{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:AFLS57KDW6OKMT2VOO2S65VUA7","short_pith_number":"pith:AFLS57KD","schema_version":"1.0","canonical_sha256":"01572efd43b79ca64f5573b52f76b407d8b0a7135f7601936c094fedb2d71d7b","source":{"kind":"arxiv","id":"1701.02527","version":1},"attestation_state":"computed","paper":{"title":"The heavy path approach to Galton-Watson trees with an application to Apollonian networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"math.PR","authors_text":"Cecilia Holmgren, Henning Sulzbach, Luc Devroye","submitted_at":"2017-01-10T11:46:38Z","abstract_excerpt":"We study the heavy path decomposition of conditional Galton-Watson trees. In a standard Galton-Watson tree conditional on its size $n$, we order all children by their subtree sizes, from large (heavy) to small. A node is marked if it is among the $k$ heaviest nodes among its siblings. Unmarked nodes and their subtrees are removed, leaving only a tree of marked nodes, which we call the $k$-heavy tree. We study various properties of these trees, including their size and the maximal distance from any original node to the $k$-heavy tree. In particular, under some moment condition, the $2$-heavy tr"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1701.02527","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-10T11:46:38Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"845989bd5b5666606fc4d4d37e04ccb060fd4a4060d1b65346eabbc714fd6f60","abstract_canon_sha256":"5bfa0c2aeb2199cd795c274971f7f70eb0d961c9196ca1c1727f15c873ab124e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:04.061348Z","signature_b64":"iNW5pwAANC/3D7+XS8BbdBol26f5l5PY72vw3sEwUOOmfHlaYUFj6x5R2bpzropTZ7YjPB7pP0/bjPQgUarDBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01572efd43b79ca64f5573b52f76b407d8b0a7135f7601936c094fedb2d71d7b","last_reissued_at":"2026-05-18T00:53:04.060832Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:04.060832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The heavy path approach to Galton-Watson trees with an application to Apollonian networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"math.PR","authors_text":"Cecilia Holmgren, Henning Sulzbach, Luc Devroye","submitted_at":"2017-01-10T11:46:38Z","abstract_excerpt":"We study the heavy path decomposition of conditional Galton-Watson trees. In a standard Galton-Watson tree conditional on its size $n$, we order all children by their subtree sizes, from large (heavy) to small. A node is marked if it is among the $k$ heaviest nodes among its siblings. Unmarked nodes and their subtrees are removed, leaving only a tree of marked nodes, which we call the $k$-heavy tree. We study various properties of these trees, including their size and the maximal distance from any original node to the $k$-heavy tree. In particular, under some moment condition, the $2$-heavy tr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02527","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1701.02527","created_at":"2026-05-18T00:53:04.060913+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.02527v1","created_at":"2026-05-18T00:53:04.060913+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02527","created_at":"2026-05-18T00:53:04.060913+00:00"},{"alias_kind":"pith_short_12","alias_value":"AFLS57KDW6OK","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"AFLS57KDW6OKMT2V","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"AFLS57KD","created_at":"2026-05-18T12:31:05.417338+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AFLS57KDW6OKMT2VOO2S65VUA7","json":"https://pith.science/pith/AFLS57KDW6OKMT2VOO2S65VUA7.json","graph_json":"https://pith.science/api/pith-number/AFLS57KDW6OKMT2VOO2S65VUA7/graph.json","events_json":"https://pith.science/api/pith-number/AFLS57KDW6OKMT2VOO2S65VUA7/events.json","paper":"https://pith.science/paper/AFLS57KD"},"agent_actions":{"view_html":"https://pith.science/pith/AFLS57KDW6OKMT2VOO2S65VUA7","download_json":"https://pith.science/pith/AFLS57KDW6OKMT2VOO2S65VUA7.json","view_paper":"https://pith.science/paper/AFLS57KD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.02527&json=true","fetch_graph":"https://pith.science/api/pith-number/AFLS57KDW6OKMT2VOO2S65VUA7/graph.json","fetch_events":"https://pith.science/api/pith-number/AFLS57KDW6OKMT2VOO2S65VUA7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AFLS57KDW6OKMT2VOO2S65VUA7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AFLS57KDW6OKMT2VOO2S65VUA7/action/storage_attestation","attest_author":"https://pith.science/pith/AFLS57KDW6OKMT2VOO2S65VUA7/action/author_attestation","sign_citation":"https://pith.science/pith/AFLS57KDW6OKMT2VOO2S65VUA7/action/citation_signature","submit_replication":"https://pith.science/pith/AFLS57KDW6OKMT2VOO2S65VUA7/action/replication_record"}},"created_at":"2026-05-18T00:53:04.060913+00:00","updated_at":"2026-05-18T00:53:04.060913+00:00"}