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In particular, $G$ admits a Gallai decomposition.\n  As a consequence, we obtain that every interval order $P$ with no infinite antichain admits a Gallai decomposition. That is, $P$ is a lexicographical sum of interval orders distinct from $P$ indexed by either a chain, an antichain, or a prime interval order.\n  Next, we prove that every prime interval order with no infinite antichain is at most countable and"},"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":"2411.06693","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-11-11T03:27:45Z","cross_cats_sorted":[],"title_canon_sha256":"0b256fa2dd459225e4a414c3d1dfb625b1ee305c5ce4077d5c1b47712d4a36e3","abstract_canon_sha256":"b3de1f6cf6a3d80aeac70b3ccc33c10faba29b34407184eeb5a19a7568223d0f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:04:37.599132Z","signature_b64":"5OV1xcKottvgKY1iQSjZEVygTvmJxW5WTFtjbF7cRtCPLW5eq+EbzVQpCyVWEMeeqJdhxKEZJJw04Ndsgs/aDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ff10a8488047f0c06596930259cd9ff25ae9f0f3ba1612ad3538203b423becc","last_reissued_at":"2026-06-09T01:04:37.598670Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:04:37.598670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The structure of interval orders with no infinite antichain","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Imed Zaguia, Maurice Pouzet","submitted_at":"2024-11-11T03:27:45Z","abstract_excerpt":"We prove that if $G=(V,E)$ is a nonprime graph with either no infinite independent set or no infinite clique, then every vertex of $G$ belongs to a maximal strong module distinct from $V$. In particular, $G$ admits a Gallai decomposition.\n  As a consequence, we obtain that every interval order $P$ with no infinite antichain admits a Gallai decomposition. That is, $P$ is a lexicographical sum of interval orders distinct from $P$ indexed by either a chain, an antichain, or a prime interval order.\n  Next, we prove that every prime interval order with no infinite antichain is at most countable and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.06693","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.06693/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2411.06693","created_at":"2026-06-09T01:04:37.598734+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.06693v2","created_at":"2026-06-09T01:04:37.598734+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.06693","created_at":"2026-06-09T01:04:37.598734+00:00"},{"alias_kind":"pith_short_12","alias_value":"R7YQVBEIAR7Q","created_at":"2026-06-09T01:04:37.598734+00:00"},{"alias_kind":"pith_short_16","alias_value":"R7YQVBEIAR7QYBSZ","created_at":"2026-06-09T01:04:37.598734+00:00"},{"alias_kind":"pith_short_8","alias_value":"R7YQVBEI","created_at":"2026-06-09T01:04:37.598734+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/R7YQVBEIAR7QYBSZNEYCLHGZ74","json":"https://pith.science/pith/R7YQVBEIAR7QYBSZNEYCLHGZ74.json","graph_json":"https://pith.science/api/pith-number/R7YQVBEIAR7QYBSZNEYCLHGZ74/graph.json","events_json":"https://pith.science/api/pith-number/R7YQVBEIAR7QYBSZNEYCLHGZ74/events.json","paper":"https://pith.science/paper/R7YQVBEI"},"agent_actions":{"view_html":"https://pith.science/pith/R7YQVBEIAR7QYBSZNEYCLHGZ74","download_json":"https://pith.science/pith/R7YQVBEIAR7QYBSZNEYCLHGZ74.json","view_paper":"https://pith.science/paper/R7YQVBEI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.06693&json=true","fetch_graph":"https://pith.science/api/pith-number/R7YQVBEIAR7QYBSZNEYCLHGZ74/graph.json","fetch_events":"https://pith.science/api/pith-number/R7YQVBEIAR7QYBSZNEYCLHGZ74/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R7YQVBEIAR7QYBSZNEYCLHGZ74/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R7YQVBEIAR7QYBSZNEYCLHGZ74/action/storage_attestation","attest_author":"https://pith.science/pith/R7YQVBEIAR7QYBSZNEYCLHGZ74/action/author_attestation","sign_citation":"https://pith.science/pith/R7YQVBEIAR7QYBSZNEYCLHGZ74/action/citation_signature","submit_replication":"https://pith.science/pith/R7YQVBEIAR7QYBSZNEYCLHGZ74/action/replication_record"}},"created_at":"2026-06-09T01:04:37.598734+00:00","updated_at":"2026-06-09T01:04:37.598734+00:00"}