{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HKUNPOI7FTWUYCJIFZLMFSHJ3F","short_pith_number":"pith:HKUNPOI7","canonical_record":{"source":{"id":"1801.01816","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-05T16:14:27Z","cross_cats_sorted":[],"title_canon_sha256":"5370e47107454e4efbf5d29e83131da8281bfdf0f36d819e79a3665800cfdd12","abstract_canon_sha256":"587bac936d4c772f2b1b77db4f668afbe435b1b0a2e451677a025b81d54c3eff"},"schema_version":"1.0"},"canonical_sha256":"3aa8d7b91f2ced4c09282e56c2c8e9d95897c6e480b4fb4d544bc16d6289de44","source":{"kind":"arxiv","id":"1801.01816","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.01816","created_at":"2026-05-18T00:26:40Z"},{"alias_kind":"arxiv_version","alias_value":"1801.01816v1","created_at":"2026-05-18T00:26:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.01816","created_at":"2026-05-18T00:26:40Z"},{"alias_kind":"pith_short_12","alias_value":"HKUNPOI7FTWU","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HKUNPOI7FTWUYCJI","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HKUNPOI7","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HKUNPOI7FTWUYCJIFZLMFSHJ3F","target":"record","payload":{"canonical_record":{"source":{"id":"1801.01816","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-05T16:14:27Z","cross_cats_sorted":[],"title_canon_sha256":"5370e47107454e4efbf5d29e83131da8281bfdf0f36d819e79a3665800cfdd12","abstract_canon_sha256":"587bac936d4c772f2b1b77db4f668afbe435b1b0a2e451677a025b81d54c3eff"},"schema_version":"1.0"},"canonical_sha256":"3aa8d7b91f2ced4c09282e56c2c8e9d95897c6e480b4fb4d544bc16d6289de44","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:40.904761Z","signature_b64":"FqoXT+/NqJoduO30mVeR09R7KFAe/vLhW280kUKWRoARDwEDw50n06ySyYQh2H8TdHTOTsoMf+JbI0P+UKOZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3aa8d7b91f2ced4c09282e56c2c8e9d95897c6e480b4fb4d544bc16d6289de44","last_reissued_at":"2026-05-18T00:26:40.904263Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:40.904263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.01816","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":"2026-05-18T00:26:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wZvLUWz7vaWbjorfsBi08/IGiXEclw8sR42tN1YDNLiK/Kcev/hZTpwLrWSRaQo/FcyMOjnStXrvvQ53dO3KBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:19:50.239097Z"},"content_sha256":"fdd4748d56d9bbbcfa4ee9085513c496d4ecaaa2f565dd2f673495c3d258739c","schema_version":"1.0","event_id":"sha256:fdd4748d56d9bbbcfa4ee9085513c496d4ecaaa2f565dd2f673495c3d258739c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HKUNPOI7FTWUYCJIFZLMFSHJ3F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finding the seed of uniform attachment trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alan S. Pereira, Gabor Lugosi","submitted_at":"2018-01-05T16:14:27Z","abstract_excerpt":"A uniform attachment tree is a random tree that is generated dynamically. Starting from a fixed \"seed\" tree, vertices are added sequentially by attaching each vertex to an existing vertex chosen uniformly at random. Upon observing a large (unlabeled) tree, one wishes to find the initial seed. We investigate to what extent seed trees can be recovered, at least partially. We consider three types of seeds: a path, a star, and a random uniform attachment tree. We propose and analyze seed-finding algorithms for all three types of seed trees."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01816","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":"2026-05-18T00:26:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"twf42ImUx0ARDrC//ofEDJuaHNp63HAzt9FrZThuQr9T54uDz0jKko9Qbl4vu1BgsYSiH3Xw2VSNLk2dEP/ODQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:19:50.239466Z"},"content_sha256":"90c9b60caab489b93255eba0c4f8d23209787299cc47bbfe503963cd26b7e32e","schema_version":"1.0","event_id":"sha256:90c9b60caab489b93255eba0c4f8d23209787299cc47bbfe503963cd26b7e32e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HKUNPOI7FTWUYCJIFZLMFSHJ3F/bundle.json","state_url":"https://pith.science/pith/HKUNPOI7FTWUYCJIFZLMFSHJ3F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HKUNPOI7FTWUYCJIFZLMFSHJ3F/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":"2026-06-04T06:19:50Z","links":{"resolver":"https://pith.science/pith/HKUNPOI7FTWUYCJIFZLMFSHJ3F","bundle":"https://pith.science/pith/HKUNPOI7FTWUYCJIFZLMFSHJ3F/bundle.json","state":"https://pith.science/pith/HKUNPOI7FTWUYCJIFZLMFSHJ3F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HKUNPOI7FTWUYCJIFZLMFSHJ3F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HKUNPOI7FTWUYCJIFZLMFSHJ3F","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":"587bac936d4c772f2b1b77db4f668afbe435b1b0a2e451677a025b81d54c3eff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-05T16:14:27Z","title_canon_sha256":"5370e47107454e4efbf5d29e83131da8281bfdf0f36d819e79a3665800cfdd12"},"schema_version":"1.0","source":{"id":"1801.01816","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.01816","created_at":"2026-05-18T00:26:40Z"},{"alias_kind":"arxiv_version","alias_value":"1801.01816v1","created_at":"2026-05-18T00:26:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.01816","created_at":"2026-05-18T00:26:40Z"},{"alias_kind":"pith_short_12","alias_value":"HKUNPOI7FTWU","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HKUNPOI7FTWUYCJI","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HKUNPOI7","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:90c9b60caab489b93255eba0c4f8d23209787299cc47bbfe503963cd26b7e32e","target":"graph","created_at":"2026-05-18T00:26:40Z","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 uniform attachment tree is a random tree that is generated dynamically. Starting from a fixed \"seed\" tree, vertices are added sequentially by attaching each vertex to an existing vertex chosen uniformly at random. Upon observing a large (unlabeled) tree, one wishes to find the initial seed. We investigate to what extent seed trees can be recovered, at least partially. We consider three types of seeds: a path, a star, and a random uniform attachment tree. We propose and analyze seed-finding algorithms for all three types of seed trees.","authors_text":"Alan S. Pereira, Gabor Lugosi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-05T16:14:27Z","title":"Finding the seed of uniform attachment trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01816","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:fdd4748d56d9bbbcfa4ee9085513c496d4ecaaa2f565dd2f673495c3d258739c","target":"record","created_at":"2026-05-18T00:26:40Z","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":"587bac936d4c772f2b1b77db4f668afbe435b1b0a2e451677a025b81d54c3eff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-05T16:14:27Z","title_canon_sha256":"5370e47107454e4efbf5d29e83131da8281bfdf0f36d819e79a3665800cfdd12"},"schema_version":"1.0","source":{"id":"1801.01816","kind":"arxiv","version":1}},"canonical_sha256":"3aa8d7b91f2ced4c09282e56c2c8e9d95897c6e480b4fb4d544bc16d6289de44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3aa8d7b91f2ced4c09282e56c2c8e9d95897c6e480b4fb4d544bc16d6289de44","first_computed_at":"2026-05-18T00:26:40.904263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:40.904263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FqoXT+/NqJoduO30mVeR09R7KFAe/vLhW280kUKWRoARDwEDw50n06ySyYQh2H8TdHTOTsoMf+JbI0P+UKOZDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:40.904761Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.01816","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fdd4748d56d9bbbcfa4ee9085513c496d4ecaaa2f565dd2f673495c3d258739c","sha256:90c9b60caab489b93255eba0c4f8d23209787299cc47bbfe503963cd26b7e32e"],"state_sha256":"5d5402c99418bba8f71ac5cf1ad4d4609626e0fd04813b027926d3315ad89fa4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Fq7BgU5iHdsXBzAJp24Mg5rs5ZIWTCROpizXb6bSNgw5lqW2dftax0XwsKjxLDpFarDqn/R6P8pRQWsUHH3AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T06:19:50.241441Z","bundle_sha256":"47f343f91b13c65511e97bf72b0f427faddaddfa8056c8d619e891a870d231fd"}}