{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4GTLYRP6QFRNC5CYA7N2ONOUOB","short_pith_number":"pith:4GTLYRP6","canonical_record":{"source":{"id":"1805.00815","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-02T13:54:31Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"0345565b63821a51c898045b4398042e3d8f85400a51775889930d26065167d3","abstract_canon_sha256":"adb36b1be286538543f3cb55dc4c679314710ae3249b9e50fd0412927f610e89"},"schema_version":"1.0"},"canonical_sha256":"e1a6bc45fe8162d1745807dba735d47057a1ee07b58e57d2a6dc33b7b89b0401","source":{"kind":"arxiv","id":"1805.00815","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00815","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00815v2","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00815","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"pith_short_12","alias_value":"4GTLYRP6QFRN","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4GTLYRP6QFRNC5CY","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4GTLYRP6","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4GTLYRP6QFRNC5CYA7N2ONOUOB","target":"record","payload":{"canonical_record":{"source":{"id":"1805.00815","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-02T13:54:31Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"0345565b63821a51c898045b4398042e3d8f85400a51775889930d26065167d3","abstract_canon_sha256":"adb36b1be286538543f3cb55dc4c679314710ae3249b9e50fd0412927f610e89"},"schema_version":"1.0"},"canonical_sha256":"e1a6bc45fe8162d1745807dba735d47057a1ee07b58e57d2a6dc33b7b89b0401","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:57.305510Z","signature_b64":"y2gBN0+9u7X/9v/bOe01uCcpfs5nibmzWFXg0OIl1bzO+K+BmLHwZdAvHx63UN5ulpAtFf/T1h9rf1SXzGWLCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1a6bc45fe8162d1745807dba735d47057a1ee07b58e57d2a6dc33b7b89b0401","last_reissued_at":"2026-05-17T23:49:57.304772Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:57.304772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.00815","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":"2026-05-17T23:49:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zD3Iz2tUH4bMJFW58iUofC8qtyIbIp0aSCRQj5td95hQA24tcLUa+8WPd+Xl4DHnXqYH9K/S7hg9oOws3ShDBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T18:27:02.389097Z"},"content_sha256":"9454ec9ac6d76e17b5996322cd8a4e6f313aabe499d01e1d8902e461818ed01c","schema_version":"1.0","event_id":"sha256:9454ec9ac6d76e17b5996322cd8a4e6f313aabe499d01e1d8902e461818ed01c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4GTLYRP6QFRNC5CYA7N2ONOUOB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Independence Posets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Hugh Thomas, Nathan Williams","submitted_at":"2018-05-02T13:54:31Z","abstract_excerpt":"Let $G$ be an acylic directed graph. For each vertex $g \\in G$, we define an involution on the independent sets of $G$. We call these involutions flips, and use them to define a new partial order on independent sets of $G$.\n  Trim lattices generalize distributive lattices by removing the graded hypothesis: a graded trim lattice is a distributive lattice, and every distributive lattice is trim. Our independence posets are a further generalization of distributive lattices, eliminating also the lattice requirement: an independence poset that is a lattice is always a trim lattice, and every trim l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00815","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":""},"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":"2026-05-17T23:49:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YqNgZCCmH1NE7NhbBt+Bm+udtb4pu+NLMHJzfvcPA571ZBYRouAF360debxmaC0gzE+wAm+cnS32dAJ4mABkBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T18:27:02.389873Z"},"content_sha256":"e1d7d697b4f19c46d26f6376bdb07367a658ada5919a9592946b7a1eeeaf70bc","schema_version":"1.0","event_id":"sha256:e1d7d697b4f19c46d26f6376bdb07367a658ada5919a9592946b7a1eeeaf70bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4GTLYRP6QFRNC5CYA7N2ONOUOB/bundle.json","state_url":"https://pith.science/pith/4GTLYRP6QFRNC5CYA7N2ONOUOB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4GTLYRP6QFRNC5CYA7N2ONOUOB/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":"2026-05-28T18:27:02Z","links":{"resolver":"https://pith.science/pith/4GTLYRP6QFRNC5CYA7N2ONOUOB","bundle":"https://pith.science/pith/4GTLYRP6QFRNC5CYA7N2ONOUOB/bundle.json","state":"https://pith.science/pith/4GTLYRP6QFRNC5CYA7N2ONOUOB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4GTLYRP6QFRNC5CYA7N2ONOUOB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4GTLYRP6QFRNC5CYA7N2ONOUOB","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":"adb36b1be286538543f3cb55dc4c679314710ae3249b9e50fd0412927f610e89","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-02T13:54:31Z","title_canon_sha256":"0345565b63821a51c898045b4398042e3d8f85400a51775889930d26065167d3"},"schema_version":"1.0","source":{"id":"1805.00815","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00815","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00815v2","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00815","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"pith_short_12","alias_value":"4GTLYRP6QFRN","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4GTLYRP6QFRNC5CY","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4GTLYRP6","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:e1d7d697b4f19c46d26f6376bdb07367a658ada5919a9592946b7a1eeeaf70bc","target":"graph","created_at":"2026-05-17T23:49:57Z","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":"Let $G$ be an acylic directed graph. For each vertex $g \\in G$, we define an involution on the independent sets of $G$. We call these involutions flips, and use them to define a new partial order on independent sets of $G$.\n  Trim lattices generalize distributive lattices by removing the graded hypothesis: a graded trim lattice is a distributive lattice, and every distributive lattice is trim. Our independence posets are a further generalization of distributive lattices, eliminating also the lattice requirement: an independence poset that is a lattice is always a trim lattice, and every trim l","authors_text":"Hugh Thomas, Nathan Williams","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-02T13:54:31Z","title":"Independence Posets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00815","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":"sha256:9454ec9ac6d76e17b5996322cd8a4e6f313aabe499d01e1d8902e461818ed01c","target":"record","created_at":"2026-05-17T23:49:57Z","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":"adb36b1be286538543f3cb55dc4c679314710ae3249b9e50fd0412927f610e89","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-02T13:54:31Z","title_canon_sha256":"0345565b63821a51c898045b4398042e3d8f85400a51775889930d26065167d3"},"schema_version":"1.0","source":{"id":"1805.00815","kind":"arxiv","version":2}},"canonical_sha256":"e1a6bc45fe8162d1745807dba735d47057a1ee07b58e57d2a6dc33b7b89b0401","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1a6bc45fe8162d1745807dba735d47057a1ee07b58e57d2a6dc33b7b89b0401","first_computed_at":"2026-05-17T23:49:57.304772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:57.304772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y2gBN0+9u7X/9v/bOe01uCcpfs5nibmzWFXg0OIl1bzO+K+BmLHwZdAvHx63UN5ulpAtFf/T1h9rf1SXzGWLCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:57.305510Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.00815","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9454ec9ac6d76e17b5996322cd8a4e6f313aabe499d01e1d8902e461818ed01c","sha256:e1d7d697b4f19c46d26f6376bdb07367a658ada5919a9592946b7a1eeeaf70bc"],"state_sha256":"bfaf23db95428f357a6de329fc79300bcd8416e8419dd5bdc3194e4a80166248"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zx1D3HkbVZMCpYAogaPADSyXyzBE2DRIGMz3+Iof2zBeHTw4qRUfu2FlAKZQSvSUlVcPpbdGXIcmxrVsZr4KDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T18:27:02.393752Z","bundle_sha256":"9a4aea1d5072ae2f072032db833a161be442ee9d9643fecc02d97753f21b6df8"}}