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We call the graph $G_n$ with vertex set $V(G_n) = \\{ 1, 2, \\ldots, n\\}$ and $\\{i,j\\} \\in E(G_n)$ if and only if $0<|i-j| \\leq 2$ a straight linear 2-tree. We define the graph $H_n$ with $V(H_n)= V(G_n)$ and $E(H_n) = (E(G_n) \\cup \\{k,k+3\\})\\setminus(\\{k+1,k+3\\}$ to be a bent linear 2-tree with bend at vertex $k$."},"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":"1712.05859","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-15T22:11:45Z","cross_cats_sorted":[],"title_canon_sha256":"989636bf3ab9ccb3e2e5f3e00a8b19d975f37bc81494468b56a1996befa8cd67","abstract_canon_sha256":"339eb73a4ca9524539d9473d57358c6027019f6bb2fee7b527f53bb80438fd6b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:51.702803Z","signature_b64":"qOcjgOh/Ncpy6QSVLs8qTJkAwsUFs8Ndei6a76dwU9VrHBjCGdjHhws1d8MZq6QIzgsVDFGJJys1/ZceXoyVAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e90e2cc2d0966396b218789b0cebcbe2319b0349b2783b5ae28294e7889fa90","last_reissued_at":"2026-05-18T00:27:51.702085Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:51.702085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Resistance distance in bent linear 2-trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amanda E. Francis, Emily J. Evans, Wayne Barrett","submitted_at":"2017-12-15T22:11:45Z","abstract_excerpt":"In this note we consider the bent linear 2-tree and provide an explicit formula for the resistance distance $r_{G_n}(1,n)$ between the first and last vertices of the graph. We call the graph $G_n$ with vertex set $V(G_n) = \\{ 1, 2, \\ldots, n\\}$ and $\\{i,j\\} \\in E(G_n)$ if and only if $0<|i-j| \\leq 2$ a straight linear 2-tree. We define the graph $H_n$ with $V(H_n)= V(G_n)$ and $E(H_n) = (E(G_n) \\cup \\{k,k+3\\})\\setminus(\\{k+1,k+3\\}$ to be a bent linear 2-tree with bend at vertex $k$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05859","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":"1712.05859","created_at":"2026-05-18T00:27:51.702201+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.05859v1","created_at":"2026-05-18T00:27:51.702201+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05859","created_at":"2026-05-18T00:27:51.702201+00:00"},{"alias_kind":"pith_short_12","alias_value":"L2IOFTBNBFTD","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"L2IOFTBNBFTDS2ZB","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"L2IOFTBN","created_at":"2026-05-18T12:31:28.150371+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/L2IOFTBNBFTDS2ZBQ6E3BTV4XY","json":"https://pith.science/pith/L2IOFTBNBFTDS2ZBQ6E3BTV4XY.json","graph_json":"https://pith.science/api/pith-number/L2IOFTBNBFTDS2ZBQ6E3BTV4XY/graph.json","events_json":"https://pith.science/api/pith-number/L2IOFTBNBFTDS2ZBQ6E3BTV4XY/events.json","paper":"https://pith.science/paper/L2IOFTBN"},"agent_actions":{"view_html":"https://pith.science/pith/L2IOFTBNBFTDS2ZBQ6E3BTV4XY","download_json":"https://pith.science/pith/L2IOFTBNBFTDS2ZBQ6E3BTV4XY.json","view_paper":"https://pith.science/paper/L2IOFTBN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.05859&json=true","fetch_graph":"https://pith.science/api/pith-number/L2IOFTBNBFTDS2ZBQ6E3BTV4XY/graph.json","fetch_events":"https://pith.science/api/pith-number/L2IOFTBNBFTDS2ZBQ6E3BTV4XY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L2IOFTBNBFTDS2ZBQ6E3BTV4XY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L2IOFTBNBFTDS2ZBQ6E3BTV4XY/action/storage_attestation","attest_author":"https://pith.science/pith/L2IOFTBNBFTDS2ZBQ6E3BTV4XY/action/author_attestation","sign_citation":"https://pith.science/pith/L2IOFTBNBFTDS2ZBQ6E3BTV4XY/action/citation_signature","submit_replication":"https://pith.science/pith/L2IOFTBNBFTDS2ZBQ6E3BTV4XY/action/replication_record"}},"created_at":"2026-05-18T00:27:51.702201+00:00","updated_at":"2026-05-18T00:27:51.702201+00:00"}