{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BVSVOB7CIY6IHS5II2W2ILTFVT","short_pith_number":"pith:BVSVOB7C","canonical_record":{"source":{"id":"1605.00939","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-03T15:10:05Z","cross_cats_sorted":[],"title_canon_sha256":"6ff7ab2cf1e8e371ed079a9f1a492a2f14b29533334063bf80747308a378f679","abstract_canon_sha256":"f43288a9134c30859a4d005aaf706dd54df49f3086f33357ddbd8a28b0e67571"},"schema_version":"1.0"},"canonical_sha256":"0d655707e2463c83cba846ada42e65ace6f408018ffc1c1169d0ab13f077f578","source":{"kind":"arxiv","id":"1605.00939","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00939","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00939v1","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00939","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"pith_short_12","alias_value":"BVSVOB7CIY6I","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"BVSVOB7CIY6IHS5I","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"BVSVOB7C","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BVSVOB7CIY6IHS5II2W2ILTFVT","target":"record","payload":{"canonical_record":{"source":{"id":"1605.00939","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-03T15:10:05Z","cross_cats_sorted":[],"title_canon_sha256":"6ff7ab2cf1e8e371ed079a9f1a492a2f14b29533334063bf80747308a378f679","abstract_canon_sha256":"f43288a9134c30859a4d005aaf706dd54df49f3086f33357ddbd8a28b0e67571"},"schema_version":"1.0"},"canonical_sha256":"0d655707e2463c83cba846ada42e65ace6f408018ffc1c1169d0ab13f077f578","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:47.643412Z","signature_b64":"KLkVjE00z5YGF+VNDJfD7cNlA9hRBYrgY9aFzV+Y3fC29s/+2Nw2Jsy+bsdLbg7ai2doUcstYVDGxiJGkl6aCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d655707e2463c83cba846ada42e65ace6f408018ffc1c1169d0ab13f077f578","last_reissued_at":"2026-05-18T01:15:47.642888Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:47.642888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.00939","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":"2026-05-18T01:15:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8dUwH16vBAn4QXS7hyqXUrumlUa0M4+GGz6cDxVv9luf62ZyWe3s6mUbIUvXD8PGr6+cSf3/hBCXMRyA6BR2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T11:00:22.779102Z"},"content_sha256":"d862cd5d967dac9ac635d99f7e48ec818d8e9bcb1e05a02e0aa3560911ea5448","schema_version":"1.0","event_id":"sha256:d862cd5d967dac9ac635d99f7e48ec818d8e9bcb1e05a02e0aa3560911ea5448"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BVSVOB7CIY6IHS5II2W2ILTFVT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Estimating discrete curvatures in terms of beta numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"S{\\l}awomir Kolasi\\'nski","submitted_at":"2016-05-03T15:10:05Z","abstract_excerpt":"For an arbitrary Radon measure $\\mu$ we estimate the integrated discrete curvature of $\\mu$ in terms of its centred variant of Jones' beta numbers. We farther relate integrals of centred and non-centred beta numbers. As a corollary, employing the recent result of Tolsa [Calc. Var. PDE, 2015], we obtain a partial converse of the theorem of Meurer [arXiv:1510.04523]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00939","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":"2026-05-18T01:15:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"stTY79pwSJjoSpNym/VKHrJ4NT8R7wj0lRGcMG2Yw183iub3Tps1lTmPPsvikmWMWQRbeG/PTwJ/fiHa8HQSBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T11:00:22.779453Z"},"content_sha256":"2f3adbf455373f3ea0e3fd1dddefa85e10985b5e2bb14a10f5062983df119f24","schema_version":"1.0","event_id":"sha256:2f3adbf455373f3ea0e3fd1dddefa85e10985b5e2bb14a10f5062983df119f24"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BVSVOB7CIY6IHS5II2W2ILTFVT/bundle.json","state_url":"https://pith.science/pith/BVSVOB7CIY6IHS5II2W2ILTFVT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BVSVOB7CIY6IHS5II2W2ILTFVT/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":"2026-06-07T11:00:22Z","links":{"resolver":"https://pith.science/pith/BVSVOB7CIY6IHS5II2W2ILTFVT","bundle":"https://pith.science/pith/BVSVOB7CIY6IHS5II2W2ILTFVT/bundle.json","state":"https://pith.science/pith/BVSVOB7CIY6IHS5II2W2ILTFVT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BVSVOB7CIY6IHS5II2W2ILTFVT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BVSVOB7CIY6IHS5II2W2ILTFVT","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":"f43288a9134c30859a4d005aaf706dd54df49f3086f33357ddbd8a28b0e67571","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-03T15:10:05Z","title_canon_sha256":"6ff7ab2cf1e8e371ed079a9f1a492a2f14b29533334063bf80747308a378f679"},"schema_version":"1.0","source":{"id":"1605.00939","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00939","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00939v1","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00939","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"pith_short_12","alias_value":"BVSVOB7CIY6I","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"BVSVOB7CIY6IHS5I","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"BVSVOB7C","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:2f3adbf455373f3ea0e3fd1dddefa85e10985b5e2bb14a10f5062983df119f24","target":"graph","created_at":"2026-05-18T01:15:47Z","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":"For an arbitrary Radon measure $\\mu$ we estimate the integrated discrete curvature of $\\mu$ in terms of its centred variant of Jones' beta numbers. We farther relate integrals of centred and non-centred beta numbers. As a corollary, employing the recent result of Tolsa [Calc. Var. PDE, 2015], we obtain a partial converse of the theorem of Meurer [arXiv:1510.04523].","authors_text":"S{\\l}awomir Kolasi\\'nski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-03T15:10:05Z","title":"Estimating discrete curvatures in terms of beta numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00939","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:d862cd5d967dac9ac635d99f7e48ec818d8e9bcb1e05a02e0aa3560911ea5448","target":"record","created_at":"2026-05-18T01:15:47Z","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":"f43288a9134c30859a4d005aaf706dd54df49f3086f33357ddbd8a28b0e67571","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-03T15:10:05Z","title_canon_sha256":"6ff7ab2cf1e8e371ed079a9f1a492a2f14b29533334063bf80747308a378f679"},"schema_version":"1.0","source":{"id":"1605.00939","kind":"arxiv","version":1}},"canonical_sha256":"0d655707e2463c83cba846ada42e65ace6f408018ffc1c1169d0ab13f077f578","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d655707e2463c83cba846ada42e65ace6f408018ffc1c1169d0ab13f077f578","first_computed_at":"2026-05-18T01:15:47.642888Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:47.642888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KLkVjE00z5YGF+VNDJfD7cNlA9hRBYrgY9aFzV+Y3fC29s/+2Nw2Jsy+bsdLbg7ai2doUcstYVDGxiJGkl6aCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:47.643412Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.00939","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d862cd5d967dac9ac635d99f7e48ec818d8e9bcb1e05a02e0aa3560911ea5448","sha256:2f3adbf455373f3ea0e3fd1dddefa85e10985b5e2bb14a10f5062983df119f24"],"state_sha256":"fdf135c8c69cf72c5356f927693cc78f6f1b3156e1b4100f8e22f361dc2e6d7e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S4D2zCZBTHQLf270whaWfCTCbkv86fDtwovrPo/ieSgQS7A1N5LteURmPc7XsBk/jekws5RqwD++Y+V2sOwVAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T11:00:22.781416Z","bundle_sha256":"868268a37a36d4dbc4ef7d8a26fd0fd7523f9f6616eca48ab82498ed43c7bea6"}}