{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MQZX4AQQSGZXGFMEH2SLMNGBJ6","short_pith_number":"pith:MQZX4AQQ","canonical_record":{"source":{"id":"1612.07136","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-21T14:29:54Z","cross_cats_sorted":[],"title_canon_sha256":"1f081ac92d1c987a386e0617786dc9d20b9a54cb8e4856e0f699d38043b56bca","abstract_canon_sha256":"054670dead6b07b0eec9feb35e9ce274c535fb530bf28b218ed7b90944fe7b58"},"schema_version":"1.0"},"canonical_sha256":"64337e021091b37315843ea4b634c14fbc9e4b8dc083bf3fc6b17cbc4721099f","source":{"kind":"arxiv","id":"1612.07136","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07136","created_at":"2026-05-18T00:15:37Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07136v2","created_at":"2026-05-18T00:15:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07136","created_at":"2026-05-18T00:15:37Z"},{"alias_kind":"pith_short_12","alias_value":"MQZX4AQQSGZX","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MQZX4AQQSGZXGFME","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MQZX4AQQ","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MQZX4AQQSGZXGFMEH2SLMNGBJ6","target":"record","payload":{"canonical_record":{"source":{"id":"1612.07136","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-21T14:29:54Z","cross_cats_sorted":[],"title_canon_sha256":"1f081ac92d1c987a386e0617786dc9d20b9a54cb8e4856e0f699d38043b56bca","abstract_canon_sha256":"054670dead6b07b0eec9feb35e9ce274c535fb530bf28b218ed7b90944fe7b58"},"schema_version":"1.0"},"canonical_sha256":"64337e021091b37315843ea4b634c14fbc9e4b8dc083bf3fc6b17cbc4721099f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:37.900514Z","signature_b64":"DJfdEGnXU/Uu6ebeJx5k2dFS37WEcETs5N+9jtjmnVmyAMJqwUBSO+HSzzVWoGznpoeii93RinV17tI835WrAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64337e021091b37315843ea4b634c14fbc9e4b8dc083bf3fc6b17cbc4721099f","last_reissued_at":"2026-05-18T00:15:37.899797Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:37.899797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.07136","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":"2026-05-18T00:15:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t4Zxch6/r9I3jenJMEVPjGg45M/eD770QueWA7Tz2QG9uSLufiUWbO5M8gpSpT+mg0KncEXKZbLQTKDyfRkECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:42:24.805543Z"},"content_sha256":"627e91d5db2e7c5e7c7fe9d2fec6722199d604c0da97f51d4d69d2cc3d0361d1","schema_version":"1.0","event_id":"sha256:627e91d5db2e7c5e7c7fe9d2fec6722199d604c0da97f51d4d69d2cc3d0361d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MQZX4AQQSGZXGFMEH2SLMNGBJ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-affine sets in analytic curves and algebraic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Antti K\\\"aenm\\\"aki, De-Jun Feng","submitted_at":"2016-12-21T14:29:54Z","abstract_excerpt":"We characterize analytic curves that contain non-trivial self-affine sets. We also prove that compact algebraic surfaces cannot contain non-trivial self-affine sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07136","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":"2026-05-18T00:15:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1VXbrwP0kInrRVPYi3DCsA9RRx9xO3Zlb4wScMPFsgrPKPzCN/zvPgwndQdAnSoAYie9baxSbqVFmlx3Cyh5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:42:24.806223Z"},"content_sha256":"c1f72d8793665aa4fd1a2df9b96f68d92edaeedacca9d95ea6cdccc866fb65b1","schema_version":"1.0","event_id":"sha256:c1f72d8793665aa4fd1a2df9b96f68d92edaeedacca9d95ea6cdccc866fb65b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MQZX4AQQSGZXGFMEH2SLMNGBJ6/bundle.json","state_url":"https://pith.science/pith/MQZX4AQQSGZXGFMEH2SLMNGBJ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MQZX4AQQSGZXGFMEH2SLMNGBJ6/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":"2026-06-11T00:42:24Z","links":{"resolver":"https://pith.science/pith/MQZX4AQQSGZXGFMEH2SLMNGBJ6","bundle":"https://pith.science/pith/MQZX4AQQSGZXGFMEH2SLMNGBJ6/bundle.json","state":"https://pith.science/pith/MQZX4AQQSGZXGFMEH2SLMNGBJ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MQZX4AQQSGZXGFMEH2SLMNGBJ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MQZX4AQQSGZXGFMEH2SLMNGBJ6","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":"054670dead6b07b0eec9feb35e9ce274c535fb530bf28b218ed7b90944fe7b58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-21T14:29:54Z","title_canon_sha256":"1f081ac92d1c987a386e0617786dc9d20b9a54cb8e4856e0f699d38043b56bca"},"schema_version":"1.0","source":{"id":"1612.07136","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07136","created_at":"2026-05-18T00:15:37Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07136v2","created_at":"2026-05-18T00:15:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07136","created_at":"2026-05-18T00:15:37Z"},{"alias_kind":"pith_short_12","alias_value":"MQZX4AQQSGZX","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MQZX4AQQSGZXGFME","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MQZX4AQQ","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:c1f72d8793665aa4fd1a2df9b96f68d92edaeedacca9d95ea6cdccc866fb65b1","target":"graph","created_at":"2026-05-18T00:15:37Z","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 characterize analytic curves that contain non-trivial self-affine sets. We also prove that compact algebraic surfaces cannot contain non-trivial self-affine sets.","authors_text":"Antti K\\\"aenm\\\"aki, De-Jun Feng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-21T14:29:54Z","title":"Self-affine sets in analytic curves and algebraic surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07136","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":"sha256:627e91d5db2e7c5e7c7fe9d2fec6722199d604c0da97f51d4d69d2cc3d0361d1","target":"record","created_at":"2026-05-18T00:15:37Z","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":"054670dead6b07b0eec9feb35e9ce274c535fb530bf28b218ed7b90944fe7b58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-21T14:29:54Z","title_canon_sha256":"1f081ac92d1c987a386e0617786dc9d20b9a54cb8e4856e0f699d38043b56bca"},"schema_version":"1.0","source":{"id":"1612.07136","kind":"arxiv","version":2}},"canonical_sha256":"64337e021091b37315843ea4b634c14fbc9e4b8dc083bf3fc6b17cbc4721099f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64337e021091b37315843ea4b634c14fbc9e4b8dc083bf3fc6b17cbc4721099f","first_computed_at":"2026-05-18T00:15:37.899797Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:37.899797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DJfdEGnXU/Uu6ebeJx5k2dFS37WEcETs5N+9jtjmnVmyAMJqwUBSO+HSzzVWoGznpoeii93RinV17tI835WrAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:37.900514Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.07136","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:627e91d5db2e7c5e7c7fe9d2fec6722199d604c0da97f51d4d69d2cc3d0361d1","sha256:c1f72d8793665aa4fd1a2df9b96f68d92edaeedacca9d95ea6cdccc866fb65b1"],"state_sha256":"f64ee2b3f9883ead8e63222974b7dc75709748386ef78b0f25acb4c4b87e394a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OuyKt550LkYvqnzd35HIXg38/sinAKtkgSa9YDDYy17Pt9xxFjmQdEp4W+v6I82RE5eLb5fb3ttdLjddIOzHBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T00:42:24.810034Z","bundle_sha256":"664b7cf9e9f338eab00ca9938f1c768e934e3d933fbd6021409a3a24c2e10338"}}