{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:EAWTA22ZPS4VPGLS53LEH23BBR","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":"5c0bbb7dee20e3d70e0b8078f86c8d852b6ffd27f50f09f13631ec2bb767498e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-05-03T12:32:55Z","title_canon_sha256":"e284de8154369574585896bdd672c4ee2e5aa5d58998274d781f7863d34999d5"},"schema_version":"1.0","source":{"id":"1105.0565","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.0565","created_at":"2026-05-18T04:08:12Z"},{"alias_kind":"arxiv_version","alias_value":"1105.0565v2","created_at":"2026-05-18T04:08:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.0565","created_at":"2026-05-18T04:08:12Z"},{"alias_kind":"pith_short_12","alias_value":"EAWTA22ZPS4V","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"EAWTA22ZPS4VPGLS","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"EAWTA22Z","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:05ff62670c3099c6dcdc4dd8f074399cca35b209f749d05780783d8b2f7f7cdb","target":"graph","created_at":"2026-05-18T04:08:12Z","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":"Spanning trees are relevant to various aspects of networks. Generally, the number of spanning trees in a network can be obtained by computing a related determinant of the Laplacian matrix of the network. However, for a large generic network, evaluating the relevant determinant is computationally intractable. In this paper, we develop a fairly generic technique for computing determinants corresponding to self-similar networks, thereby providing a method to determine the numbers of spanning trees in networks exhibiting self-similarity. We describe the computation process with a family of network","authors_text":"Bin Wu, Guanrong Chen, Yuan Lin, Zhongzhi Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-05-03T12:32:55Z","title":"Counting spanning trees in self-similar networks by evaluating determinants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0565","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":"sha256:071eacbf3c0d7aa0ff6bb851cda010e3def28b15db33e2e93204fb11312ac3fd","target":"record","created_at":"2026-05-18T04:08:12Z","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":"5c0bbb7dee20e3d70e0b8078f86c8d852b6ffd27f50f09f13631ec2bb767498e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-05-03T12:32:55Z","title_canon_sha256":"e284de8154369574585896bdd672c4ee2e5aa5d58998274d781f7863d34999d5"},"schema_version":"1.0","source":{"id":"1105.0565","kind":"arxiv","version":2}},"canonical_sha256":"202d306b597cb9579972eed643eb610c7a3c0249ed4063a7ad50f391489dec01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"202d306b597cb9579972eed643eb610c7a3c0249ed4063a7ad50f391489dec01","first_computed_at":"2026-05-18T04:08:12.464122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:12.464122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nVKauShphaZfwgOmV+fL9lcPb2oDmZlVn/FLsKDEkv3lI0JAT8k3sbgKHIvdenFYDHuHJkkvtqqRj1FS79orAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:12.464652Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.0565","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:071eacbf3c0d7aa0ff6bb851cda010e3def28b15db33e2e93204fb11312ac3fd","sha256:05ff62670c3099c6dcdc4dd8f074399cca35b209f749d05780783d8b2f7f7cdb"],"state_sha256":"a14ced76a3511eae5dc272968eb71e2dcaf1c23b71aa47ffb39f49d1c7c5fb17"}