{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:7BD4GOGU2UBN2JY2AE56TOXEWY","short_pith_number":"pith:7BD4GOGU","canonical_record":{"source":{"id":"2601.18571","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.CO","submitted_at":"2026-01-26T15:14:21Z","cross_cats_sorted":["cs.FL","cs.LO"],"title_canon_sha256":"da77fb51708b2b183960f741badbb1734bb75679ee2737eda4881da62bfa3e98","abstract_canon_sha256":"0fc7cf8ac6e3177ef5fa5672448627c706f39cbe0e8eeaade907084485dd64c9"},"schema_version":"1.0"},"canonical_sha256":"f847c338d4d502dd271a013be9bae4b6090da9b5ee1362dd6fe11f63e59b2056","source":{"kind":"arxiv","id":"2601.18571","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.18571","created_at":"2026-05-28T02:04:45Z"},{"alias_kind":"arxiv_version","alias_value":"2601.18571v2","created_at":"2026-05-28T02:04:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.18571","created_at":"2026-05-28T02:04:45Z"},{"alias_kind":"pith_short_12","alias_value":"7BD4GOGU2UBN","created_at":"2026-05-28T02:04:45Z"},{"alias_kind":"pith_short_16","alias_value":"7BD4GOGU2UBN2JY2","created_at":"2026-05-28T02:04:45Z"},{"alias_kind":"pith_short_8","alias_value":"7BD4GOGU","created_at":"2026-05-28T02:04:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:7BD4GOGU2UBN2JY2AE56TOXEWY","target":"record","payload":{"canonical_record":{"source":{"id":"2601.18571","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.CO","submitted_at":"2026-01-26T15:14:21Z","cross_cats_sorted":["cs.FL","cs.LO"],"title_canon_sha256":"da77fb51708b2b183960f741badbb1734bb75679ee2737eda4881da62bfa3e98","abstract_canon_sha256":"0fc7cf8ac6e3177ef5fa5672448627c706f39cbe0e8eeaade907084485dd64c9"},"schema_version":"1.0"},"canonical_sha256":"f847c338d4d502dd271a013be9bae4b6090da9b5ee1362dd6fe11f63e59b2056","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T02:04:45.490447Z","signature_b64":"z4LJbIDn3g8bncF3YVuzinn47szbg8Wa4gbrn6XUQvEvVaZc0rHNkUE9/e+GUY6jPNz5q4BB4WMw6MuyKnUjAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f847c338d4d502dd271a013be9bae4b6090da9b5ee1362dd6fe11f63e59b2056","last_reissued_at":"2026-05-28T02:04:45.489941Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T02:04:45.489941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2601.18571","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-28T02:04:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2+HXd/2PJdB/ZUAYZli+Kp7Yi1JUNXgcOtDEM2tYo7DIA7Pikuji4eEyp8xzrpEF5yemjDYFoxYZpXvMT+pgBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T04:06:42.182874Z"},"content_sha256":"e5a1d3f06a0d510c993ee86dc0c37af7d5e4664f18b184a73ecb93ffb7860c82","schema_version":"1.0","event_id":"sha256:e5a1d3f06a0d510c993ee86dc0c37af7d5e4664f18b184a73ecb93ffb7860c82"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:7BD4GOGU2UBN2JY2AE56TOXEWY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Well-quasi-ordered classes of bounded clique-width","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.FL","cs.LO"],"primary_cat":"math.CO","authors_text":"Aliaume Lopez, Ma\\\"el Dumas","submitted_at":"2026-01-26T15:14:21Z","abstract_excerpt":"We study classes of graphs with bounded clique-width that are well-quasi-ordered by the induced subgraph relation, in the presence of labels on the vertices. We prove that, given a finite presentation of a class of graphs, one can decide whether the class is labelled-well-quasi-ordered. This solves an open problem raised by Daligault, Rao and Thomass\\'e in 2010, and answers positively to two conjectures of Pouzet in the restricted case of bounded clique-width classes. Namely, we prove that being labelled-well-quasi-ordered by a set of size 2 or by a well-quasi-ordered infinite set are equivale"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.18571","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/2601.18571/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":"2026-05-28T02:04:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VQXA7N9dybcrg1V5tvY4ZLNDcPFU7PWIFrAJNmFoJRUhfApASN0iTvldC1FVGL98/fG09rzaevMZdExGxbRRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T04:06:42.183255Z"},"content_sha256":"5fb517d1e67f7f1e08a8c872479243799936c2291905e321b0351bea753db2c5","schema_version":"1.0","event_id":"sha256:5fb517d1e67f7f1e08a8c872479243799936c2291905e321b0351bea753db2c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7BD4GOGU2UBN2JY2AE56TOXEWY/bundle.json","state_url":"https://pith.science/pith/7BD4GOGU2UBN2JY2AE56TOXEWY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7BD4GOGU2UBN2JY2AE56TOXEWY/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":"2026-07-02T04:06:42Z","links":{"resolver":"https://pith.science/pith/7BD4GOGU2UBN2JY2AE56TOXEWY","bundle":"https://pith.science/pith/7BD4GOGU2UBN2JY2AE56TOXEWY/bundle.json","state":"https://pith.science/pith/7BD4GOGU2UBN2JY2AE56TOXEWY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7BD4GOGU2UBN2JY2AE56TOXEWY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7BD4GOGU2UBN2JY2AE56TOXEWY","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":"0fc7cf8ac6e3177ef5fa5672448627c706f39cbe0e8eeaade907084485dd64c9","cross_cats_sorted":["cs.FL","cs.LO"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.CO","submitted_at":"2026-01-26T15:14:21Z","title_canon_sha256":"da77fb51708b2b183960f741badbb1734bb75679ee2737eda4881da62bfa3e98"},"schema_version":"1.0","source":{"id":"2601.18571","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.18571","created_at":"2026-05-28T02:04:45Z"},{"alias_kind":"arxiv_version","alias_value":"2601.18571v2","created_at":"2026-05-28T02:04:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.18571","created_at":"2026-05-28T02:04:45Z"},{"alias_kind":"pith_short_12","alias_value":"7BD4GOGU2UBN","created_at":"2026-05-28T02:04:45Z"},{"alias_kind":"pith_short_16","alias_value":"7BD4GOGU2UBN2JY2","created_at":"2026-05-28T02:04:45Z"},{"alias_kind":"pith_short_8","alias_value":"7BD4GOGU","created_at":"2026-05-28T02:04:45Z"}],"graph_snapshots":[{"event_id":"sha256:5fb517d1e67f7f1e08a8c872479243799936c2291905e321b0351bea753db2c5","target":"graph","created_at":"2026-05-28T02:04:45Z","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/2601.18571/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study classes of graphs with bounded clique-width that are well-quasi-ordered by the induced subgraph relation, in the presence of labels on the vertices. We prove that, given a finite presentation of a class of graphs, one can decide whether the class is labelled-well-quasi-ordered. This solves an open problem raised by Daligault, Rao and Thomass\\'e in 2010, and answers positively to two conjectures of Pouzet in the restricted case of bounded clique-width classes. Namely, we prove that being labelled-well-quasi-ordered by a set of size 2 or by a well-quasi-ordered infinite set are equivale","authors_text":"Aliaume Lopez, Ma\\\"el Dumas","cross_cats":["cs.FL","cs.LO"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.CO","submitted_at":"2026-01-26T15:14:21Z","title":"Well-quasi-ordered classes of bounded clique-width"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.18571","kind":"arxiv","version":2},"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:e5a1d3f06a0d510c993ee86dc0c37af7d5e4664f18b184a73ecb93ffb7860c82","target":"record","created_at":"2026-05-28T02:04:45Z","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":"0fc7cf8ac6e3177ef5fa5672448627c706f39cbe0e8eeaade907084485dd64c9","cross_cats_sorted":["cs.FL","cs.LO"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.CO","submitted_at":"2026-01-26T15:14:21Z","title_canon_sha256":"da77fb51708b2b183960f741badbb1734bb75679ee2737eda4881da62bfa3e98"},"schema_version":"1.0","source":{"id":"2601.18571","kind":"arxiv","version":2}},"canonical_sha256":"f847c338d4d502dd271a013be9bae4b6090da9b5ee1362dd6fe11f63e59b2056","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f847c338d4d502dd271a013be9bae4b6090da9b5ee1362dd6fe11f63e59b2056","first_computed_at":"2026-05-28T02:04:45.489941Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T02:04:45.489941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z4LJbIDn3g8bncF3YVuzinn47szbg8Wa4gbrn6XUQvEvVaZc0rHNkUE9/e+GUY6jPNz5q4BB4WMw6MuyKnUjAQ==","signature_status":"signed_v1","signed_at":"2026-05-28T02:04:45.490447Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.18571","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5a1d3f06a0d510c993ee86dc0c37af7d5e4664f18b184a73ecb93ffb7860c82","sha256:5fb517d1e67f7f1e08a8c872479243799936c2291905e321b0351bea753db2c5"],"state_sha256":"728938080ddabb76c9ec08ddf803875b674a20a057b8506af5d0bef5e7e815be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vMcy3XQ4pYc5eSp7xfodl9P5gYsClf/KLDueqcrnVyUkMuWw9G0fbkYeZe2p+tpS3WWNXqGMM+n2IXEyztzLBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T04:06:42.185336Z","bundle_sha256":"d9af3defe7126a6e7e16df596fa9f758ab6d4f826092c594535d254dc5b0b5d1"}}