{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7N5DCRFIL4JCXXMGIMJBTUTBAN","short_pith_number":"pith:7N5DCRFI","canonical_record":{"source":{"id":"1603.07501","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-24T09:41:50Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"6ea90fb1562e6c96ad245bcf6df2e4b03ecfc5523bb780d52693ddfa35736c72","abstract_canon_sha256":"bd150ed71e03b489e6ae13c3f28a3836ce5b11004a8f3c3ef7910011b3b2a310"},"schema_version":"1.0"},"canonical_sha256":"fb7a3144a85f122bdd86431219d261035403fba1795444263eb9797095b1ed02","source":{"kind":"arxiv","id":"1603.07501","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07501","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07501v1","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07501","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"pith_short_12","alias_value":"7N5DCRFIL4JC","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7N5DCRFIL4JCXXMG","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7N5DCRFI","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7N5DCRFIL4JCXXMGIMJBTUTBAN","target":"record","payload":{"canonical_record":{"source":{"id":"1603.07501","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-24T09:41:50Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"6ea90fb1562e6c96ad245bcf6df2e4b03ecfc5523bb780d52693ddfa35736c72","abstract_canon_sha256":"bd150ed71e03b489e6ae13c3f28a3836ce5b11004a8f3c3ef7910011b3b2a310"},"schema_version":"1.0"},"canonical_sha256":"fb7a3144a85f122bdd86431219d261035403fba1795444263eb9797095b1ed02","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:20.718187Z","signature_b64":"Qvw4ih/qXHAbf65xrvWU+PAmJyyv82g8E513CzgYCFE6D0i5C2LS2kBRCTaMibFTtOBzsfjKmvUtE/wWsDIyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb7a3144a85f122bdd86431219d261035403fba1795444263eb9797095b1ed02","last_reissued_at":"2026-05-18T01:18:20.717472Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:20.717472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.07501","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":"2026-05-18T01:18:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aUzjjcQ1c3tN52bDx+yDHrFj6cdJvXY15qUz4KEBUP+BT+Ga8PWqOW5J1q3r63G4ZdgTQF2gJT41rzlerMuUBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:36:35.697351Z"},"content_sha256":"8a8fa23c6d9130d3f2a18ab8c34eed2f7f782ec28fd8f5ef7ab74285dbde3ff9","schema_version":"1.0","event_id":"sha256:8a8fa23c6d9130d3f2a18ab8c34eed2f7f782ec28fd8f5ef7ab74285dbde3ff9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7N5DCRFIL4JCXXMGIMJBTUTBAN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Measures and fibers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.LO","authors_text":"Piotr Borodulin-Nadzieja","submitted_at":"2016-03-24T09:41:50Z","abstract_excerpt":"We study measures on compact spaces by analyzing the properties of fibers of continuous mappings into 2^omega. We show that if a compact zerodimensional space K carries a measure of uncountable Maharam type, then such a mapping has a non-scattered fiber and, if we assume additionally a weak version of Martin's Axiom, such a mapping has a fiber carrying a measure of uncountable Maharam type. Also, we prove that every compact zerodimensional space which supports a strictly positive measure and which can be mapped into 2^omega by a finite-to-one function is separable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07501","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":"2026-05-18T01:18:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wGes6IwemGlYp6H1ppZ3wWlqyN0WoBYhCnr1pVjIcJPWm00Gw7nFCa3pbbrvG5mJzdrx0yYPUwK6Yl3tHve3Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:36:35.697696Z"},"content_sha256":"3e6124ec273404140e824169e3dd3b5c04cba12af7a8ad349cfcd307c11648d9","schema_version":"1.0","event_id":"sha256:3e6124ec273404140e824169e3dd3b5c04cba12af7a8ad349cfcd307c11648d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7N5DCRFIL4JCXXMGIMJBTUTBAN/bundle.json","state_url":"https://pith.science/pith/7N5DCRFIL4JCXXMGIMJBTUTBAN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7N5DCRFIL4JCXXMGIMJBTUTBAN/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":"2026-06-21T20:36:35Z","links":{"resolver":"https://pith.science/pith/7N5DCRFIL4JCXXMGIMJBTUTBAN","bundle":"https://pith.science/pith/7N5DCRFIL4JCXXMGIMJBTUTBAN/bundle.json","state":"https://pith.science/pith/7N5DCRFIL4JCXXMGIMJBTUTBAN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7N5DCRFIL4JCXXMGIMJBTUTBAN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7N5DCRFIL4JCXXMGIMJBTUTBAN","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":"bd150ed71e03b489e6ae13c3f28a3836ce5b11004a8f3c3ef7910011b3b2a310","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-24T09:41:50Z","title_canon_sha256":"6ea90fb1562e6c96ad245bcf6df2e4b03ecfc5523bb780d52693ddfa35736c72"},"schema_version":"1.0","source":{"id":"1603.07501","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07501","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07501v1","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07501","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"pith_short_12","alias_value":"7N5DCRFIL4JC","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7N5DCRFIL4JCXXMG","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7N5DCRFI","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:3e6124ec273404140e824169e3dd3b5c04cba12af7a8ad349cfcd307c11648d9","target":"graph","created_at":"2026-05-18T01:18:20Z","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 study measures on compact spaces by analyzing the properties of fibers of continuous mappings into 2^omega. We show that if a compact zerodimensional space K carries a measure of uncountable Maharam type, then such a mapping has a non-scattered fiber and, if we assume additionally a weak version of Martin's Axiom, such a mapping has a fiber carrying a measure of uncountable Maharam type. Also, we prove that every compact zerodimensional space which supports a strictly positive measure and which can be mapped into 2^omega by a finite-to-one function is separable.","authors_text":"Piotr Borodulin-Nadzieja","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-24T09:41:50Z","title":"Measures and fibers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07501","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":"sha256:8a8fa23c6d9130d3f2a18ab8c34eed2f7f782ec28fd8f5ef7ab74285dbde3ff9","target":"record","created_at":"2026-05-18T01:18:20Z","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":"bd150ed71e03b489e6ae13c3f28a3836ce5b11004a8f3c3ef7910011b3b2a310","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-24T09:41:50Z","title_canon_sha256":"6ea90fb1562e6c96ad245bcf6df2e4b03ecfc5523bb780d52693ddfa35736c72"},"schema_version":"1.0","source":{"id":"1603.07501","kind":"arxiv","version":1}},"canonical_sha256":"fb7a3144a85f122bdd86431219d261035403fba1795444263eb9797095b1ed02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb7a3144a85f122bdd86431219d261035403fba1795444263eb9797095b1ed02","first_computed_at":"2026-05-18T01:18:20.717472Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:20.717472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qvw4ih/qXHAbf65xrvWU+PAmJyyv82g8E513CzgYCFE6D0i5C2LS2kBRCTaMibFTtOBzsfjKmvUtE/wWsDIyAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:20.718187Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07501","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a8fa23c6d9130d3f2a18ab8c34eed2f7f782ec28fd8f5ef7ab74285dbde3ff9","sha256:3e6124ec273404140e824169e3dd3b5c04cba12af7a8ad349cfcd307c11648d9"],"state_sha256":"72a50b5abc2f2aa18dfffdd2ab013b814d5a4f705aeee130c874aa3e926469a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6iYeph4kd+kHAk9DYxC6nQtIdvtc9B4lZBzcoSmMELVzS2F8xBQ7CYrTgSDTFS/PxdPdAvYNGlfIHg41Bj8aBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T20:36:35.699665Z","bundle_sha256":"5843498dbf0172ebaee13613556d24311c93251ed9f2d4cc0947f579716d71f1"}}