{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VVXFZXCUYALE3IUAY4FGWJRKN2","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":"67a78568c6af417eadce91136c3bbfdae81954966775947ca1b242970fd1f167","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-01T08:32:21Z","title_canon_sha256":"2477718476b2887fb28079b6531f2850662248e746af292f4028a7c574d58fa1"},"schema_version":"1.0","source":{"id":"2607.00608","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.00608","created_at":"2026-07-02T01:17:49Z"},{"alias_kind":"arxiv_version","alias_value":"2607.00608v1","created_at":"2026-07-02T01:17:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00608","created_at":"2026-07-02T01:17:49Z"},{"alias_kind":"pith_short_12","alias_value":"VVXFZXCUYALE","created_at":"2026-07-02T01:17:49Z"},{"alias_kind":"pith_short_16","alias_value":"VVXFZXCUYALE3IUA","created_at":"2026-07-02T01:17:49Z"},{"alias_kind":"pith_short_8","alias_value":"VVXFZXCU","created_at":"2026-07-02T01:17:49Z"}],"graph_snapshots":[{"event_id":"sha256:f402369645127193d06a408143a38118380cdedf845c4c60ffbe5214539b2482","target":"graph","created_at":"2026-07-02T01:17:49Z","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/2607.00608/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A connected graph is matching covered if it has at least one edge and every edge lies in some perfect matching.Lov\\'asz proved that every matching covered graph G can be uniquely decomposed into a list of bricks and braces up to multiple edges. Denote by b(G) the number of bricks in such a decomposition. An edge e of G is removable if G-e is also matching covered; is b-invariant if e is removable and b(G-e)=b(G). Furthermore, an edge e of G is a forcing edge if it lies in precisely one perfect matching of G. Lucchesi and Murty proposed the problem of characterizing bricks, distinct from K_4, \\","authors_text":"Fuliang Lu, Yaxian Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-01T08:32:21Z","title":"Near-bipartite bricks in which every b-invariant edge is a forcing edge"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00608","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":"sha256:6b69e6276b321a2a761bd562fadbf0f773dee5888715f34ab78a0aea173771b7","target":"record","created_at":"2026-07-02T01:17:49Z","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":"67a78568c6af417eadce91136c3bbfdae81954966775947ca1b242970fd1f167","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-01T08:32:21Z","title_canon_sha256":"2477718476b2887fb28079b6531f2850662248e746af292f4028a7c574d58fa1"},"schema_version":"1.0","source":{"id":"2607.00608","kind":"arxiv","version":1}},"canonical_sha256":"ad6e5cdc54c0164da280c70a6b262a6ea68183103a2ee226984ff64dd88bd9ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad6e5cdc54c0164da280c70a6b262a6ea68183103a2ee226984ff64dd88bd9ac","first_computed_at":"2026-07-02T01:17:49.036500Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T01:17:49.036500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XTwU1ttxaTnp2MXgjsoJQ7vcSIbf5GtsXSm3+or3VgbWKa8AqpkZJFssYPETA4vsj69JQW2NdQ+62ODU22PZCA==","signature_status":"signed_v1","signed_at":"2026-07-02T01:17:49.036894Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.00608","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b69e6276b321a2a761bd562fadbf0f773dee5888715f34ab78a0aea173771b7","sha256:f402369645127193d06a408143a38118380cdedf845c4c60ffbe5214539b2482"],"state_sha256":"6ba6aa263af8398cd71a14f27dcd06368a558016886f58a3bbff301707a2e9c4"}