{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:TT6XLPAI4N24NSWFJCW43E6KLI","short_pith_number":"pith:TT6XLPAI","canonical_record":{"source":{"id":"math/0702585","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GN","submitted_at":"2007-02-20T17:37:50Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"b2c5505e4d12110c04313dfd7ac2bfc08caa992de4dc9982a886fc1f47c791bb","abstract_canon_sha256":"26a873f6ce486e23945340d5d2118417a9b5da7a342e83ae0e0c948b338fd4aa"},"schema_version":"1.0"},"canonical_sha256":"9cfd75bc08e375c6cac548adcd93ca5a2c894e638f5a8e5ab01d039ea56db6ec","source":{"kind":"arxiv","id":"math/0702585","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0702585","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/0702585v1","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702585","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"pith_short_12","alias_value":"TT6XLPAI4N24","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"TT6XLPAI4N24NSWF","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"TT6XLPAI","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:TT6XLPAI4N24NSWFJCW43E6KLI","target":"record","payload":{"canonical_record":{"source":{"id":"math/0702585","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GN","submitted_at":"2007-02-20T17:37:50Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"b2c5505e4d12110c04313dfd7ac2bfc08caa992de4dc9982a886fc1f47c791bb","abstract_canon_sha256":"26a873f6ce486e23945340d5d2118417a9b5da7a342e83ae0e0c948b338fd4aa"},"schema_version":"1.0"},"canonical_sha256":"9cfd75bc08e375c6cac548adcd93ca5a2c894e638f5a8e5ab01d039ea56db6ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:34.276310Z","signature_b64":"QuI9ySdR/NzwcuFteIT9L4H08FZ7j/atRv3NHlRrUGAqDiupRkKyghytgTDVTDTy9yfXrwMo+ptWWuohb27TAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9cfd75bc08e375c6cac548adcd93ca5a2c894e638f5a8e5ab01d039ea56db6ec","last_reissued_at":"2026-05-18T03:42:34.275781Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:34.275781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0702585","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":"2026-05-18T03:42:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GxiZ+but6HOpJixfSrq7EuqDSZ/98XzK704YySv3QlZfItxRMtCJcgSeqWtJmZBXomt5R26dGwXNA++vJjo2CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:59:40.281093Z"},"content_sha256":"bf43ba408a32c93e37e0892fdf8402d39d3c40b4ac4aeab070a4aaa3e95aea4c","schema_version":"1.0","event_id":"sha256:bf43ba408a32c93e37e0892fdf8402d39d3c40b4ac4aeab070a4aaa3e95aea4c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:TT6XLPAI4N24NSWFJCW43E6KLI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Poset algebras over well quasi-ordered posets","license":"","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Robert Bonnet, Uri Abraham, Wieslaw Kubis","submitted_at":"2007-02-20T17:37:50Z","abstract_excerpt":"A new class of partial order-types, class $\\gbqo^+$ is defined and investigated here. A poset $P$ is in the class $W^+ $ iff the free poset algebra $F(P)$ is generated by a better quasi-order $G$ that is included in the free lattice $L(P)$.\n  We prove that if $P$ is any well quasi-ordering, then $L(P)$ is well founded, and is a countable union of well quasi-orderings. We prove that the class $W^+$ is contained in the class of well quasi-ordered sets. We prove that $W^+$ is preserved under homomorphic image, finite products, and lexicographic sum over better quasi-ordered index sets. We prove a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702585","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":""},"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":"2026-05-18T03:42:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+rhiwgl1bcjpmBvRVaQ3YE69sqRjNYZBnkCSuVjZb/myOWStKaRZCeneJRwpP9//DA5GTtatFiv1meQLb5oDCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:59:40.282080Z"},"content_sha256":"46143ff744fe460c8e83df3aada61f4492d814225aabc8f2af14b6c2c1b8729a","schema_version":"1.0","event_id":"sha256:46143ff744fe460c8e83df3aada61f4492d814225aabc8f2af14b6c2c1b8729a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TT6XLPAI4N24NSWFJCW43E6KLI/bundle.json","state_url":"https://pith.science/pith/TT6XLPAI4N24NSWFJCW43E6KLI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TT6XLPAI4N24NSWFJCW43E6KLI/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":"2026-05-31T12:59:40Z","links":{"resolver":"https://pith.science/pith/TT6XLPAI4N24NSWFJCW43E6KLI","bundle":"https://pith.science/pith/TT6XLPAI4N24NSWFJCW43E6KLI/bundle.json","state":"https://pith.science/pith/TT6XLPAI4N24NSWFJCW43E6KLI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TT6XLPAI4N24NSWFJCW43E6KLI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:TT6XLPAI4N24NSWFJCW43E6KLI","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":"26a873f6ce486e23945340d5d2118417a9b5da7a342e83ae0e0c948b338fd4aa","cross_cats_sorted":["math.LO"],"license":"","primary_cat":"math.GN","submitted_at":"2007-02-20T17:37:50Z","title_canon_sha256":"b2c5505e4d12110c04313dfd7ac2bfc08caa992de4dc9982a886fc1f47c791bb"},"schema_version":"1.0","source":{"id":"math/0702585","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0702585","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/0702585v1","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702585","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"pith_short_12","alias_value":"TT6XLPAI4N24","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"TT6XLPAI4N24NSWF","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"TT6XLPAI","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:46143ff744fe460c8e83df3aada61f4492d814225aabc8f2af14b6c2c1b8729a","target":"graph","created_at":"2026-05-18T03:42:34Z","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"},"paper":{"abstract_excerpt":"A new class of partial order-types, class $\\gbqo^+$ is defined and investigated here. A poset $P$ is in the class $W^+ $ iff the free poset algebra $F(P)$ is generated by a better quasi-order $G$ that is included in the free lattice $L(P)$.\n  We prove that if $P$ is any well quasi-ordering, then $L(P)$ is well founded, and is a countable union of well quasi-orderings. We prove that the class $W^+$ is contained in the class of well quasi-ordered sets. We prove that $W^+$ is preserved under homomorphic image, finite products, and lexicographic sum over better quasi-ordered index sets. We prove a","authors_text":"Robert Bonnet, Uri Abraham, Wieslaw Kubis","cross_cats":["math.LO"],"headline":"","license":"","primary_cat":"math.GN","submitted_at":"2007-02-20T17:37:50Z","title":"Poset algebras over well quasi-ordered posets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702585","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:bf43ba408a32c93e37e0892fdf8402d39d3c40b4ac4aeab070a4aaa3e95aea4c","target":"record","created_at":"2026-05-18T03:42:34Z","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":"26a873f6ce486e23945340d5d2118417a9b5da7a342e83ae0e0c948b338fd4aa","cross_cats_sorted":["math.LO"],"license":"","primary_cat":"math.GN","submitted_at":"2007-02-20T17:37:50Z","title_canon_sha256":"b2c5505e4d12110c04313dfd7ac2bfc08caa992de4dc9982a886fc1f47c791bb"},"schema_version":"1.0","source":{"id":"math/0702585","kind":"arxiv","version":1}},"canonical_sha256":"9cfd75bc08e375c6cac548adcd93ca5a2c894e638f5a8e5ab01d039ea56db6ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cfd75bc08e375c6cac548adcd93ca5a2c894e638f5a8e5ab01d039ea56db6ec","first_computed_at":"2026-05-18T03:42:34.275781Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:34.275781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QuI9ySdR/NzwcuFteIT9L4H08FZ7j/atRv3NHlRrUGAqDiupRkKyghytgTDVTDTy9yfXrwMo+ptWWuohb27TAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:34.276310Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0702585","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf43ba408a32c93e37e0892fdf8402d39d3c40b4ac4aeab070a4aaa3e95aea4c","sha256:46143ff744fe460c8e83df3aada61f4492d814225aabc8f2af14b6c2c1b8729a"],"state_sha256":"fbce44a7469575b50cc7fde710c58f69fa414b5a4eb560ae8360acfac63b4bef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"37ePLCVMxb/plZFjP71yI8I3kNeMlUXK0WpIh+lyg5OoeDkzfQiC4tBDmbX9BwJ99G0AGnUChbhBlr64qmS8AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T12:59:40.286499Z","bundle_sha256":"3cae03388f3fd06edfde0164bf6a8d938a11ad57c368c02861b115b9c24bddbe"}}