1566d5e2866ac76903e196197f8e43260f2e8a825be43ad1ecc6925b","last_reissued_at":"2026-05-18T00:15:05.171385Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:05.171385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.01206","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":"2026-05-18T00:15:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z0F+qQPcyBP1MqDJLv1bBK4hhvD+8C9Hh+CNMY/fQjBD/aMnNSZ/Vi/HBuBi+y0HxLT8zNrSNcRm4CQ9WDOQCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:32:22.830162Z"},"content_sha256":"0da4abaf43cbfda2c21c0738d5659111fafa16c804a87af9ee47518ee35640e7","schema_version":"1.0","event_id":"sha256:0da4abaf43cbfda2c21c0738d5659111fafa16c804a87af9ee47518ee35640e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:2BISACYVM3K6FBTKY5UQHYMWDF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Refining the Two-Dimensional Signed Small Ball Inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"math.CA","authors_text":"Noah Kravitz","submitted_at":"2017-12-04T17:13:32Z","abstract_excerpt":"The two-dimensional signed small ball inequality states that for all possible choices of signs, $$ \\left\\| \\sum_{|R| = 2^{-n}}{ \\varepsilon_R h_R} \\right\\|_{L^{\\infty}} \\gtrsim n,$$ where the summation runs over all dyadic rectangles in the unit square and $h_R$ denotes the associated Haar function. This inequality first appeared in the work of Talagrand, and alternative proofs are due to Temlyakov and Bilyk & Feldheim (who showed that the supremum equals $n+1$ in all cases). We prove that for all integers $0\\leq k \\leq n+1$ and all possible choices of signs, $$ \\left| \\left\\{ x \\in [0,1)^2: \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.01206","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":""},"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":"2026-05-18T00:15:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gG3wYg1F2ahsYPD1PTCDSzQ7Oo+Jeqv3DnHae9nIiHZFkW6pOq12cw+X4VT1LjhkhzH1mQiCE7cbgBBDvmM/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:32:22.830529Z"},"content_sha256":"98084cf5085463c416db147157907216842b0f02fac2af5822d64eba08c9733d","schema_version":"1.0","event_id":"sha256:98084cf5085463c416db147157907216842b0f02fac2af5822d64eba08c9733d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2BISACYVM3K6FBTKY5UQHYMWDF/bundle.json","state_url":"https://pith.science/pith/2BISACYVM3K6FBTKY5UQHYMWDF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2BISACYVM3K6FBTKY5UQHYMWDF/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":"2026-06-30T23:32:22Z","links":{"resolver":"https://pith.science/pith/2BISACYVM3K6FBTKY5UQHYMWDF","bundle":"https://pith.science/pith/2BISACYVM3K6FBTKY5UQHYMWDF/bundle.json","state":"https://pith.science/pith/2BISACYVM3K6FBTKY5UQHYMWDF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2BISACYVM3K6FBTKY5UQHYMWDF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2BISACYVM3K6FBTKY5UQHYMWDF","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":"c6f78389402781824fdb9d787ee8022fda32c2adb47f1914e2746c1d465ec042","cross_cats_sorted":["math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-12-04T17:13:32Z","title_canon_sha256":"f70b4a1c477bbd5e1095acae1b63cdd6b8f998bb31b3075908e5b7c81199efec"},"schema_version":"1.0","source":{"id":"1712.01206","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.01206","created_at":"2026-05-18T00:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"1712.01206v2","created_at":"2026-05-18T00:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.01206","created_at":"2026-05-18T00:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"2BISACYVM3K6","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2BISACYVM3K6FBTK","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2BISACYV","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:98084cf5085463c416db147157907216842b0f02fac2af5822d64eba08c9733d","target":"graph","created_at":"2026-05-18T00:15:05Z","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":"The two-dimensional signed small ball inequality states that for all possible choices of signs, $$ \\left\\| \\sum_{|R| = 2^{-n}}{ \\varepsilon_R h_R} \\right\\|_{L^{\\infty}} \\gtrsim n,$$ where the summation runs over all dyadic rectangles in the unit square and $h_R$ denotes the associated Haar function. This inequality first appeared in the work of Talagrand, and alternative proofs are due to Temlyakov and Bilyk & Feldheim (who showed that the supremum equals $n+1$ in all cases). We prove that for all integers $0\\leq k \\leq n+1$ and all possible choices of signs, $$ \\left| \\left\\{ x \\in [0,1)^2: \\","authors_text":"Noah Kravitz","cross_cats":["math.CO","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-12-04T17:13:32Z","title":"Refining the Two-Dimensional Signed Small Ball Inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.01206","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":"sha256:0da4abaf43cbfda2c21c0738d5659111fafa16c804a87af9ee47518ee35640e7","target":"record","created_at":"2026-05-18T00:15:05Z","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":"c6f78389402781824fdb9d787ee8022fda32c2adb47f1914e2746c1d465ec042","cross_cats_sorted":["math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-12-04T17:13:32Z","title_canon_sha256":"f70b4a1c477bbd5e1095acae1b63cdd6b8f998bb31b3075908e5b7c81199efec"},"schema_version":"1.0","source":{"id":"1712.01206","kind":"arxiv","version":2}},"canonical_sha256":"d051200b1566d5e2866ac76903e196197f8e43260f2e8a825be43ad1ecc6925b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d051200b1566d5e2866ac76903e196197f8e43260f2e8a825be43ad1ecc6925b","first_computed_at":"2026-05-18T00:15:05.171385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:05.171385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/Y5TL1kbQennZbdmcnlIZ43iOcerN/mEHWUc1OZE/1Gx7sqyQ6yfnvgDKBejy9Cq706NeD8bh9BpotNtIOCfDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:05.171974Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.01206","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0da4abaf43cbfda2c21c0738d5659111fafa16c804a87af9ee47518ee35640e7","sha256:98084cf5085463c416db147157907216842b0f02fac2af5822d64eba08c9733d"],"state_sha256":"659d78fa8e1ee1a8796e612befbdd548605d2bed0e5f508fe3d0b6373f3dae45"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yuDriSZQ5wftxDeC8jrT79R2RJpEQSZKDK2fNwCaNScE0HtFfxbmT2YrJgHBWRmTe6LJetozba8a7RnxJN2EBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T23:32:22.832781Z","bundle_sha256":"0ad23e56e2ddc53fa2ae01f2aecf7ab84ef7a94b87f829d418fb810536350f92"}}