{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:LKCJNQEPSUOEVQVVSQOWENQO3N","short_pith_number":"pith:LKCJNQEP","schema_version":"1.0","canonical_sha256":"5a8496c08f951c4ac2b5941d62360edb6676c3144ac32822554ccc4bf9f9c7fc","source":{"kind":"arxiv","id":"1611.07899","version":2},"attestation_state":"computed","paper":{"title":"Generating Near-Bipartite Bricks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nishad Kothari","submitted_at":"2016-11-23T17:35:28Z","abstract_excerpt":"A $3$-connected graph $G$ is a brick if, for any two vertices $u$ and $v$, the graph $G-\\{u,v\\}$ has a perfect matching. Deleting an edge $e$ from a brick $G$ results in a graph with zero, one or two vertices of degree two. The bicontraction of a vertex of degree two consists of contracting the two edges incident with it; and the retract of $G-e$ is the graph $J$ obtained from it by bicontracting all its vertices of degree two. An edge $e$ is thin if $J$ is also a brick. Carvalho, Lucchesi and Murty [How to build a brick, Discrete Mathematics 306 (2006), 2383-2410] showed that every brick, dis"},"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":"1611.07899","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-23T17:35:28Z","cross_cats_sorted":[],"title_canon_sha256":"9654548b4d6debc97a268f39c32cf3aeb7601927218238a10fa2f94eba822cc8","abstract_canon_sha256":"8222e2d71dfe3e0517b29f71638ef711bda91d49438698eb94ef529149abc51b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:23.903917Z","signature_b64":"9EW+rYjvCrVgGm5hpwcJj3SZuAjm/OtCjhrLtvk+AI999/pfEwjnG4xhrG2QK6DASCZ5sDhGGAYs07y+2LN6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a8496c08f951c4ac2b5941d62360edb6676c3144ac32822554ccc4bf9f9c7fc","last_reissued_at":"2026-05-18T00:08:23.903306Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:23.903306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generating Near-Bipartite Bricks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nishad Kothari","submitted_at":"2016-11-23T17:35:28Z","abstract_excerpt":"A $3$-connected graph $G$ is a brick if, for any two vertices $u$ and $v$, the graph $G-\\{u,v\\}$ has a perfect matching. Deleting an edge $e$ from a brick $G$ results in a graph with zero, one or two vertices of degree two. The bicontraction of a vertex of degree two consists of contracting the two edges incident with it; and the retract of $G-e$ is the graph $J$ obtained from it by bicontracting all its vertices of degree two. An edge $e$ is thin if $J$ is also a brick. Carvalho, Lucchesi and Murty [How to build a brick, Discrete Mathematics 306 (2006), 2383-2410] showed that every brick, dis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07899","kind":"arxiv","version":2},"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":"1611.07899","created_at":"2026-05-18T00:08:23.903405+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.07899v2","created_at":"2026-05-18T00:08:23.903405+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07899","created_at":"2026-05-18T00:08:23.903405+00:00"},{"alias_kind":"pith_short_12","alias_value":"LKCJNQEPSUOE","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"LKCJNQEPSUOEVQVV","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"LKCJNQEP","created_at":"2026-05-18T12:30:29.479603+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/LKCJNQEPSUOEVQVVSQOWENQO3N","json":"https://pith.science/pith/LKCJNQEPSUOEVQVVSQOWENQO3N.json","graph_json":"https://pith.science/api/pith-number/LKCJNQEPSUOEVQVVSQOWENQO3N/graph.json","events_json":"https://pith.science/api/pith-number/LKCJNQEPSUOEVQVVSQOWENQO3N/events.json","paper":"https://pith.science/paper/LKCJNQEP"},"agent_actions":{"view_html":"https://pith.science/pith/LKCJNQEPSUOEVQVVSQOWENQO3N","download_json":"https://pith.science/pith/LKCJNQEPSUOEVQVVSQOWENQO3N.json","view_paper":"https://pith.science/paper/LKCJNQEP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.07899&json=true","fetch_graph":"https://pith.science/api/pith-number/LKCJNQEPSUOEVQVVSQOWENQO3N/graph.json","fetch_events":"https://pith.science/api/pith-number/LKCJNQEPSUOEVQVVSQOWENQO3N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LKCJNQEPSUOEVQVVSQOWENQO3N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LKCJNQEPSUOEVQVVSQOWENQO3N/action/storage_attestation","attest_author":"https://pith.science/pith/LKCJNQEPSUOEVQVVSQOWENQO3N/action/author_attestation","sign_citation":"https://pith.science/pith/LKCJNQEPSUOEVQVVSQOWENQO3N/action/citation_signature","submit_replication":"https://pith.science/pith/LKCJNQEPSUOEVQVVSQOWENQO3N/action/replication_record"}},"created_at":"2026-05-18T00:08:23.903405+00:00","updated_at":"2026-05-18T00:08:23.903405+00:00"}