{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:XBBTBETYXWCHFHR6DYM34VEGXR","short_pith_number":"pith:XBBTBETY","canonical_record":{"source":{"id":"1401.0407","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-02T10:22:38Z","cross_cats_sorted":["math.CA","math.CV"],"title_canon_sha256":"d6ed2bceba2c679118d43cf4044bc97b2b56d450b61ba9da1732718abbb57868","abstract_canon_sha256":"cad74e083ed8bb2914399709fa577cb2abcc517a37823d9d1a1bac044a2b5fed"},"schema_version":"1.0"},"canonical_sha256":"b843309278bd84729e3e1e19be5486bc6d44f275854d18cebfcf22cd817b17fb","source":{"kind":"arxiv","id":"1401.0407","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0407","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0407v2","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0407","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"pith_short_12","alias_value":"XBBTBETYXWCH","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XBBTBETYXWCHFHR6","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XBBTBETY","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:XBBTBETYXWCHFHR6DYM34VEGXR","target":"record","payload":{"canonical_record":{"source":{"id":"1401.0407","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-02T10:22:38Z","cross_cats_sorted":["math.CA","math.CV"],"title_canon_sha256":"d6ed2bceba2c679118d43cf4044bc97b2b56d450b61ba9da1732718abbb57868","abstract_canon_sha256":"cad74e083ed8bb2914399709fa577cb2abcc517a37823d9d1a1bac044a2b5fed"},"schema_version":"1.0"},"canonical_sha256":"b843309278bd84729e3e1e19be5486bc6d44f275854d18cebfcf22cd817b17fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:39.274429Z","signature_b64":"i/c8PjLiN/Gtr2vEvQZAG0IpT+IB2FjjgQQM75sAIpkhx2k7baMjTqHep6QphmEaWwLIIt+rODYAdZ8EUzrRAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b843309278bd84729e3e1e19be5486bc6d44f275854d18cebfcf22cd817b17fb","last_reissued_at":"2026-05-18T02:54:39.273778Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:39.273778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.0407","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":"2026-05-18T02:54:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7+3R996CNNQFptlNT0aJEfQx7CzqD4bWewP1xbkwyDLpXZSd0ey1pUvgRNLOyaZEXiUT+1trERcUZdsqw0SDAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T07:43:45.893212Z"},"content_sha256":"5e7f816599fc542254b2deb5429dc99a8740bcc405bf2f2bf17119df08add7fc","schema_version":"1.0","event_id":"sha256:5e7f816599fc542254b2deb5429dc99a8740bcc405bf2f2bf17119df08add7fc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:XBBTBETYXWCHFHR6DYM34VEGXR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Almost-additivity of analytic capacity and Cauchy independent measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV"],"primary_cat":"math.AP","authors_text":"Alexander Reznikov, Alexander Volberg, Vladimir Eiderman","submitted_at":"2014-01-02T10:22:38Z","abstract_excerpt":"We show that, given a family of discs centered at a chord-arc curve, the analytic capacity of a union of arbitrary subsets of these discs (one subset in each disc) is comparable with the sum of their analytic capacities. We show a sort of converse to this geometric statement as well. However, we need that the discs in question would be separated, and it is not clear whether the separation condition is essential or not. We apply this result to find families $\\{\\mu_j\\}$ of measures in $\\mathbb{C}$ with the following property. If the Cauchy integral operators $\\mathcal{C}_{\\mu_j}$ from $L^2(\\mu_j"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0407","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":"2026-05-18T02:54:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BlsqosZ4nX6B9/H2piP67gtaLPtDLQ++HHm8HdwtHUUM8eRdsANcJ127Q3m6aIpHp2d36M6w/e5GW8nAk4TvAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T07:43:45.893889Z"},"content_sha256":"dec3435200bcd6e41d7cc4bd185a6d42d6528d58724eec87f6a9df0abbed622e","schema_version":"1.0","event_id":"sha256:dec3435200bcd6e41d7cc4bd185a6d42d6528d58724eec87f6a9df0abbed622e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XBBTBETYXWCHFHR6DYM34VEGXR/bundle.json","state_url":"https://pith.science/pith/XBBTBETYXWCHFHR6DYM34VEGXR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XBBTBETYXWCHFHR6DYM34VEGXR/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":"2026-06-11T07:43:45Z","links":{"resolver":"https://pith.science/pith/XBBTBETYXWCHFHR6DYM34VEGXR","bundle":"https://pith.science/pith/XBBTBETYXWCHFHR6DYM34VEGXR/bundle.json","state":"https://pith.science/pith/XBBTBETYXWCHFHR6DYM34VEGXR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XBBTBETYXWCHFHR6DYM34VEGXR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XBBTBETYXWCHFHR6DYM34VEGXR","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":"cad74e083ed8bb2914399709fa577cb2abcc517a37823d9d1a1bac044a2b5fed","cross_cats_sorted":["math.CA","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-02T10:22:38Z","title_canon_sha256":"d6ed2bceba2c679118d43cf4044bc97b2b56d450b61ba9da1732718abbb57868"},"schema_version":"1.0","source":{"id":"1401.0407","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0407","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0407v2","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0407","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"pith_short_12","alias_value":"XBBTBETYXWCH","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XBBTBETYXWCHFHR6","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XBBTBETY","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:dec3435200bcd6e41d7cc4bd185a6d42d6528d58724eec87f6a9df0abbed622e","target":"graph","created_at":"2026-05-18T02:54:39Z","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 show that, given a family of discs centered at a chord-arc curve, the analytic capacity of a union of arbitrary subsets of these discs (one subset in each disc) is comparable with the sum of their analytic capacities. We show a sort of converse to this geometric statement as well. However, we need that the discs in question would be separated, and it is not clear whether the separation condition is essential or not. We apply this result to find families $\\{\\mu_j\\}$ of measures in $\\mathbb{C}$ with the following property. If the Cauchy integral operators $\\mathcal{C}_{\\mu_j}$ from $L^2(\\mu_j","authors_text":"Alexander Reznikov, Alexander Volberg, Vladimir Eiderman","cross_cats":["math.CA","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-02T10:22:38Z","title":"Almost-additivity of analytic capacity and Cauchy independent measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0407","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":"sha256:5e7f816599fc542254b2deb5429dc99a8740bcc405bf2f2bf17119df08add7fc","target":"record","created_at":"2026-05-18T02:54:39Z","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":"cad74e083ed8bb2914399709fa577cb2abcc517a37823d9d1a1bac044a2b5fed","cross_cats_sorted":["math.CA","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-02T10:22:38Z","title_canon_sha256":"d6ed2bceba2c679118d43cf4044bc97b2b56d450b61ba9da1732718abbb57868"},"schema_version":"1.0","source":{"id":"1401.0407","kind":"arxiv","version":2}},"canonical_sha256":"b843309278bd84729e3e1e19be5486bc6d44f275854d18cebfcf22cd817b17fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b843309278bd84729e3e1e19be5486bc6d44f275854d18cebfcf22cd817b17fb","first_computed_at":"2026-05-18T02:54:39.273778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:39.273778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i/c8PjLiN/Gtr2vEvQZAG0IpT+IB2FjjgQQM75sAIpkhx2k7baMjTqHep6QphmEaWwLIIt+rODYAdZ8EUzrRAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:39.274429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0407","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e7f816599fc542254b2deb5429dc99a8740bcc405bf2f2bf17119df08add7fc","sha256:dec3435200bcd6e41d7cc4bd185a6d42d6528d58724eec87f6a9df0abbed622e"],"state_sha256":"0c21bf14037b50eb1b0b67bb5e563c62d7ba7711e6119f3285089224b4be387c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XkLQEuJbEji+GPkrouEKgsX//qBXlsl8EQJREhDBlxYuByx8IDFaMILKiMrlcpJLUi42wsuc/Zyb0z+FoAPHBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T07:43:45.897883Z","bundle_sha256":"713755fa3e260ad706b7118f3a4f52284f5c82eefae5f2c490cd0030c3aa5f59"}}