{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:5JELCQQHR2EPW2MHAFQRCGEQUG","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":"f411846d5b1c6cb1f9b0874d31b7e203cc84eaf8eff5d860c8751cfd87bc73cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-10T05:10:59Z","title_canon_sha256":"75d13c72f990f62a21c32e812c94b75fad2ef2c03e373007f0ed8357afdb62a4"},"schema_version":"1.0","source":{"id":"2403.06096","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.06096","created_at":"2026-07-05T07:54:18Z"},{"alias_kind":"arxiv_version","alias_value":"2403.06096v1","created_at":"2026-07-05T07:54:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.06096","created_at":"2026-07-05T07:54:18Z"},{"alias_kind":"pith_short_12","alias_value":"5JELCQQHR2EP","created_at":"2026-07-05T07:54:18Z"},{"alias_kind":"pith_short_16","alias_value":"5JELCQQHR2EPW2MH","created_at":"2026-07-05T07:54:18Z"},{"alias_kind":"pith_short_8","alias_value":"5JELCQQH","created_at":"2026-07-05T07:54:18Z"}],"graph_snapshots":[{"event_id":"sha256:f83fa746e1fe73b242e40ba027571e0f782ba2163caff9ab579f1900c524f1eb","target":"graph","created_at":"2026-07-05T07:54:18Z","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/2403.06096/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G=(V(G),E(G))$ be a graph with vertex set $V(G)$ and edge set $E(G)$. The resistance distance $R_G(x,y)$ between two vertices $x,y$ of $G$ is defined to be the effective resistance between the two vertices in the corresponding electrical network in which each edge of $G$ is replaced by a unit resistor. The resistance spectrum $\\mathrm{RS}(G)$ of a graph $G$ is the multiset of the resistance distances of all pairs of vertices in the graph. This paper presents a method for constructing graphs with the same resistance spectrum. It is obtained that for any positive integer $k$, there exist at","authors_text":"Huan Zhou, Si-Ao Xu, Xiang-Feng Pan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-10T05:10:59Z","title":"A method for constructing graphs with the same resistance spectrum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.06096","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:a85d1ef38faa9540c37d49556b6308dc741c141d010a69a0b25a7149c105792c","target":"record","created_at":"2026-07-05T07:54:18Z","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":"f411846d5b1c6cb1f9b0874d31b7e203cc84eaf8eff5d860c8751cfd87bc73cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-10T05:10:59Z","title_canon_sha256":"75d13c72f990f62a21c32e812c94b75fad2ef2c03e373007f0ed8357afdb62a4"},"schema_version":"1.0","source":{"id":"2403.06096","kind":"arxiv","version":1}},"canonical_sha256":"ea48b142078e88fb69870161111890a180a5df637af421d479987f62f1aed208","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea48b142078e88fb69870161111890a180a5df637af421d479987f62f1aed208","first_computed_at":"2026-07-05T07:54:18.057127Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:54:18.057127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"svPnnhNoOCQLU+43tjE+xsvxOT5bksT4ZHcWa8MjrNo9qM3L/m2rBYIeYOtu0DDZdQ1XIOC6A4ylDz2grpNqAg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:54:18.057567Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.06096","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a85d1ef38faa9540c37d49556b6308dc741c141d010a69a0b25a7149c105792c","sha256:f83fa746e1fe73b242e40ba027571e0f782ba2163caff9ab579f1900c524f1eb"],"state_sha256":"820d53eb7aeaee79c50e45dbe012be8b5b993b92dbdca52905fd2ed6c38da493"}