{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6YHQDI5JMLUL2SHVZRAMPYMRLL","short_pith_number":"pith:6YHQDI5J","canonical_record":{"source":{"id":"1811.07063","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-16T23:33:29Z","cross_cats_sorted":["math.CV","math.GT"],"title_canon_sha256":"9df2a010b23957e8df22c7f962eef546d3aa21eb463565136a40b691b28ea95f","abstract_canon_sha256":"302d6459ab75a89e20fcb15c3f799dbbbf352ee40628b6fb7b8bf6013388ad17"},"schema_version":"1.0"},"canonical_sha256":"f60f01a3a962e8bd48f5cc40c7e1915aebd4c3a46cb940db5354cd5a73c17953","source":{"kind":"arxiv","id":"1811.07063","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.07063","created_at":"2026-05-18T00:00:29Z"},{"alias_kind":"arxiv_version","alias_value":"1811.07063v1","created_at":"2026-05-18T00:00:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.07063","created_at":"2026-05-18T00:00:29Z"},{"alias_kind":"pith_short_12","alias_value":"6YHQDI5JMLUL","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6YHQDI5JMLUL2SHV","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6YHQDI5J","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6YHQDI5JMLUL2SHVZRAMPYMRLL","target":"record","payload":{"canonical_record":{"source":{"id":"1811.07063","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-16T23:33:29Z","cross_cats_sorted":["math.CV","math.GT"],"title_canon_sha256":"9df2a010b23957e8df22c7f962eef546d3aa21eb463565136a40b691b28ea95f","abstract_canon_sha256":"302d6459ab75a89e20fcb15c3f799dbbbf352ee40628b6fb7b8bf6013388ad17"},"schema_version":"1.0"},"canonical_sha256":"f60f01a3a962e8bd48f5cc40c7e1915aebd4c3a46cb940db5354cd5a73c17953","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:29.092547Z","signature_b64":"2yXF+DVVdSrjz9N7yc8q2brWOaEnp1Xgib0AtAEkrmknz1JBgMY44cOfEqPYt3yHFVLAg+WSL3FrSqmRBoVaAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f60f01a3a962e8bd48f5cc40c7e1915aebd4c3a46cb940db5354cd5a73c17953","last_reissued_at":"2026-05-18T00:00:29.091722Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:29.091722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.07063","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":"2026-05-18T00:00:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g+glutQe4GtQTvjjH03ZLcLos+7JF5BQ2RDZ3cWk4Fxs4npbM8Qmud1avjLn5lEchzYHXzcSf+IRVou87MnIAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:19:04.081446Z"},"content_sha256":"4b4138768eb2c7cd93ed345b208c8d39009bdc840c25eb73261c6768ca81e9b6","schema_version":"1.0","event_id":"sha256:4b4138768eb2c7cd93ed345b208c8d39009bdc840c25eb73261c6768ca81e9b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6YHQDI5JMLUL2SHVZRAMPYMRLL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extreme points in limit sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.GT"],"primary_cat":"math.DS","authors_text":"Alden Walker, Danny Calegari","submitted_at":"2018-11-16T23:33:29Z","abstract_excerpt":"Given an iterated function system of affine dilations with fixed points the vertices of a regular polygon, we characterize which points in the limit set lie on the boundary of its convex hull."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07063","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":"2026-05-18T00:00:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3T8vPKUyBTEEYVE7lPmISzX+A1arOfZz02NnHptovo2g6oTarpfrRiyBDU5NPYxZf3Q3ZLs85PhtOmzR1SV3Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:19:04.082103Z"},"content_sha256":"ff361cc141c018132998efcb8bb3018d70a8bb00573dd9b793405fce0af683ce","schema_version":"1.0","event_id":"sha256:ff361cc141c018132998efcb8bb3018d70a8bb00573dd9b793405fce0af683ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6YHQDI5JMLUL2SHVZRAMPYMRLL/bundle.json","state_url":"https://pith.science/pith/6YHQDI5JMLUL2SHVZRAMPYMRLL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6YHQDI5JMLUL2SHVZRAMPYMRLL/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":"2026-05-27T11:19:04Z","links":{"resolver":"https://pith.science/pith/6YHQDI5JMLUL2SHVZRAMPYMRLL","bundle":"https://pith.science/pith/6YHQDI5JMLUL2SHVZRAMPYMRLL/bundle.json","state":"https://pith.science/pith/6YHQDI5JMLUL2SHVZRAMPYMRLL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6YHQDI5JMLUL2SHVZRAMPYMRLL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6YHQDI5JMLUL2SHVZRAMPYMRLL","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":"302d6459ab75a89e20fcb15c3f799dbbbf352ee40628b6fb7b8bf6013388ad17","cross_cats_sorted":["math.CV","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-16T23:33:29Z","title_canon_sha256":"9df2a010b23957e8df22c7f962eef546d3aa21eb463565136a40b691b28ea95f"},"schema_version":"1.0","source":{"id":"1811.07063","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.07063","created_at":"2026-05-18T00:00:29Z"},{"alias_kind":"arxiv_version","alias_value":"1811.07063v1","created_at":"2026-05-18T00:00:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.07063","created_at":"2026-05-18T00:00:29Z"},{"alias_kind":"pith_short_12","alias_value":"6YHQDI5JMLUL","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6YHQDI5JMLUL2SHV","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6YHQDI5J","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:ff361cc141c018132998efcb8bb3018d70a8bb00573dd9b793405fce0af683ce","target":"graph","created_at":"2026-05-18T00:00:29Z","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":"Given an iterated function system of affine dilations with fixed points the vertices of a regular polygon, we characterize which points in the limit set lie on the boundary of its convex hull.","authors_text":"Alden Walker, Danny Calegari","cross_cats":["math.CV","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-16T23:33:29Z","title":"Extreme points in limit sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07063","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":"sha256:4b4138768eb2c7cd93ed345b208c8d39009bdc840c25eb73261c6768ca81e9b6","target":"record","created_at":"2026-05-18T00:00:29Z","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":"302d6459ab75a89e20fcb15c3f799dbbbf352ee40628b6fb7b8bf6013388ad17","cross_cats_sorted":["math.CV","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-16T23:33:29Z","title_canon_sha256":"9df2a010b23957e8df22c7f962eef546d3aa21eb463565136a40b691b28ea95f"},"schema_version":"1.0","source":{"id":"1811.07063","kind":"arxiv","version":1}},"canonical_sha256":"f60f01a3a962e8bd48f5cc40c7e1915aebd4c3a46cb940db5354cd5a73c17953","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f60f01a3a962e8bd48f5cc40c7e1915aebd4c3a46cb940db5354cd5a73c17953","first_computed_at":"2026-05-18T00:00:29.091722Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:29.091722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2yXF+DVVdSrjz9N7yc8q2brWOaEnp1Xgib0AtAEkrmknz1JBgMY44cOfEqPYt3yHFVLAg+WSL3FrSqmRBoVaAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:29.092547Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.07063","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b4138768eb2c7cd93ed345b208c8d39009bdc840c25eb73261c6768ca81e9b6","sha256:ff361cc141c018132998efcb8bb3018d70a8bb00573dd9b793405fce0af683ce"],"state_sha256":"291429c5b682f3ba325bf5757ae2163f6b212f1940632ed516d7a9adf5fcd0a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YDvjGo1KSKuBmbmmIsJDg3DuFvNsX8Zukmx5o3sKjj65M/t72/8WQyxvbVfB5HxQNLSngVAxnlEGY++UsC5QCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:19:04.085382Z","bundle_sha256":"c5038fc11ff8a4297ed57bdf39684a9720acbf6822a12d5e9350b439643f0df6"}}