{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:GKUR4VKS23HMEWNAPRERU2Q7G5","short_pith_number":"pith:GKUR4VKS","canonical_record":{"source":{"id":"0704.0836","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2007-04-06T02:43:59Z","cross_cats_sorted":[],"title_canon_sha256":"73ea3d8826fc2b849663a6b492486bfa0a5046559c29499c96d1cf81c2bc46f4","abstract_canon_sha256":"1bdd18b0dc441d1220a12a62ed90336f82e69c80704360b039b5079ee2f40d73"},"schema_version":"1.0"},"canonical_sha256":"32a91e5552d6cec259a07c491a6a1f376884f5b040a897871572f05e736704b2","source":{"kind":"arxiv","id":"0704.0836","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.0836","created_at":"2026-05-18T04:34:37Z"},{"alias_kind":"arxiv_version","alias_value":"0704.0836v2","created_at":"2026-05-18T04:34:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.0836","created_at":"2026-05-18T04:34:37Z"},{"alias_kind":"pith_short_12","alias_value":"GKUR4VKS23HM","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"GKUR4VKS23HMEWNA","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"GKUR4VKS","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:GKUR4VKS23HMEWNAPRERU2Q7G5","target":"record","payload":{"canonical_record":{"source":{"id":"0704.0836","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2007-04-06T02:43:59Z","cross_cats_sorted":[],"title_canon_sha256":"73ea3d8826fc2b849663a6b492486bfa0a5046559c29499c96d1cf81c2bc46f4","abstract_canon_sha256":"1bdd18b0dc441d1220a12a62ed90336f82e69c80704360b039b5079ee2f40d73"},"schema_version":"1.0"},"canonical_sha256":"32a91e5552d6cec259a07c491a6a1f376884f5b040a897871572f05e736704b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:37.659605Z","signature_b64":"/bB+EP67Q40BFiPPes7PlsXeTQWW3hF7a7FT+qt6mb5qQ1IwX0RzuUoZ7gq++L+3h5S9ssXesVGq+rEEuUl4BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32a91e5552d6cec259a07c491a6a1f376884f5b040a897871572f05e736704b2","last_reissued_at":"2026-05-18T04:34:37.658925Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:37.658925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0704.0836","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":"2026-05-18T04:34:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tAOm10MJ9c+k1JZZNwQhrJhjghWPclzIzQJEOKBy/haqWgH2a8vh+6Lar2FW1SNJ9hqHboA2ykMEQHsMAci1CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:52:55.935376Z"},"content_sha256":"51564e766e8aeb7b72454180ccb107c935cd62533d6aa1efc7482292aa7ca4f6","schema_version":"1.0","event_id":"sha256:51564e766e8aeb7b72454180ccb107c935cd62533d6aa1efc7482292aa7ca4f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:GKUR4VKS23HMEWNAPRERU2Q7G5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A matroid-friendly basis for the quasisymmetric functions","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kurt W. Luoto","submitted_at":"2007-04-06T02:43:59Z","abstract_excerpt":"A new Z-basis for the space of quasisymmetric functions (QSym, for short) is presented. It is shown to have nonnegative structure constants, and several interesting properties relative to the space of quasisymmetric functions associated to matroids by the Hopf algebra morphism (F) of Billera, Jia, and Reiner. In particular, for loopless matroids, this basis reflects the grading by matroid rank, as well as by the size of the ground set. It is shown that the morphism F is injective on the set of rank two matroids, and that decomposability of the quasisymmetric function of a rank two matroid mirr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.0836","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":"2026-05-18T04:34:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sh8kxgFG2Ymvr70UMG9NM7cT8SIaFrS4h9x5kOV9tpS7ZxR5MHevMdaHNrPPjIuDFO1TSv5Ga+t/dL2ejZMrBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:52:55.936075Z"},"content_sha256":"d6e85c216c0ae3261c159d6becadb7641d46780bd7a27f610820abdacef4580b","schema_version":"1.0","event_id":"sha256:d6e85c216c0ae3261c159d6becadb7641d46780bd7a27f610820abdacef4580b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GKUR4VKS23HMEWNAPRERU2Q7G5/bundle.json","state_url":"https://pith.science/pith/GKUR4VKS23HMEWNAPRERU2Q7G5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GKUR4VKS23HMEWNAPRERU2Q7G5/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":"2026-06-07T22:52:55Z","links":{"resolver":"https://pith.science/pith/GKUR4VKS23HMEWNAPRERU2Q7G5","bundle":"https://pith.science/pith/GKUR4VKS23HMEWNAPRERU2Q7G5/bundle.json","state":"https://pith.science/pith/GKUR4VKS23HMEWNAPRERU2Q7G5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GKUR4VKS23HMEWNAPRERU2Q7G5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:GKUR4VKS23HMEWNAPRERU2Q7G5","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":"1bdd18b0dc441d1220a12a62ed90336f82e69c80704360b039b5079ee2f40d73","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"2007-04-06T02:43:59Z","title_canon_sha256":"73ea3d8826fc2b849663a6b492486bfa0a5046559c29499c96d1cf81c2bc46f4"},"schema_version":"1.0","source":{"id":"0704.0836","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.0836","created_at":"2026-05-18T04:34:37Z"},{"alias_kind":"arxiv_version","alias_value":"0704.0836v2","created_at":"2026-05-18T04:34:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.0836","created_at":"2026-05-18T04:34:37Z"},{"alias_kind":"pith_short_12","alias_value":"GKUR4VKS23HM","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"GKUR4VKS23HMEWNA","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"GKUR4VKS","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:d6e85c216c0ae3261c159d6becadb7641d46780bd7a27f610820abdacef4580b","target":"graph","created_at":"2026-05-18T04:34:37Z","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 Z-basis for the space of quasisymmetric functions (QSym, for short) is presented. It is shown to have nonnegative structure constants, and several interesting properties relative to the space of quasisymmetric functions associated to matroids by the Hopf algebra morphism (F) of Billera, Jia, and Reiner. In particular, for loopless matroids, this basis reflects the grading by matroid rank, as well as by the size of the ground set. It is shown that the morphism F is injective on the set of rank two matroids, and that decomposability of the quasisymmetric function of a rank two matroid mirr","authors_text":"Kurt W. Luoto","cross_cats":[],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2007-04-06T02:43:59Z","title":"A matroid-friendly basis for the quasisymmetric functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.0836","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":"sha256:51564e766e8aeb7b72454180ccb107c935cd62533d6aa1efc7482292aa7ca4f6","target":"record","created_at":"2026-05-18T04:34:37Z","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":"1bdd18b0dc441d1220a12a62ed90336f82e69c80704360b039b5079ee2f40d73","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"2007-04-06T02:43:59Z","title_canon_sha256":"73ea3d8826fc2b849663a6b492486bfa0a5046559c29499c96d1cf81c2bc46f4"},"schema_version":"1.0","source":{"id":"0704.0836","kind":"arxiv","version":2}},"canonical_sha256":"32a91e5552d6cec259a07c491a6a1f376884f5b040a897871572f05e736704b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32a91e5552d6cec259a07c491a6a1f376884f5b040a897871572f05e736704b2","first_computed_at":"2026-05-18T04:34:37.658925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:37.658925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/bB+EP67Q40BFiPPes7PlsXeTQWW3hF7a7FT+qt6mb5qQ1IwX0RzuUoZ7gq++L+3h5S9ssXesVGq+rEEuUl4BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:37.659605Z","signed_message":"canonical_sha256_bytes"},"source_id":"0704.0836","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51564e766e8aeb7b72454180ccb107c935cd62533d6aa1efc7482292aa7ca4f6","sha256:d6e85c216c0ae3261c159d6becadb7641d46780bd7a27f610820abdacef4580b"],"state_sha256":"f86d96fbd35f17c58b58f053de3192412faa682b7877a3e601f065910ad149ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cXjDqZ+UBQttzxeUR0UnJfcCyLEUtYSF4MfaODqf5NZnvpTRnIijemvJBTTsQlBHhQ79x7MbjDADjmG5A+kXAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T22:52:55.940473Z","bundle_sha256":"9987f058fe7d3925a1e3961a7092193f8972e6f6a1fcb8269321c9dfd9ca5955"}}