{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4MNJOTK7WUBZYTB43KKRPVPMLT","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":"a810e4316f7726d2c2dd1e69f776ffcd04a1fe6dfe3179e8e3408eaf738151e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-19T11:44:38Z","title_canon_sha256":"ade7283a83bc2d4d8b62805d0eb8d54051e55d4f150d467e3ead69b547087ac2"},"schema_version":"1.0","source":{"id":"2605.19707","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.19707","created_at":"2026-05-20T01:05:58Z"},{"alias_kind":"arxiv_version","alias_value":"2605.19707v1","created_at":"2026-05-20T01:05:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19707","created_at":"2026-05-20T01:05:58Z"},{"alias_kind":"pith_short_12","alias_value":"4MNJOTK7WUBZ","created_at":"2026-05-20T01:05:58Z"},{"alias_kind":"pith_short_16","alias_value":"4MNJOTK7WUBZYTB4","created_at":"2026-05-20T01:05:58Z"},{"alias_kind":"pith_short_8","alias_value":"4MNJOTK7","created_at":"2026-05-20T01:05:58Z"}],"graph_snapshots":[{"event_id":"sha256:eefc77e80fb6544c44628a7a8827b0e059b9c24e5e00e34a1d8705d03e16af07","target":"graph","created_at":"2026-05-20T01:05:58Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.19707/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $F(G)$ be the number of spanning forests in a graph $G$ and $\\mathcal{C}(n,d)$ be the set of all connected $d$-regular simple graphs of order $n$. Define $\\widehat{f}_{d}=\\liminf_{n\\rightarrow \\infty}\\{F(G)^{1/n}:G\\in \\mathcal{C}(n,d)\\}$. Let $n_i$ be the number of vertices of degree $i$ in $G$. In this paper we give two lower bounds for $F(G)$ in terms of $n_i$ in connected graphs whose vertex degrees belong to $\\{2,3\\}$ and $\\{2,3,4\\}$, respectively. Furthermore, we determine the exact values of $\\widehat{f}_3$ and $\\widehat{f}_4$.","authors_text":"Kexiang Xu, Shaohan Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-19T11:44:38Z","title":"On asymptotic values for the minimum number of spanning forests in simple regular graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19707","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":"sha256:7ce5e4ce535a5bcc611029309d3c36467d58ad5d315fafd1ac68393d11dde5cc","target":"record","created_at":"2026-05-20T01:05:58Z","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":"a810e4316f7726d2c2dd1e69f776ffcd04a1fe6dfe3179e8e3408eaf738151e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-19T11:44:38Z","title_canon_sha256":"ade7283a83bc2d4d8b62805d0eb8d54051e55d4f150d467e3ead69b547087ac2"},"schema_version":"1.0","source":{"id":"2605.19707","kind":"arxiv","version":1}},"canonical_sha256":"e31a974d5fb5039c4c3cda9517d5ec5cfd8ff6ed17724816ca86302c1d352c0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e31a974d5fb5039c4c3cda9517d5ec5cfd8ff6ed17724816ca86302c1d352c0a","first_computed_at":"2026-05-20T01:05:58.586988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T01:05:58.586988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UeGjKyTvPYaK/7qCT8JOkT/6lu8ObeFe4nuYfFO+NED1XfdL0hR9mkykD/jYFnMMjgyp0oHNCu2nKNDcTZLQAA==","signature_status":"signed_v1","signed_at":"2026-05-20T01:05:58.587593Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.19707","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ce5e4ce535a5bcc611029309d3c36467d58ad5d315fafd1ac68393d11dde5cc","sha256:eefc77e80fb6544c44628a7a8827b0e059b9c24e5e00e34a1d8705d03e16af07"],"state_sha256":"fbdd9c85c5693d01f693d9ef5308ffd07b73186f9099d2539623e69cd45c9f47"}