{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:L2S4KWIYWYKHCE27EW6LLSSJRN","short_pith_number":"pith:L2S4KWIY","canonical_record":{"source":{"id":"1008.0588","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-08-03T16:35:40Z","cross_cats_sorted":[],"title_canon_sha256":"9315ab47cfaf54b0cf40d5594fd9bdeac59f12d6478c0d3d417ce85eb4c126cd","abstract_canon_sha256":"3c585b5fc08822dae2bda42cf4e1203a24d41035626feaa3c1da7a919e16ddbc"},"schema_version":"1.0"},"canonical_sha256":"5ea5c55918b61471135f25bcb5ca498b7e83badd0b4333cc54e56eee9dd3d40f","source":{"kind":"arxiv","id":"1008.0588","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.0588","created_at":"2026-05-18T04:42:42Z"},{"alias_kind":"arxiv_version","alias_value":"1008.0588v1","created_at":"2026-05-18T04:42:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0588","created_at":"2026-05-18T04:42:42Z"},{"alias_kind":"pith_short_12","alias_value":"L2S4KWIYWYKH","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"L2S4KWIYWYKHCE27","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"L2S4KWIY","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:L2S4KWIYWYKHCE27EW6LLSSJRN","target":"record","payload":{"canonical_record":{"source":{"id":"1008.0588","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-08-03T16:35:40Z","cross_cats_sorted":[],"title_canon_sha256":"9315ab47cfaf54b0cf40d5594fd9bdeac59f12d6478c0d3d417ce85eb4c126cd","abstract_canon_sha256":"3c585b5fc08822dae2bda42cf4e1203a24d41035626feaa3c1da7a919e16ddbc"},"schema_version":"1.0"},"canonical_sha256":"5ea5c55918b61471135f25bcb5ca498b7e83badd0b4333cc54e56eee9dd3d40f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:42.677983Z","signature_b64":"/Gn1ZaokNMM1McZm4BtnYkZpaH5zMfWSgV7UyzU+EndEtl9/SLr1z+AorIPE/57IWLB9cXLhCPNk9hK8OJ6RBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ea5c55918b61471135f25bcb5ca498b7e83badd0b4333cc54e56eee9dd3d40f","last_reissued_at":"2026-05-18T04:42:42.677544Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:42.677544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.0588","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":"2026-05-18T04:42:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N0ObOl39n0PoTCBVbJJRphvtUD5RVdaQORHwbnCAsWwtKXXK6JHfz8t5U7zp2Q17OViIulV+sHXAC/Xj4KoJBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T14:23:55.102085Z"},"content_sha256":"231ac15da7f335994073582eefd857e8a741d63349da78fd3bc1cfcdcf253a9b","schema_version":"1.0","event_id":"sha256:231ac15da7f335994073582eefd857e8a741d63349da78fd3bc1cfcdcf253a9b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:L2S4KWIYWYKHCE27EW6LLSSJRN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalization of the Wallace-Simson line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Christopher Bradley","submitted_at":"2010-08-03T16:35:40Z","abstract_excerpt":"A Wallace-Simson line of a point J has the property that it passes through the midpoint Q of HJ, where H is the orthocentre. By allowing Q to move on the perpendicular bisector of HJ we obtain generalized Wallace-Simson lines. These turn out to be known in another context."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0588","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":"2026-05-18T04:42:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bBiyzgGU8bRDx6BF2sTCgipW4bBG0OpiIJniERf3jEurO6kaWKeXsEV5mkVHYkbHEPwerweXsVcbAxRwfJYKBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T14:23:55.102915Z"},"content_sha256":"d80c1addcf730175d091621de329c1ac13ff26062fd9be7539ffd971d3eca1ca","schema_version":"1.0","event_id":"sha256:d80c1addcf730175d091621de329c1ac13ff26062fd9be7539ffd971d3eca1ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L2S4KWIYWYKHCE27EW6LLSSJRN/bundle.json","state_url":"https://pith.science/pith/L2S4KWIYWYKHCE27EW6LLSSJRN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L2S4KWIYWYKHCE27EW6LLSSJRN/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":"2026-08-14T14:23:55Z","links":{"resolver":"https://pith.science/pith/L2S4KWIYWYKHCE27EW6LLSSJRN","bundle":"https://pith.science/pith/L2S4KWIYWYKHCE27EW6LLSSJRN/bundle.json","state":"https://pith.science/pith/L2S4KWIYWYKHCE27EW6LLSSJRN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L2S4KWIYWYKHCE27EW6LLSSJRN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:L2S4KWIYWYKHCE27EW6LLSSJRN","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":"3c585b5fc08822dae2bda42cf4e1203a24d41035626feaa3c1da7a919e16ddbc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-08-03T16:35:40Z","title_canon_sha256":"9315ab47cfaf54b0cf40d5594fd9bdeac59f12d6478c0d3d417ce85eb4c126cd"},"schema_version":"1.0","source":{"id":"1008.0588","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.0588","created_at":"2026-05-18T04:42:42Z"},{"alias_kind":"arxiv_version","alias_value":"1008.0588v1","created_at":"2026-05-18T04:42:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0588","created_at":"2026-05-18T04:42:42Z"},{"alias_kind":"pith_short_12","alias_value":"L2S4KWIYWYKH","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"L2S4KWIYWYKHCE27","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"L2S4KWIY","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:d80c1addcf730175d091621de329c1ac13ff26062fd9be7539ffd971d3eca1ca","target":"graph","created_at":"2026-05-18T04:42:42Z","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":"A Wallace-Simson line of a point J has the property that it passes through the midpoint Q of HJ, where H is the orthocentre. By allowing Q to move on the perpendicular bisector of HJ we obtain generalized Wallace-Simson lines. These turn out to be known in another context.","authors_text":"Christopher Bradley","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-08-03T16:35:40Z","title":"Generalization of the Wallace-Simson line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0588","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":"sha256:231ac15da7f335994073582eefd857e8a741d63349da78fd3bc1cfcdcf253a9b","target":"record","created_at":"2026-05-18T04:42:42Z","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":"3c585b5fc08822dae2bda42cf4e1203a24d41035626feaa3c1da7a919e16ddbc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-08-03T16:35:40Z","title_canon_sha256":"9315ab47cfaf54b0cf40d5594fd9bdeac59f12d6478c0d3d417ce85eb4c126cd"},"schema_version":"1.0","source":{"id":"1008.0588","kind":"arxiv","version":1}},"canonical_sha256":"5ea5c55918b61471135f25bcb5ca498b7e83badd0b4333cc54e56eee9dd3d40f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ea5c55918b61471135f25bcb5ca498b7e83badd0b4333cc54e56eee9dd3d40f","first_computed_at":"2026-05-18T04:42:42.677544Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:42.677544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/Gn1ZaokNMM1McZm4BtnYkZpaH5zMfWSgV7UyzU+EndEtl9/SLr1z+AorIPE/57IWLB9cXLhCPNk9hK8OJ6RBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:42.677983Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.0588","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:231ac15da7f335994073582eefd857e8a741d63349da78fd3bc1cfcdcf253a9b","sha256:d80c1addcf730175d091621de329c1ac13ff26062fd9be7539ffd971d3eca1ca"],"state_sha256":"c3dcda0eafd2c019ccf69155e07a4ff507cd06fcaf526dd58ccd22cdd936a447"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1ooul9mm6IlBx44Gciv347viqhSl64Q7tzt8+mYfZqpNSbNBef6Qk8KKPqkkmBdoa59ir6H1VyhFZWWfjE4RCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T14:23:55.109318Z","bundle_sha256":"583bbb0e35b6422b06da73d0ad1333de304792349a195b8b45a6ce68d9ef2afe"}}