{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:45LFEC5REMUXMBE4GFNMEVI4VU","short_pith_number":"pith:45LFEC5R","canonical_record":{"source":{"id":"1610.08786","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-27T14:07:39Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9df00951426b82190f72b42997986a5fb3d8d51db7d94a8c2ada6818800feb0f","abstract_canon_sha256":"9809a6ac9928617e6f80be477262b4e03dce432964f0aa572f0ec33e0722b9d1"},"schema_version":"1.0"},"canonical_sha256":"e756520bb1232976049c315ac2551cad1e5d0f98b66560720cb5b8fb0bca4042","source":{"kind":"arxiv","id":"1610.08786","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08786","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08786v2","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08786","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"pith_short_12","alias_value":"45LFEC5REMUX","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"45LFEC5REMUXMBE4","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"45LFEC5R","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:45LFEC5REMUXMBE4GFNMEVI4VU","target":"record","payload":{"canonical_record":{"source":{"id":"1610.08786","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-27T14:07:39Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9df00951426b82190f72b42997986a5fb3d8d51db7d94a8c2ada6818800feb0f","abstract_canon_sha256":"9809a6ac9928617e6f80be477262b4e03dce432964f0aa572f0ec33e0722b9d1"},"schema_version":"1.0"},"canonical_sha256":"e756520bb1232976049c315ac2551cad1e5d0f98b66560720cb5b8fb0bca4042","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:08.639193Z","signature_b64":"a+YPEAkJVBQZzfXuHkvAKBoD8Ez7k++4F7G+eJ5tM5c5B+tVCfsihgF0WdyxgsJqEK/X91bAVT0Nasww8ns3Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e756520bb1232976049c315ac2551cad1e5d0f98b66560720cb5b8fb0bca4042","last_reissued_at":"2026-05-17T23:52:08.638816Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:08.638816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.08786","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":"2026-05-17T23:52:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dc3bYKW/LksMu3dtAP2fkZSe7ZuIexgs3L4Icbxi5CyNyhsttRQJoZ4o9k3Ul2vl2cLv/0ixwdz/W0Bz9YlRDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:44:37.215974Z"},"content_sha256":"a0030dcbf30581cdc42e2398c25a49d8cd3da7e46784696ca00bcfadf1806c8c","schema_version":"1.0","event_id":"sha256:a0030dcbf30581cdc42e2398c25a49d8cd3da7e46784696ca00bcfadf1806c8c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:45LFEC5REMUXMBE4GFNMEVI4VU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parking on a random tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Christina Goldschmidt, Micha{\\l} Przykucki","submitted_at":"2016-10-27T14:07:39Z","abstract_excerpt":"Consider a uniform random rooted tree on vertices labelled by $[n] = \\{1,2,\\ldots,n\\}$, with edges directed towards the root. We imagine that each node of the tree has space for a single car to park. A number $m \\le n$ of cars arrive one by one, each at a node chosen independently and uniformly at random. If a car arrives at a space which is already occupied, it follows the unique path oriented towards the root until it encounters an empty space, in which case it parks there; if there is no empty space, it leaves the tree. Consider $m =[\\alpha n]$ and let $A_{n,\\alpha}$ denote the event that a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08786","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":"2026-05-17T23:52:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g4yLONQAu2saRD7/eQlC14Z6U5O/0/MaAj6fzjtK0CZR1qruojsKf9PzFYgqIIkcberCFEl+V7k8LwwVkKbaCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:44:37.216638Z"},"content_sha256":"2b7cb6ca48357cb10305bd35cb0bb30d84c5d5110f6196b9ec471d2d8d0cd93a","schema_version":"1.0","event_id":"sha256:2b7cb6ca48357cb10305bd35cb0bb30d84c5d5110f6196b9ec471d2d8d0cd93a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/45LFEC5REMUXMBE4GFNMEVI4VU/bundle.json","state_url":"https://pith.science/pith/45LFEC5REMUXMBE4GFNMEVI4VU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/45LFEC5REMUXMBE4GFNMEVI4VU/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":"2026-05-30T18:44:37Z","links":{"resolver":"https://pith.science/pith/45LFEC5REMUXMBE4GFNMEVI4VU","bundle":"https://pith.science/pith/45LFEC5REMUXMBE4GFNMEVI4VU/bundle.json","state":"https://pith.science/pith/45LFEC5REMUXMBE4GFNMEVI4VU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/45LFEC5REMUXMBE4GFNMEVI4VU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:45LFEC5REMUXMBE4GFNMEVI4VU","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":"9809a6ac9928617e6f80be477262b4e03dce432964f0aa572f0ec33e0722b9d1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-27T14:07:39Z","title_canon_sha256":"9df00951426b82190f72b42997986a5fb3d8d51db7d94a8c2ada6818800feb0f"},"schema_version":"1.0","source":{"id":"1610.08786","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08786","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08786v2","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08786","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"pith_short_12","alias_value":"45LFEC5REMUX","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"45LFEC5REMUXMBE4","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"45LFEC5R","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:2b7cb6ca48357cb10305bd35cb0bb30d84c5d5110f6196b9ec471d2d8d0cd93a","target":"graph","created_at":"2026-05-17T23:52:08Z","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":"Consider a uniform random rooted tree on vertices labelled by $[n] = \\{1,2,\\ldots,n\\}$, with edges directed towards the root. We imagine that each node of the tree has space for a single car to park. A number $m \\le n$ of cars arrive one by one, each at a node chosen independently and uniformly at random. If a car arrives at a space which is already occupied, it follows the unique path oriented towards the root until it encounters an empty space, in which case it parks there; if there is no empty space, it leaves the tree. Consider $m =[\\alpha n]$ and let $A_{n,\\alpha}$ denote the event that a","authors_text":"Christina Goldschmidt, Micha{\\l} Przykucki","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-27T14:07:39Z","title":"Parking on a random tree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08786","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:a0030dcbf30581cdc42e2398c25a49d8cd3da7e46784696ca00bcfadf1806c8c","target":"record","created_at":"2026-05-17T23:52:08Z","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":"9809a6ac9928617e6f80be477262b4e03dce432964f0aa572f0ec33e0722b9d1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-27T14:07:39Z","title_canon_sha256":"9df00951426b82190f72b42997986a5fb3d8d51db7d94a8c2ada6818800feb0f"},"schema_version":"1.0","source":{"id":"1610.08786","kind":"arxiv","version":2}},"canonical_sha256":"e756520bb1232976049c315ac2551cad1e5d0f98b66560720cb5b8fb0bca4042","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e756520bb1232976049c315ac2551cad1e5d0f98b66560720cb5b8fb0bca4042","first_computed_at":"2026-05-17T23:52:08.638816Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:08.638816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a+YPEAkJVBQZzfXuHkvAKBoD8Ez7k++4F7G+eJ5tM5c5B+tVCfsihgF0WdyxgsJqEK/X91bAVT0Nasww8ns3Dw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:08.639193Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.08786","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0030dcbf30581cdc42e2398c25a49d8cd3da7e46784696ca00bcfadf1806c8c","sha256:2b7cb6ca48357cb10305bd35cb0bb30d84c5d5110f6196b9ec471d2d8d0cd93a"],"state_sha256":"beeb74995a7b1597e5c90c279c6aa5d083add00eb9b569bfb181b434a7803488"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y5zsAh+wbdPni8G2tM1g9EbNf5U2aYFcan5+nvbz9k/624Is/s5zagTkx3XSBrbkE7ff+FbHADBRawL97HHJDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T18:44:37.220133Z","bundle_sha256":"be21f2252edb9060d16c9ef9735fdf25eea200b8ecdde9dbe4d643f372b7a8a8"}}