{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:QN3YNK4XCAJYVJ5QV4OTIMUZGQ","short_pith_number":"pith:QN3YNK4X","schema_version":"1.0","canonical_sha256":"837786ab9710138aa7b0af1d343299340ac2d19ce9019573b00b8aa8b104e517","source":{"kind":"arxiv","id":"2606.08523","version":1},"attestation_state":"computed","paper":{"title":"Fixed-Parameter Tractability of $t$-Uniform Hypergraphicality","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","cs.DM"],"primary_cat":"math.CO","authors_text":"Istvan Miklos, Riley Brown","submitted_at":"2026-06-07T09:01:50Z","abstract_excerpt":"We study the $t$-uniform hypergraphicality problem under a compressed representation of the degree sequence. Instead of listing all vertex degrees explicitly, the input consists of pairs $$ (\\delta_1,n_1),\\dots,(\\delta_k,n_k), $$ meaning that exactly $n_i$ vertices have degree $\\delta_i$. Thus the parameter $k$ denotes the number of distinct degrees.\n  Although deciding $t$-hypergraphicality is NP-complete for every fixed $t>2$, we prove that the problem is fixed-parameter tractable parameterized by $(k,t)$. Our result shows that tractability extends substantially beyond previously known bound"},"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":"2606.08523","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-07T09:01:50Z","cross_cats_sorted":["cs.CC","cs.DM"],"title_canon_sha256":"33ca23e19037fb019c3cd4f2d3da460aae02e4769e389c5776f71656cd98982b","abstract_canon_sha256":"a857bb108f8c90cd8db96a9af51e231a9d99d35ca89c195dd15019d576239504"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:05:38.991506Z","signature_b64":"m8LwCrYaOVyseZRTYSq9pv3EoUIzAUzv396z6ORN5yAf5zdmgIZSGYb5lkZewpFx/4SxTJFYOG10foeu0yIKAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"837786ab9710138aa7b0af1d343299340ac2d19ce9019573b00b8aa8b104e517","last_reissued_at":"2026-06-09T01:05:38.991062Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:05:38.991062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fixed-Parameter Tractability of $t$-Uniform Hypergraphicality","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","cs.DM"],"primary_cat":"math.CO","authors_text":"Istvan Miklos, Riley Brown","submitted_at":"2026-06-07T09:01:50Z","abstract_excerpt":"We study the $t$-uniform hypergraphicality problem under a compressed representation of the degree sequence. Instead of listing all vertex degrees explicitly, the input consists of pairs $$ (\\delta_1,n_1),\\dots,(\\delta_k,n_k), $$ meaning that exactly $n_i$ vertices have degree $\\delta_i$. Thus the parameter $k$ denotes the number of distinct degrees.\n  Although deciding $t$-hypergraphicality is NP-complete for every fixed $t>2$, we prove that the problem is fixed-parameter tractable parameterized by $(k,t)$. Our result shows that tractability extends substantially beyond previously known bound"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08523","kind":"arxiv","version":1},"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/2606.08523/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":"2606.08523","created_at":"2026-06-09T01:05:38.991115+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.08523v1","created_at":"2026-06-09T01:05:38.991115+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08523","created_at":"2026-06-09T01:05:38.991115+00:00"},{"alias_kind":"pith_short_12","alias_value":"QN3YNK4XCAJY","created_at":"2026-06-09T01:05:38.991115+00:00"},{"alias_kind":"pith_short_16","alias_value":"QN3YNK4XCAJYVJ5Q","created_at":"2026-06-09T01:05:38.991115+00:00"},{"alias_kind":"pith_short_8","alias_value":"QN3YNK4X","created_at":"2026-06-09T01:05:38.991115+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/QN3YNK4XCAJYVJ5QV4OTIMUZGQ","json":"https://pith.science/pith/QN3YNK4XCAJYVJ5QV4OTIMUZGQ.json","graph_json":"https://pith.science/api/pith-number/QN3YNK4XCAJYVJ5QV4OTIMUZGQ/graph.json","events_json":"https://pith.science/api/pith-number/QN3YNK4XCAJYVJ5QV4OTIMUZGQ/events.json","paper":"https://pith.science/paper/QN3YNK4X"},"agent_actions":{"view_html":"https://pith.science/pith/QN3YNK4XCAJYVJ5QV4OTIMUZGQ","download_json":"https://pith.science/pith/QN3YNK4XCAJYVJ5QV4OTIMUZGQ.json","view_paper":"https://pith.science/paper/QN3YNK4X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.08523&json=true","fetch_graph":"https://pith.science/api/pith-number/QN3YNK4XCAJYVJ5QV4OTIMUZGQ/graph.json","fetch_events":"https://pith.science/api/pith-number/QN3YNK4XCAJYVJ5QV4OTIMUZGQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QN3YNK4XCAJYVJ5QV4OTIMUZGQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QN3YNK4XCAJYVJ5QV4OTIMUZGQ/action/storage_attestation","attest_author":"https://pith.science/pith/QN3YNK4XCAJYVJ5QV4OTIMUZGQ/action/author_attestation","sign_citation":"https://pith.science/pith/QN3YNK4XCAJYVJ5QV4OTIMUZGQ/action/citation_signature","submit_replication":"https://pith.science/pith/QN3YNK4XCAJYVJ5QV4OTIMUZGQ/action/replication_record"}},"created_at":"2026-06-09T01:05:38.991115+00:00","updated_at":"2026-06-09T01:05:38.991115+00:00"}