{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:QN3YNK4XCAJYVJ5QV4OTIMUZGQ","short_pith_number":"pith:QN3YNK4X","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"},"canonical_sha256":"837786ab9710138aa7b0af1d343299340ac2d19ce9019573b00b8aa8b104e517","source":{"kind":"arxiv","id":"2606.08523","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08523","created_at":"2026-06-09T01:05:38Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08523v1","created_at":"2026-06-09T01:05:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08523","created_at":"2026-06-09T01:05:38Z"},{"alias_kind":"pith_short_12","alias_value":"QN3YNK4XCAJY","created_at":"2026-06-09T01:05:38Z"},{"alias_kind":"pith_short_16","alias_value":"QN3YNK4XCAJYVJ5Q","created_at":"2026-06-09T01:05:38Z"},{"alias_kind":"pith_short_8","alias_value":"QN3YNK4X","created_at":"2026-06-09T01:05:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:QN3YNK4XCAJYVJ5QV4OTIMUZGQ","target":"record","payload":{"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"},"canonical_sha256":"837786ab9710138aa7b0af1d343299340ac2d19ce9019573b00b8aa8b104e517","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"},"source_kind":"arxiv","source_id":"2606.08523","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-09T01:05:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"je+UD/DAn2uNYvtb+ZhdEAUa5l2lp9xwa3AW65JjCeRsvg7CivPj/k/+6+HTHHoyU1uTYQzkLLYpEydtvVXTCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:45:13.168104Z"},"content_sha256":"66763cd3dffc573fd2a5bb89faa0c852181c39082b894f75f1f2e7c0c5bd3712","schema_version":"1.0","event_id":"sha256:66763cd3dffc573fd2a5bb89faa0c852181c39082b894f75f1f2e7c0c5bd3712"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:QN3YNK4XCAJYVJ5QV4OTIMUZGQ","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-09T01:05:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OEMbeLZpEdvKF6tol5++m2b5aAUFvn787M0scRzWme0IjnalfSiFa5fQUYUw65bth0ZChX5VWtd1iiljnbOFBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:45:13.168503Z"},"content_sha256":"12c0bd673a115cf70f361e7004a490c4ee4d129a85a869f965f251a37bfc1d78","schema_version":"1.0","event_id":"sha256:12c0bd673a115cf70f361e7004a490c4ee4d129a85a869f965f251a37bfc1d78"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QN3YNK4XCAJYVJ5QV4OTIMUZGQ/bundle.json","state_url":"https://pith.science/pith/QN3YNK4XCAJYVJ5QV4OTIMUZGQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QN3YNK4XCAJYVJ5QV4OTIMUZGQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T22:45:13Z","links":{"resolver":"https://pith.science/pith/QN3YNK4XCAJYVJ5QV4OTIMUZGQ","bundle":"https://pith.science/pith/QN3YNK4XCAJYVJ5QV4OTIMUZGQ/bundle.json","state":"https://pith.science/pith/QN3YNK4XCAJYVJ5QV4OTIMUZGQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QN3YNK4XCAJYVJ5QV4OTIMUZGQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QN3YNK4XCAJYVJ5QV4OTIMUZGQ","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":"a857bb108f8c90cd8db96a9af51e231a9d99d35ca89c195dd15019d576239504","cross_cats_sorted":["cs.CC","cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-07T09:01:50Z","title_canon_sha256":"33ca23e19037fb019c3cd4f2d3da460aae02e4769e389c5776f71656cd98982b"},"schema_version":"1.0","source":{"id":"2606.08523","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08523","created_at":"2026-06-09T01:05:38Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08523v1","created_at":"2026-06-09T01:05:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08523","created_at":"2026-06-09T01:05:38Z"},{"alias_kind":"pith_short_12","alias_value":"QN3YNK4XCAJY","created_at":"2026-06-09T01:05:38Z"},{"alias_kind":"pith_short_16","alias_value":"QN3YNK4XCAJYVJ5Q","created_at":"2026-06-09T01:05:38Z"},{"alias_kind":"pith_short_8","alias_value":"QN3YNK4X","created_at":"2026-06-09T01:05:38Z"}],"graph_snapshots":[{"event_id":"sha256:12c0bd673a115cf70f361e7004a490c4ee4d129a85a869f965f251a37bfc1d78","target":"graph","created_at":"2026-06-09T01:05:38Z","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/2606.08523/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Istvan Miklos, Riley Brown","cross_cats":["cs.CC","cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-07T09:01:50Z","title":"Fixed-Parameter Tractability of $t$-Uniform Hypergraphicality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08523","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":"sha256:66763cd3dffc573fd2a5bb89faa0c852181c39082b894f75f1f2e7c0c5bd3712","target":"record","created_at":"2026-06-09T01:05:38Z","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":"a857bb108f8c90cd8db96a9af51e231a9d99d35ca89c195dd15019d576239504","cross_cats_sorted":["cs.CC","cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-07T09:01:50Z","title_canon_sha256":"33ca23e19037fb019c3cd4f2d3da460aae02e4769e389c5776f71656cd98982b"},"schema_version":"1.0","source":{"id":"2606.08523","kind":"arxiv","version":1}},"canonical_sha256":"837786ab9710138aa7b0af1d343299340ac2d19ce9019573b00b8aa8b104e517","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"837786ab9710138aa7b0af1d343299340ac2d19ce9019573b00b8aa8b104e517","first_computed_at":"2026-06-09T01:05:38.991062Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:38.991062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m8LwCrYaOVyseZRTYSq9pv3EoUIzAUzv396z6ORN5yAf5zdmgIZSGYb5lkZewpFx/4SxTJFYOG10foeu0yIKAA==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:38.991506Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.08523","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66763cd3dffc573fd2a5bb89faa0c852181c39082b894f75f1f2e7c0c5bd3712","sha256:12c0bd673a115cf70f361e7004a490c4ee4d129a85a869f965f251a37bfc1d78"],"state_sha256":"0a7775c4961941c516cc3c3d9b55d4329ef6f7951134e7aa9d63a1e90fccab3d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vy2oLy/aioxci88w74NNCO3rFZ1dTI/j9vmDdsdrw1viOJcstY5gmXuufn/B1i6TtHh8f+akm2ahwNJ8pyf6Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T22:45:13.170489Z","bundle_sha256":"37d1cc4c6a3e80f17b25cdb39a768a69a8ecfc5044bf8aa5c9ceca53ff782f94"}}