{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:NNX6FRHN22VM2SLPHAZNTZ5GJR","short_pith_number":"pith:NNX6FRHN","schema_version":"1.0","canonical_sha256":"6b6fe2c4edd6aacd496f3832d9e7a64c69b17f3d664f00cbe44880a7b8079ceb","source":{"kind":"arxiv","id":"2510.01852","version":5},"attestation_state":"computed","paper":{"title":"Well quasi-order and atomicity for combinatorial structures under consecutive orders","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A general framework decides well quasi-order and atomicity for avoidance sets of combinatorial structures under consecutive orders.","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nik Ru\\v{s}kuc, Victoria Ironmonger","submitted_at":"2025-10-02T09:51:54Z","abstract_excerpt":"We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a partially ordered set, we may ask decidability questions about its avoidance sets: subsets defined by a finite number of forbidden substructures. Two such questions ask, given a finite set of structures, whether its avoidance set is well quasi-ordered (i.e. contains no infinite antichains) or atomic (i.e. cannot be expressed as the union of two proper subsets)."},"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":"2510.01852","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-10-02T09:51:54Z","cross_cats_sorted":[],"title_canon_sha256":"3beb66278feb38bd7c834eeefd0d25e8082e49fd3dd8adc3c97c2f31339b4426","abstract_canon_sha256":"463b2bd0eb91c966c6ae5a0464cc40b715f056c6963b9a27ee546c3ac7e5a759"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-01T01:02:22.243018Z","signature_b64":"yGR97XLfWmxn8/pO5Ql2ELeAEI0CbJ7pG/1kTvjxV2ri/HXuaaR4RTbrENb49I5iT4SKJCHxv3nh/UhxLY+7BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b6fe2c4edd6aacd496f3832d9e7a64c69b17f3d664f00cbe44880a7b8079ceb","last_reissued_at":"2026-06-01T01:02:22.242186Z","signature_status":"signed_v1","first_computed_at":"2026-06-01T01:02:22.242186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Well quasi-order and atomicity for combinatorial structures under consecutive orders","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A general framework decides well quasi-order and atomicity for avoidance sets of combinatorial structures under consecutive orders.","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nik Ru\\v{s}kuc, Victoria Ironmonger","submitted_at":"2025-10-02T09:51:54Z","abstract_excerpt":"We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a partially ordered set, we may ask decidability questions about its avoidance sets: subsets defined by a finite number of forbidden substructures. Two such questions ask, given a finite set of structures, whether its avoidance set is well quasi-ordered (i.e. contains no infinite antichains) or atomic (i.e. cannot be expressed as the union of two proper subsets)."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We will establish a general framework, which enables us to answer these problems for a wide class of combinatorial structures, including graphs, digraphs and collections of relations.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the consecutive embedding order on the structures permits the extension of recent approaches into a single general framework that covers the stated wide class without additional restrictions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Establishes a general framework to answer decidability questions on well quasi-order and atomicity for avoidance sets in posets of combinatorial structures under consecutive orders, covering graphs, digraphs and relations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A general framework decides well quasi-order and atomicity for avoidance sets of combinatorial structures under consecutive orders.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1f34b7a27131989a17aa2e3c00a6a79ab6f23f0d2f15ec0a442de760090d5865"},"source":{"id":"2510.01852","kind":"arxiv","version":5},"verdict":{"id":"3aa790a1-e52a-418c-b93b-abf4af7f335f","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-18T10:48:28.366621Z","strongest_claim":"We will establish a general framework, which enables us to answer these problems for a wide class of combinatorial structures, including graphs, digraphs and collections of relations.","one_line_summary":"Establishes a general framework to answer decidability questions on well quasi-order and atomicity for avoidance sets in posets of combinatorial structures under consecutive orders, covering graphs, digraphs and relations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the consecutive embedding order on the structures permits the extension of recent approaches into a single general framework that covers the stated wide class without additional restrictions.","pith_extraction_headline":"A general framework decides well quasi-order and atomicity for avoidance sets of combinatorial structures under consecutive orders."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.01852/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":"2510.01852","created_at":"2026-06-01T01:02:22.242304+00:00"},{"alias_kind":"arxiv_version","alias_value":"2510.01852v5","created_at":"2026-06-01T01:02:22.242304+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.01852","created_at":"2026-06-01T01:02:22.242304+00:00"},{"alias_kind":"pith_short_12","alias_value":"NNX6FRHN22VM","created_at":"2026-06-01T01:02:22.242304+00:00"},{"alias_kind":"pith_short_16","alias_value":"NNX6FRHN22VM2SLP","created_at":"2026-06-01T01:02:22.242304+00:00"},{"alias_kind":"pith_short_8","alias_value":"NNX6FRHN","created_at":"2026-06-01T01:02:22.242304+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/NNX6FRHN22VM2SLPHAZNTZ5GJR","json":"https://pith.science/pith/NNX6FRHN22VM2SLPHAZNTZ5GJR.json","graph_json":"https://pith.science/api/pith-number/NNX6FRHN22VM2SLPHAZNTZ5GJR/graph.json","events_json":"https://pith.science/api/pith-number/NNX6FRHN22VM2SLPHAZNTZ5GJR/events.json","paper":"https://pith.science/paper/NNX6FRHN"},"agent_actions":{"view_html":"https://pith.science/pith/NNX6FRHN22VM2SLPHAZNTZ5GJR","download_json":"https://pith.science/pith/NNX6FRHN22VM2SLPHAZNTZ5GJR.json","view_paper":"https://pith.science/paper/NNX6FRHN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2510.01852&json=true","fetch_graph":"https://pith.science/api/pith-number/NNX6FRHN22VM2SLPHAZNTZ5GJR/graph.json","fetch_events":"https://pith.science/api/pith-number/NNX6FRHN22VM2SLPHAZNTZ5GJR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NNX6FRHN22VM2SLPHAZNTZ5GJR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NNX6FRHN22VM2SLPHAZNTZ5GJR/action/storage_attestation","attest_author":"https://pith.science/pith/NNX6FRHN22VM2SLPHAZNTZ5GJR/action/author_attestation","sign_citation":"https://pith.science/pith/NNX6FRHN22VM2SLPHAZNTZ5GJR/action/citation_signature","submit_replication":"https://pith.science/pith/NNX6FRHN22VM2SLPHAZNTZ5GJR/action/replication_record"}},"created_at":"2026-06-01T01:02:22.242304+00:00","updated_at":"2026-06-01T01:02:22.242304+00:00"}