{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:WPG3ULP5PO4IHELBWT42CS2RYF","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":"50c7fd9406f02dbf98ab98dd2ba131dec1be6a41d3a5de879d37b739f0324d48","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-06-04T06:38:02Z","title_canon_sha256":"e1beed86a7e85550c5f51379eca9def449c41e8deb8c79565926cd59d4c50efa"},"schema_version":"1.0","source":{"id":"0806.0701","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.0701","created_at":"2026-05-18T03:05:07Z"},{"alias_kind":"arxiv_version","alias_value":"0806.0701v1","created_at":"2026-05-18T03:05:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.0701","created_at":"2026-05-18T03:05:07Z"},{"alias_kind":"pith_short_12","alias_value":"WPG3ULP5PO4I","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"WPG3ULP5PO4IHELB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"WPG3ULP5","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:5cc603c1070002401bf37cdcb9b9a21268d03b249e34c600da95a95daf13f852","target":"graph","created_at":"2026-05-18T03:05:07Z","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":"We study the number of connected spanning subgraphs $f_{d,b}(n)$ on the generalized Sierpinski gasket $SG_{d,b}(n)$ at stage $n$ with dimension $d$ equal to two, three and four for $b=2$, and layer $b$ equal to three and four for $d=2$. The upper and lower bounds for the asymptotic growth constant, defined as $z_{SG_{d,b}}=\\lim_{v \\to \\infty} \\ln f_{d,b}(n)/v$ where $v$ is the number of vertices, on $SG_{2,b}(n)$ with $b=2,3,4$ are derived in terms of the results at a certain stage. The numerical values of $z_{SG_{d,b}}$ are obtained.","authors_text":"Lung-Chi Chen, Shu-Chiuan Chang","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-06-04T06:38:02Z","title":"Number of connected spanning subgraphs on the Sierpinski gasket"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.0701","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":"sha256:6627250a3eded08eed852d4163230b9071d3b6212ca7f5faec0222a52eb2a90d","target":"record","created_at":"2026-05-18T03:05:07Z","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":"50c7fd9406f02dbf98ab98dd2ba131dec1be6a41d3a5de879d37b739f0324d48","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-06-04T06:38:02Z","title_canon_sha256":"e1beed86a7e85550c5f51379eca9def449c41e8deb8c79565926cd59d4c50efa"},"schema_version":"1.0","source":{"id":"0806.0701","kind":"arxiv","version":1}},"canonical_sha256":"b3cdba2dfd7bb8839161b4f9a14b51c147167d51f374c1eb3bbe5fed521edca4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3cdba2dfd7bb8839161b4f9a14b51c147167d51f374c1eb3bbe5fed521edca4","first_computed_at":"2026-05-18T03:05:07.962899Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:07.962899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ClE4camaYRz3zPOb5co+00GyOHiY9CeQFgfPGrlHdYxSrV9cb8Uwd4iBPwLWQYm890Zxk5WnSvsf1EtXGBfvAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:07.963473Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.0701","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6627250a3eded08eed852d4163230b9071d3b6212ca7f5faec0222a52eb2a90d","sha256:5cc603c1070002401bf37cdcb9b9a21268d03b249e34c600da95a95daf13f852"],"state_sha256":"6f069febba21f087ca13bff92c15c566f9dc78e768d961163a7d4a215d22b087"}