{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:RTDTXKBAISW44NSNZFKTFMJQAG","short_pith_number":"pith:RTDTXKBA","canonical_record":{"source":{"id":"2406.13902","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-06-20T00:24:37Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"bdffb9c12c62b40929b724e59039088060a02e462f758fc9b865975fb7d92967","abstract_canon_sha256":"16082ead0f973b8fee1b068d4f4ba8b690c17cd3191de634f7b6d33a7f4b5576"},"schema_version":"1.0"},"canonical_sha256":"8cc73ba82044adce364dc95532b130019d7b28b4f01e0ad8d31810fe68a0ed1c","source":{"kind":"arxiv","id":"2406.13902","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.13902","created_at":"2026-07-05T09:53:41Z"},{"alias_kind":"arxiv_version","alias_value":"2406.13902v3","created_at":"2026-07-05T09:53:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.13902","created_at":"2026-07-05T09:53:41Z"},{"alias_kind":"pith_short_12","alias_value":"RTDTXKBAISW4","created_at":"2026-07-05T09:53:41Z"},{"alias_kind":"pith_short_16","alias_value":"RTDTXKBAISW44NSN","created_at":"2026-07-05T09:53:41Z"},{"alias_kind":"pith_short_8","alias_value":"RTDTXKBA","created_at":"2026-07-05T09:53:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:RTDTXKBAISW44NSNZFKTFMJQAG","target":"record","payload":{"canonical_record":{"source":{"id":"2406.13902","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-06-20T00:24:37Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"bdffb9c12c62b40929b724e59039088060a02e462f758fc9b865975fb7d92967","abstract_canon_sha256":"16082ead0f973b8fee1b068d4f4ba8b690c17cd3191de634f7b6d33a7f4b5576"},"schema_version":"1.0"},"canonical_sha256":"8cc73ba82044adce364dc95532b130019d7b28b4f01e0ad8d31810fe68a0ed1c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:53:41.798180Z","signature_b64":"KOISzRYovi2gEi8qRuLXUW4E4EbRyZhPt5TqLfOS9DrJtexX63cDi1DYMBTdsUVu1KA2VaDOzT/9NqTCoeLaAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8cc73ba82044adce364dc95532b130019d7b28b4f01e0ad8d31810fe68a0ed1c","last_reissued_at":"2026-07-05T09:53:41.797739Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:53:41.797739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.13902","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:53:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Negh3wIhS2pIX6zVjUZS885P+NN20VLxcssZnQ89uIvbR6r7YlOQhTW8qHSfUEz2bDa743JIpik69xcIrjIyAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T14:15:41.701900Z"},"content_sha256":"84152febedf4cd64ab6372d5319dcadff1d323c58df2d331e2e73b799116a15d","schema_version":"1.0","event_id":"sha256:84152febedf4cd64ab6372d5319dcadff1d323c58df2d331e2e73b799116a15d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:RTDTXKBAISW44NSNZFKTFMJQAG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Signed combinatorial interpretations in algebraic combinatorics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Colleen Robichaux, Igor Pak","submitted_at":"2024-06-20T00:24:37Z","abstract_excerpt":"We prove the existence of signed combinatorial interpretations for several large families of structure constants. These families include standard bases of symmetric and quasisymmetric polynomials, as well as various bases in Schubert theory. The results are stated in the language of computational complexity, while the proofs are based on the effective M\\\"obius inversion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.13902","kind":"arxiv","version":3},"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/2406.13902/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":"2026-07-05T09:53:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Atp9/blVvkg81FKccBbs3eV/+Y7jA7h+daRFLKTW9nFi0N+vhPyCbZnd0DTJDTc6B7K935RdFAttY2gfeyXAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T14:15:41.702531Z"},"content_sha256":"cf7dfbd668108eab94a74c985e5c49541ceceba15879d6787094142af4bd6d0f","schema_version":"1.0","event_id":"sha256:cf7dfbd668108eab94a74c985e5c49541ceceba15879d6787094142af4bd6d0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RTDTXKBAISW44NSNZFKTFMJQAG/bundle.json","state_url":"https://pith.science/pith/RTDTXKBAISW44NSNZFKTFMJQAG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RTDTXKBAISW44NSNZFKTFMJQAG/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":"2026-08-03T14:15:41Z","links":{"resolver":"https://pith.science/pith/RTDTXKBAISW44NSNZFKTFMJQAG","bundle":"https://pith.science/pith/RTDTXKBAISW44NSNZFKTFMJQAG/bundle.json","state":"https://pith.science/pith/RTDTXKBAISW44NSNZFKTFMJQAG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RTDTXKBAISW44NSNZFKTFMJQAG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:RTDTXKBAISW44NSNZFKTFMJQAG","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":"16082ead0f973b8fee1b068d4f4ba8b690c17cd3191de634f7b6d33a7f4b5576","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-06-20T00:24:37Z","title_canon_sha256":"bdffb9c12c62b40929b724e59039088060a02e462f758fc9b865975fb7d92967"},"schema_version":"1.0","source":{"id":"2406.13902","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.13902","created_at":"2026-07-05T09:53:41Z"},{"alias_kind":"arxiv_version","alias_value":"2406.13902v3","created_at":"2026-07-05T09:53:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.13902","created_at":"2026-07-05T09:53:41Z"},{"alias_kind":"pith_short_12","alias_value":"RTDTXKBAISW4","created_at":"2026-07-05T09:53:41Z"},{"alias_kind":"pith_short_16","alias_value":"RTDTXKBAISW44NSN","created_at":"2026-07-05T09:53:41Z"},{"alias_kind":"pith_short_8","alias_value":"RTDTXKBA","created_at":"2026-07-05T09:53:41Z"}],"graph_snapshots":[{"event_id":"sha256:cf7dfbd668108eab94a74c985e5c49541ceceba15879d6787094142af4bd6d0f","target":"graph","created_at":"2026-07-05T09:53:41Z","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/2406.13902/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove the existence of signed combinatorial interpretations for several large families of structure constants. These families include standard bases of symmetric and quasisymmetric polynomials, as well as various bases in Schubert theory. The results are stated in the language of computational complexity, while the proofs are based on the effective M\\\"obius inversion.","authors_text":"Colleen Robichaux, Igor Pak","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-06-20T00:24:37Z","title":"Signed combinatorial interpretations in algebraic combinatorics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.13902","kind":"arxiv","version":3},"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":"sha256:84152febedf4cd64ab6372d5319dcadff1d323c58df2d331e2e73b799116a15d","target":"record","created_at":"2026-07-05T09:53:41Z","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":"16082ead0f973b8fee1b068d4f4ba8b690c17cd3191de634f7b6d33a7f4b5576","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-06-20T00:24:37Z","title_canon_sha256":"bdffb9c12c62b40929b724e59039088060a02e462f758fc9b865975fb7d92967"},"schema_version":"1.0","source":{"id":"2406.13902","kind":"arxiv","version":3}},"canonical_sha256":"8cc73ba82044adce364dc95532b130019d7b28b4f01e0ad8d31810fe68a0ed1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8cc73ba82044adce364dc95532b130019d7b28b4f01e0ad8d31810fe68a0ed1c","first_computed_at":"2026-07-05T09:53:41.797739Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:53:41.797739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KOISzRYovi2gEi8qRuLXUW4E4EbRyZhPt5TqLfOS9DrJtexX63cDi1DYMBTdsUVu1KA2VaDOzT/9NqTCoeLaAg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:53:41.798180Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.13902","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84152febedf4cd64ab6372d5319dcadff1d323c58df2d331e2e73b799116a15d","sha256:cf7dfbd668108eab94a74c985e5c49541ceceba15879d6787094142af4bd6d0f"],"state_sha256":"39a7fba23d2b003b92397aca20c231e609e6a3116b37f99b3594b1e7ce233385"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+TSI1GqsXzVpaIKecS1f7kIp/kKjV+FMV3FOiZiR7m8A2ZmBrHvaVDYfaMvFUL4c55QvqZOuq8y1tsjit2biDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T14:15:41.706766Z","bundle_sha256":"0b4abaca1a271c59b2035bcab7c08aa6c340fef037afcf8fa805a64180511fb6"}}