{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MXO5ZIKHBZZ4Y3SXQYMJHDFZSO","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":"f231cfced9c8c7a1614500f58d6f04c10dab5569137b2ed5116477fc37d7f3b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-14T09:51:16Z","title_canon_sha256":"e74f33b321d4c462d135cfd736751028ca313c4ca05878de6f27dab0018b5b6e"},"schema_version":"1.0","source":{"id":"1308.3074","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.3074","created_at":"2026-05-18T03:15:56Z"},{"alias_kind":"arxiv_version","alias_value":"1308.3074v1","created_at":"2026-05-18T03:15:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3074","created_at":"2026-05-18T03:15:56Z"},{"alias_kind":"pith_short_12","alias_value":"MXO5ZIKHBZZ4","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MXO5ZIKHBZZ4Y3SX","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MXO5ZIKH","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:e2a51a6c2af9680dfeacf5925daa1b7692ada060b8261cb9186f87eeab05ca48","target":"graph","created_at":"2026-05-18T03:15:56Z","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"},"paper":{"abstract_excerpt":"Given a graph $G=(V,E)$, a subset $X$ of $V$ is an interval of $G$ provided that for any $a, b\\in X$ and $ x\\in V \\setminus X$, $\\{a,x\\}\\in E$ if and only if $\\{b,x\\}\\in E$. For example, $\\emptyset$, $\\{x\\}(x\\in V)$ and $V$ are intervals of $G$, called trivial intervals. A graph whose intervals are trivial is indecomposable; otherwise, it is decomposable. According to Ille, the indecomposability graph of an undirected indecomposable graph $G$ is the graph $\\mathbb I(G)$ whose vertices are those of $G$ and edges are the unordered pairs of distinct vertices $\\{x,y\\}$ such that the induced subgra","authors_text":"Imed Boudabbous, Rim Ben Hamadou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-14T09:51:16Z","title":"Graphs whose indecomposability graph is 2-covered"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3074","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":"sha256:89d5442e21d30f3c4397e4aed2b8697d93f4963ac0deeecd74bf5ec9e6dc8e2f","target":"record","created_at":"2026-05-18T03:15:56Z","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":"f231cfced9c8c7a1614500f58d6f04c10dab5569137b2ed5116477fc37d7f3b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-14T09:51:16Z","title_canon_sha256":"e74f33b321d4c462d135cfd736751028ca313c4ca05878de6f27dab0018b5b6e"},"schema_version":"1.0","source":{"id":"1308.3074","kind":"arxiv","version":1}},"canonical_sha256":"65dddca1470e73cc6e578618938cb993965df609ac0e90ad87d3ac4ed08222c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65dddca1470e73cc6e578618938cb993965df609ac0e90ad87d3ac4ed08222c4","first_computed_at":"2026-05-18T03:15:56.729903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:56.729903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ng1rJf6v3ZyLafD+6ifk6G0Tn2Bz9lDCdiO0rqSdRmzGrcJSGh+miJ40CNBi1fMV5FgsvHyrlXeI8t+DoibgCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:56.730681Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.3074","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89d5442e21d30f3c4397e4aed2b8697d93f4963ac0deeecd74bf5ec9e6dc8e2f","sha256:e2a51a6c2af9680dfeacf5925daa1b7692ada060b8261cb9186f87eeab05ca48"],"state_sha256":"60a5ac6aff45adbb93db3738bf9af4ffbb4427e4cc1cb0c831d82a4ab4dc6a01"}