{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QV7TBEXYNP5KYX3F65BC3L7JF4","short_pith_number":"pith:QV7TBEXY","canonical_record":{"source":{"id":"1511.09002","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-11-29T12:27:31Z","cross_cats_sorted":[],"title_canon_sha256":"6c49fbaa54bab61f7947b0e548cbfd240e34709060ab2fb7a510764dcdd4910a","abstract_canon_sha256":"ec5f48fa778cd66153efe93a3be708dd91a7ec63d6db97c769d6fde52343842c"},"schema_version":"1.0"},"canonical_sha256":"857f3092f86bfaac5f65f7422dafe92f2113a096c066f38dcad8e1d43fcd3aac","source":{"kind":"arxiv","id":"1511.09002","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.09002","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"arxiv_version","alias_value":"1511.09002v2","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.09002","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"pith_short_12","alias_value":"QV7TBEXYNP5K","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QV7TBEXYNP5KYX3F","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QV7TBEXY","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QV7TBEXYNP5KYX3F65BC3L7JF4","target":"record","payload":{"canonical_record":{"source":{"id":"1511.09002","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-11-29T12:27:31Z","cross_cats_sorted":[],"title_canon_sha256":"6c49fbaa54bab61f7947b0e548cbfd240e34709060ab2fb7a510764dcdd4910a","abstract_canon_sha256":"ec5f48fa778cd66153efe93a3be708dd91a7ec63d6db97c769d6fde52343842c"},"schema_version":"1.0"},"canonical_sha256":"857f3092f86bfaac5f65f7422dafe92f2113a096c066f38dcad8e1d43fcd3aac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:35.132643Z","signature_b64":"WXJe44XrbatQfvMFQuL+1tz8sCClp/17UOCn2H614nEYysoNsUELnrt6xa/pFwIQ/7Ug6NzKE7hG7yYZUD2mDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"857f3092f86bfaac5f65f7422dafe92f2113a096c066f38dcad8e1d43fcd3aac","last_reissued_at":"2026-05-18T00:45:35.131221Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:35.131221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.09002","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":"2026-05-18T00:45:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EKOd2nw70hGOxeJUHzQ2jN15g4FCKM0q52uaJLQA5dk+BdTHlHwsNT56EtpHNBbGXohu7kssAvDNam5V3paCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:15:30.098802Z"},"content_sha256":"0edf03c0ac4fe6c146144ecfec056d167514b6d83b536da4313112bbf6d98aca","schema_version":"1.0","event_id":"sha256:0edf03c0ac4fe6c146144ecfec056d167514b6d83b536da4313112bbf6d98aca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QV7TBEXYNP5KYX3F65BC3L7JF4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Elementary proofs of Kempe universality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"S. C. Power","submitted_at":"2015-11-29T12:27:31Z","abstract_excerpt":"An elementary proof is given to show that a parametrised algebraic curve in the plane may be traced out, in the sense of A. B. Kempe, by a finite pinned linkage. Additionally it is shown that any parametrised continuous curve \\gamma: [0,1] to R^2 may be traced out by an infinite linkage where the valencies of the joints is uniformly bounded. We also discuss related Kempe universality theorems and give a novel correction of Kempe's original argument."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09002","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":"2026-05-18T00:45:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9K9m0CiInTv68vezs8CpGXUDXOkNmr7m+ZJtnSlixI/Mz+BnCbyvoqaWD/zbcPPeq8j3EjvGuLXj84SvcjFFAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:15:30.099450Z"},"content_sha256":"cb6183d4caeb6d37a0c94d407138179ae45b1d8c244f8e9d8280e9b5846b8329","schema_version":"1.0","event_id":"sha256:cb6183d4caeb6d37a0c94d407138179ae45b1d8c244f8e9d8280e9b5846b8329"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QV7TBEXYNP5KYX3F65BC3L7JF4/bundle.json","state_url":"https://pith.science/pith/QV7TBEXYNP5KYX3F65BC3L7JF4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QV7TBEXYNP5KYX3F65BC3L7JF4/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":"2026-06-10T21:15:30Z","links":{"resolver":"https://pith.science/pith/QV7TBEXYNP5KYX3F65BC3L7JF4","bundle":"https://pith.science/pith/QV7TBEXYNP5KYX3F65BC3L7JF4/bundle.json","state":"https://pith.science/pith/QV7TBEXYNP5KYX3F65BC3L7JF4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QV7TBEXYNP5KYX3F65BC3L7JF4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QV7TBEXYNP5KYX3F65BC3L7JF4","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":"ec5f48fa778cd66153efe93a3be708dd91a7ec63d6db97c769d6fde52343842c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-11-29T12:27:31Z","title_canon_sha256":"6c49fbaa54bab61f7947b0e548cbfd240e34709060ab2fb7a510764dcdd4910a"},"schema_version":"1.0","source":{"id":"1511.09002","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.09002","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"arxiv_version","alias_value":"1511.09002v2","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.09002","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"pith_short_12","alias_value":"QV7TBEXYNP5K","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QV7TBEXYNP5KYX3F","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QV7TBEXY","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:cb6183d4caeb6d37a0c94d407138179ae45b1d8c244f8e9d8280e9b5846b8329","target":"graph","created_at":"2026-05-18T00:45:35Z","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":"An elementary proof is given to show that a parametrised algebraic curve in the plane may be traced out, in the sense of A. B. Kempe, by a finite pinned linkage. Additionally it is shown that any parametrised continuous curve \\gamma: [0,1] to R^2 may be traced out by an infinite linkage where the valencies of the joints is uniformly bounded. We also discuss related Kempe universality theorems and give a novel correction of Kempe's original argument.","authors_text":"S. C. Power","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-11-29T12:27:31Z","title":"Elementary proofs of Kempe universality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09002","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":"sha256:0edf03c0ac4fe6c146144ecfec056d167514b6d83b536da4313112bbf6d98aca","target":"record","created_at":"2026-05-18T00:45:35Z","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":"ec5f48fa778cd66153efe93a3be708dd91a7ec63d6db97c769d6fde52343842c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-11-29T12:27:31Z","title_canon_sha256":"6c49fbaa54bab61f7947b0e548cbfd240e34709060ab2fb7a510764dcdd4910a"},"schema_version":"1.0","source":{"id":"1511.09002","kind":"arxiv","version":2}},"canonical_sha256":"857f3092f86bfaac5f65f7422dafe92f2113a096c066f38dcad8e1d43fcd3aac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"857f3092f86bfaac5f65f7422dafe92f2113a096c066f38dcad8e1d43fcd3aac","first_computed_at":"2026-05-18T00:45:35.131221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:35.131221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WXJe44XrbatQfvMFQuL+1tz8sCClp/17UOCn2H614nEYysoNsUELnrt6xa/pFwIQ/7Ug6NzKE7hG7yYZUD2mDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:35.132643Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.09002","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0edf03c0ac4fe6c146144ecfec056d167514b6d83b536da4313112bbf6d98aca","sha256:cb6183d4caeb6d37a0c94d407138179ae45b1d8c244f8e9d8280e9b5846b8329"],"state_sha256":"068ab4ae61995f06b9e12aa93e689c0edc9fc744dd60a4b4ffedbc5ee5ebfe03"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CIrI3dgoNLibHIDt0sewIkbd6DUkgcNpZhY1301tcCXihqFImWyKvZ+ccReKVys82clmrNBzTYiYs3YI2WoOCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T21:15:30.102809Z","bundle_sha256":"d828eceef62129747595c32720ca33ee545b1123c20793764adfe927c44d32bd"}}