{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:HTYAFHIMOKVCEXW6RXCXPSXQH6","short_pith_number":"pith:HTYAFHIM","canonical_record":{"source":{"id":"2206.11832","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2022-06-23T16:59:40Z","cross_cats_sorted":[],"title_canon_sha256":"0ca96f85170f72a941c975dacbc5fb3e9936e95be3a39a25cd0e71b596033d72","abstract_canon_sha256":"4a95920d804c2bb95b9f3320353787aeeb15d15213bba10b7a55e52a4231a142"},"schema_version":"1.0"},"canonical_sha256":"3cf0029d0c72aa225ede8dc577caf03f83fd4852e7b5d79fa0a338a05cb856a1","source":{"kind":"arxiv","id":"2206.11832","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.11832","created_at":"2026-07-05T10:16:04Z"},{"alias_kind":"arxiv_version","alias_value":"2206.11832v6","created_at":"2026-07-05T10:16:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.11832","created_at":"2026-07-05T10:16:04Z"},{"alias_kind":"pith_short_12","alias_value":"HTYAFHIMOKVC","created_at":"2026-07-05T10:16:04Z"},{"alias_kind":"pith_short_16","alias_value":"HTYAFHIMOKVCEXW6","created_at":"2026-07-05T10:16:04Z"},{"alias_kind":"pith_short_8","alias_value":"HTYAFHIM","created_at":"2026-07-05T10:16:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:HTYAFHIMOKVCEXW6RXCXPSXQH6","target":"record","payload":{"canonical_record":{"source":{"id":"2206.11832","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2022-06-23T16:59:40Z","cross_cats_sorted":[],"title_canon_sha256":"0ca96f85170f72a941c975dacbc5fb3e9936e95be3a39a25cd0e71b596033d72","abstract_canon_sha256":"4a95920d804c2bb95b9f3320353787aeeb15d15213bba10b7a55e52a4231a142"},"schema_version":"1.0"},"canonical_sha256":"3cf0029d0c72aa225ede8dc577caf03f83fd4852e7b5d79fa0a338a05cb856a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:16:04.830553Z","signature_b64":"ph8bTbAKYTHZkvQGUtRzfqonQBUHOzp38qebeorohAGv4QJ67RDPToGy6KK2zemVZY0cu9TI3nNjgtObCDkPBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cf0029d0c72aa225ede8dc577caf03f83fd4852e7b5d79fa0a338a05cb856a1","last_reissued_at":"2026-07-05T10:16:04.830112Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:16:04.830112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2206.11832","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:16:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ci4rme6GMKWdqXBwgkwf9KMYu7bvjJT81taxqmbaJY3ycRK6y3DxvmIqzGA3OJeJ/U7uHDqN8iKLe69pIsZrBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:57:07.970014Z"},"content_sha256":"c4ecad1720ad2f3f7f16b6f114c660ead16d04e86a3ca8770eeaeceab8233981","schema_version":"1.0","event_id":"sha256:c4ecad1720ad2f3f7f16b6f114c660ead16d04e86a3ca8770eeaeceab8233981"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:HTYAFHIMOKVCEXW6RXCXPSXQH6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the parameterized complexity of computing tree-partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Carla Groenland, Hans L. Bodlaender, Hugo Jacob","submitted_at":"2022-06-23T16:59:40Z","abstract_excerpt":"We study the parameterized complexity of computing the tree-partition-width, a graph parameter equivalent to treewidth on graphs of bounded maximum degree. On one hand, we can obtain approximations of the tree-partition-width efficiently: we show that there is an algorithm that, given an $n$-vertex graph $G$ and an integer $k$, constructs a tree-partition of width $O(k^7)$ for $G$ or reports that $G$ has tree-partition-width more than $k$, in time $k^{O(1)}n^2$. We can improve slightly on the approximation factor by sacrificing the dependence on $k$, or on $n$. On the other hand, we show the p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.11832","kind":"arxiv","version":6},"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/2206.11832/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":"2026-07-05T10:16:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ft/uDnzapECyYutUciaMzOV+FaI1+3EcRQnTMd2girtXFlxY3ywGsfBTLQQBFdz8lhNKyqDWexHlcbp1uVsBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:57:07.971095Z"},"content_sha256":"fe0c08452480fedbacdc8d6f533e3db0228e47a26a8ef2e18a766c5927d2eb63","schema_version":"1.0","event_id":"sha256:fe0c08452480fedbacdc8d6f533e3db0228e47a26a8ef2e18a766c5927d2eb63"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HTYAFHIMOKVCEXW6RXCXPSXQH6/bundle.json","state_url":"https://pith.science/pith/HTYAFHIMOKVCEXW6RXCXPSXQH6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HTYAFHIMOKVCEXW6RXCXPSXQH6/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":"2026-08-09T03:57:07Z","links":{"resolver":"https://pith.science/pith/HTYAFHIMOKVCEXW6RXCXPSXQH6","bundle":"https://pith.science/pith/HTYAFHIMOKVCEXW6RXCXPSXQH6/bundle.json","state":"https://pith.science/pith/HTYAFHIMOKVCEXW6RXCXPSXQH6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HTYAFHIMOKVCEXW6RXCXPSXQH6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:HTYAFHIMOKVCEXW6RXCXPSXQH6","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":"4a95920d804c2bb95b9f3320353787aeeb15d15213bba10b7a55e52a4231a142","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2022-06-23T16:59:40Z","title_canon_sha256":"0ca96f85170f72a941c975dacbc5fb3e9936e95be3a39a25cd0e71b596033d72"},"schema_version":"1.0","source":{"id":"2206.11832","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.11832","created_at":"2026-07-05T10:16:04Z"},{"alias_kind":"arxiv_version","alias_value":"2206.11832v6","created_at":"2026-07-05T10:16:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.11832","created_at":"2026-07-05T10:16:04Z"},{"alias_kind":"pith_short_12","alias_value":"HTYAFHIMOKVC","created_at":"2026-07-05T10:16:04Z"},{"alias_kind":"pith_short_16","alias_value":"HTYAFHIMOKVCEXW6","created_at":"2026-07-05T10:16:04Z"},{"alias_kind":"pith_short_8","alias_value":"HTYAFHIM","created_at":"2026-07-05T10:16:04Z"}],"graph_snapshots":[{"event_id":"sha256:fe0c08452480fedbacdc8d6f533e3db0228e47a26a8ef2e18a766c5927d2eb63","target":"graph","created_at":"2026-07-05T10:16:04Z","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/2206.11832/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the parameterized complexity of computing the tree-partition-width, a graph parameter equivalent to treewidth on graphs of bounded maximum degree. On one hand, we can obtain approximations of the tree-partition-width efficiently: we show that there is an algorithm that, given an $n$-vertex graph $G$ and an integer $k$, constructs a tree-partition of width $O(k^7)$ for $G$ or reports that $G$ has tree-partition-width more than $k$, in time $k^{O(1)}n^2$. We can improve slightly on the approximation factor by sacrificing the dependence on $k$, or on $n$. On the other hand, we show the p","authors_text":"Carla Groenland, Hans L. Bodlaender, Hugo Jacob","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2022-06-23T16:59:40Z","title":"On the parameterized complexity of computing tree-partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.11832","kind":"arxiv","version":6},"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:c4ecad1720ad2f3f7f16b6f114c660ead16d04e86a3ca8770eeaeceab8233981","target":"record","created_at":"2026-07-05T10:16:04Z","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":"4a95920d804c2bb95b9f3320353787aeeb15d15213bba10b7a55e52a4231a142","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2022-06-23T16:59:40Z","title_canon_sha256":"0ca96f85170f72a941c975dacbc5fb3e9936e95be3a39a25cd0e71b596033d72"},"schema_version":"1.0","source":{"id":"2206.11832","kind":"arxiv","version":6}},"canonical_sha256":"3cf0029d0c72aa225ede8dc577caf03f83fd4852e7b5d79fa0a338a05cb856a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cf0029d0c72aa225ede8dc577caf03f83fd4852e7b5d79fa0a338a05cb856a1","first_computed_at":"2026-07-05T10:16:04.830112Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:16:04.830112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ph8bTbAKYTHZkvQGUtRzfqonQBUHOzp38qebeorohAGv4QJ67RDPToGy6KK2zemVZY0cu9TI3nNjgtObCDkPBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:16:04.830553Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.11832","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4ecad1720ad2f3f7f16b6f114c660ead16d04e86a3ca8770eeaeceab8233981","sha256:fe0c08452480fedbacdc8d6f533e3db0228e47a26a8ef2e18a766c5927d2eb63"],"state_sha256":"2286398ea073608b284638d29739fad434b658d46eb7dddac56d953f1343ac9f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7AR+WWiBhn5JY6s4WFQyEKKih2kmcPa69tw14vLqt38xbRZh5igiDmbdj6exKc/Gde+wpT6P1zd/55SdnqABDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T03:57:07.978579Z","bundle_sha256":"0810ca57fa5f70c91e3dc6f4552716565c764e169d1be95b8e4a817004d2dba0"}}