{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2FSEIK6D6MFPRWP3KXDKNIF2TH","short_pith_number":"pith:2FSEIK6D","canonical_record":{"source":{"id":"1611.05948","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-11-18T01:54:14Z","cross_cats_sorted":[],"title_canon_sha256":"bfe1abb40aa61a1f0bb7190a47511488e095f3b3b184f6920bd662a707c47461","abstract_canon_sha256":"9947c6855d1b2b05ff9ee78810f4bd351f2995e568a847bab2928560d1ca5eef"},"schema_version":"1.0"},"canonical_sha256":"d164442bc3f30af8d9fb55c6a6a0ba99d0fa2270a4f6681125f8b684f2ab0421","source":{"kind":"arxiv","id":"1611.05948","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.05948","created_at":"2026-05-18T00:03:19Z"},{"alias_kind":"arxiv_version","alias_value":"1611.05948v2","created_at":"2026-05-18T00:03:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.05948","created_at":"2026-05-18T00:03:19Z"},{"alias_kind":"pith_short_12","alias_value":"2FSEIK6D6MFP","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2FSEIK6D6MFPRWP3","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2FSEIK6D","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2FSEIK6D6MFPRWP3KXDKNIF2TH","target":"record","payload":{"canonical_record":{"source":{"id":"1611.05948","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-11-18T01:54:14Z","cross_cats_sorted":[],"title_canon_sha256":"bfe1abb40aa61a1f0bb7190a47511488e095f3b3b184f6920bd662a707c47461","abstract_canon_sha256":"9947c6855d1b2b05ff9ee78810f4bd351f2995e568a847bab2928560d1ca5eef"},"schema_version":"1.0"},"canonical_sha256":"d164442bc3f30af8d9fb55c6a6a0ba99d0fa2270a4f6681125f8b684f2ab0421","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:19.937929Z","signature_b64":"TtcRifjoYnhVxG8kILl1OpUJNLjY0rstQAgboxcHmzaM+wlF9Rc3ysEJDAQt1MyqgHqRt0d/OlyMu4lkHH6XCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d164442bc3f30af8d9fb55c6a6a0ba99d0fa2270a4f6681125f8b684f2ab0421","last_reissued_at":"2026-05-18T00:03:19.937478Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:19.937478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.05948","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":"2026-05-18T00:03:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U5TJkViaiA+rwr/lXjPJzr6lSJ9674HCl8z15o17sxaUJocgUGJ2J49ZgKVvteAkB1myEBNEc+Vk+Xz5VWP6Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:32:08.848764Z"},"content_sha256":"c3f9229a2cea89b8e01fef8d6b4703e2e80a45b526237d9227dfbe3c32ffff40","schema_version":"1.0","event_id":"sha256:c3f9229a2cea89b8e01fef8d6b4703e2e80a45b526237d9227dfbe3c32ffff40"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2FSEIK6D6MFPRWP3KXDKNIF2TH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interval projections of self-similar sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"\\'Abel Farkas","submitted_at":"2016-11-18T01:54:14Z","abstract_excerpt":"We show that if $K$ is a self-similar $1$-set that is not contained in a line and either satisfies the strong separation condition or is defined via homotheties then there are at most finitely many lines through the origin such that the projection of $K$ onto them is an interval."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05948","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":"2026-05-18T00:03:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DQcrl5DxwT46EvoxCJF8+XKHHUiCFzgBFBHYFiQz23dFxDC/z89g1kx2H8r5l5m+rsEUPzoVVQuezmQmL7U4DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:32:08.849225Z"},"content_sha256":"23705d9d6833e1c256797a54ef5e21df825f0d822d4ab1ea4d820acadc558bc0","schema_version":"1.0","event_id":"sha256:23705d9d6833e1c256797a54ef5e21df825f0d822d4ab1ea4d820acadc558bc0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2FSEIK6D6MFPRWP3KXDKNIF2TH/bundle.json","state_url":"https://pith.science/pith/2FSEIK6D6MFPRWP3KXDKNIF2TH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2FSEIK6D6MFPRWP3KXDKNIF2TH/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":"2026-06-22T16:32:08Z","links":{"resolver":"https://pith.science/pith/2FSEIK6D6MFPRWP3KXDKNIF2TH","bundle":"https://pith.science/pith/2FSEIK6D6MFPRWP3KXDKNIF2TH/bundle.json","state":"https://pith.science/pith/2FSEIK6D6MFPRWP3KXDKNIF2TH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2FSEIK6D6MFPRWP3KXDKNIF2TH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2FSEIK6D6MFPRWP3KXDKNIF2TH","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":"9947c6855d1b2b05ff9ee78810f4bd351f2995e568a847bab2928560d1ca5eef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-11-18T01:54:14Z","title_canon_sha256":"bfe1abb40aa61a1f0bb7190a47511488e095f3b3b184f6920bd662a707c47461"},"schema_version":"1.0","source":{"id":"1611.05948","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.05948","created_at":"2026-05-18T00:03:19Z"},{"alias_kind":"arxiv_version","alias_value":"1611.05948v2","created_at":"2026-05-18T00:03:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.05948","created_at":"2026-05-18T00:03:19Z"},{"alias_kind":"pith_short_12","alias_value":"2FSEIK6D6MFP","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2FSEIK6D6MFPRWP3","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2FSEIK6D","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:23705d9d6833e1c256797a54ef5e21df825f0d822d4ab1ea4d820acadc558bc0","target":"graph","created_at":"2026-05-18T00:03:19Z","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 if $K$ is a self-similar $1$-set that is not contained in a line and either satisfies the strong separation condition or is defined via homotheties then there are at most finitely many lines through the origin such that the projection of $K$ onto them is an interval.","authors_text":"\\'Abel Farkas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-11-18T01:54:14Z","title":"Interval projections of self-similar sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05948","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:c3f9229a2cea89b8e01fef8d6b4703e2e80a45b526237d9227dfbe3c32ffff40","target":"record","created_at":"2026-05-18T00:03:19Z","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":"9947c6855d1b2b05ff9ee78810f4bd351f2995e568a847bab2928560d1ca5eef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-11-18T01:54:14Z","title_canon_sha256":"bfe1abb40aa61a1f0bb7190a47511488e095f3b3b184f6920bd662a707c47461"},"schema_version":"1.0","source":{"id":"1611.05948","kind":"arxiv","version":2}},"canonical_sha256":"d164442bc3f30af8d9fb55c6a6a0ba99d0fa2270a4f6681125f8b684f2ab0421","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d164442bc3f30af8d9fb55c6a6a0ba99d0fa2270a4f6681125f8b684f2ab0421","first_computed_at":"2026-05-18T00:03:19.937478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:19.937478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TtcRifjoYnhVxG8kILl1OpUJNLjY0rstQAgboxcHmzaM+wlF9Rc3ysEJDAQt1MyqgHqRt0d/OlyMu4lkHH6XCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:19.937929Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.05948","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3f9229a2cea89b8e01fef8d6b4703e2e80a45b526237d9227dfbe3c32ffff40","sha256:23705d9d6833e1c256797a54ef5e21df825f0d822d4ab1ea4d820acadc558bc0"],"state_sha256":"7f50691c9527de7768d17bdba713508855bd0a1227b87ff94ad8b785f942d71c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+iHSS1GxsUFoBm/YArbK3nAhpd4hB1gQ2fIp403IuijGiT1+3yc0m0jYzyzF2gAWYWA2dBILABlT/9LuDvMACg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T16:32:08.851773Z","bundle_sha256":"b338ba82e98a0a825557b17841f53de08c308304c4e325e73aefdc603214c74c"}}