{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:3JIQZJEDDPXPJFNF7F4Y4BFOSE","short_pith_number":"pith:3JIQZJED","schema_version":"1.0","canonical_sha256":"da510ca4831beef495a5f9798e04ae913372847589f7f666b6e84ac4b45771bd","source":{"kind":"arxiv","id":"1007.0021","version":1},"attestation_state":"computed","paper":{"title":"Weighted spanning trees on some self-similar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Alfredo Donno, Daniele D'Angeli","submitted_at":"2010-06-30T20:27:36Z","abstract_excerpt":"We compute the complexity of two infinite families of finite graphs: the Sierpi\\'{n}ski graphs, which are finite approximations of the well-known Sierpi\\'nsky gasket, and the Schreier graphs of the Hanoi Towers group $H^{(3)}$ acting on the rooted ternary tree. For both of them, we study the weighted generating functions of the spanning trees, associated with several natural labellings of the edge sets."},"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":"1007.0021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-06-30T20:27:36Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"8d5a190cada50bdf3d7483b9e7a557fadbe6d554bced46a52dd554f59d4a1b8e","abstract_canon_sha256":"9b905bd403cb31b8de6587bc025bf29c4174d780c56be3353b453e1a9f23e760"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:54.221140Z","signature_b64":"SUNNNtsuWBuH0ZIcpDUeif5Ft6AONk/YSa47saep4EhgiUB8BpTw2UN4RXHPpMeu5tjm/ih4Iz8VLnuZtanfCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da510ca4831beef495a5f9798e04ae913372847589f7f666b6e84ac4b45771bd","last_reissued_at":"2026-05-18T01:20:54.220664Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:54.220664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weighted spanning trees on some self-similar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Alfredo Donno, Daniele D'Angeli","submitted_at":"2010-06-30T20:27:36Z","abstract_excerpt":"We compute the complexity of two infinite families of finite graphs: the Sierpi\\'{n}ski graphs, which are finite approximations of the well-known Sierpi\\'nsky gasket, and the Schreier graphs of the Hanoi Towers group $H^{(3)}$ acting on the rooted ternary tree. For both of them, we study the weighted generating functions of the spanning trees, associated with several natural labellings of the edge sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0021","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":"1007.0021","created_at":"2026-05-18T01:20:54.220741+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.0021v1","created_at":"2026-05-18T01:20:54.220741+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0021","created_at":"2026-05-18T01:20:54.220741+00:00"},{"alias_kind":"pith_short_12","alias_value":"3JIQZJEDDPXP","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"3JIQZJEDDPXPJFNF","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"3JIQZJED","created_at":"2026-05-18T12:26:03.138858+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/3JIQZJEDDPXPJFNF7F4Y4BFOSE","json":"https://pith.science/pith/3JIQZJEDDPXPJFNF7F4Y4BFOSE.json","graph_json":"https://pith.science/api/pith-number/3JIQZJEDDPXPJFNF7F4Y4BFOSE/graph.json","events_json":"https://pith.science/api/pith-number/3JIQZJEDDPXPJFNF7F4Y4BFOSE/events.json","paper":"https://pith.science/paper/3JIQZJED"},"agent_actions":{"view_html":"https://pith.science/pith/3JIQZJEDDPXPJFNF7F4Y4BFOSE","download_json":"https://pith.science/pith/3JIQZJEDDPXPJFNF7F4Y4BFOSE.json","view_paper":"https://pith.science/paper/3JIQZJED","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.0021&json=true","fetch_graph":"https://pith.science/api/pith-number/3JIQZJEDDPXPJFNF7F4Y4BFOSE/graph.json","fetch_events":"https://pith.science/api/pith-number/3JIQZJEDDPXPJFNF7F4Y4BFOSE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3JIQZJEDDPXPJFNF7F4Y4BFOSE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3JIQZJEDDPXPJFNF7F4Y4BFOSE/action/storage_attestation","attest_author":"https://pith.science/pith/3JIQZJEDDPXPJFNF7F4Y4BFOSE/action/author_attestation","sign_citation":"https://pith.science/pith/3JIQZJEDDPXPJFNF7F4Y4BFOSE/action/citation_signature","submit_replication":"https://pith.science/pith/3JIQZJEDDPXPJFNF7F4Y4BFOSE/action/replication_record"}},"created_at":"2026-05-18T01:20:54.220741+00:00","updated_at":"2026-05-18T01:20:54.220741+00:00"}