{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:MFCOFANHA64KP6WZURTNLY7H7A","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":"66456d7f599b0e8986253e0565a1e4bbb8dd71a700ab9bde64535630448ff536","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-09-29T13:14:39Z","title_canon_sha256":"98c8c6e0e825ecda956a360d6fb0c2d9b32595c29159a8208fc3322df15acd05"},"schema_version":"1.0","source":{"id":"0909.5334","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.5334","created_at":"2026-07-04T15:53:16Z"},{"alias_kind":"arxiv_version","alias_value":"0909.5334v1","created_at":"2026-07-04T15:53:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.5334","created_at":"2026-07-04T15:53:16Z"},{"alias_kind":"pith_short_12","alias_value":"MFCOFANHA64K","created_at":"2026-07-04T15:53:16Z"},{"alias_kind":"pith_short_16","alias_value":"MFCOFANHA64KP6WZ","created_at":"2026-07-04T15:53:16Z"},{"alias_kind":"pith_short_8","alias_value":"MFCOFANH","created_at":"2026-07-04T15:53:16Z"}],"graph_snapshots":[{"event_id":"sha256:ff0634606f86ecac43f3c30ee1c67acbca464f383ff20a0884e05634497279c3","target":"graph","created_at":"2026-07-04T15:53:16Z","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/0909.5334/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Gurevich, Pyatov and Saponov recently stated an expansion for the product of two Schur functions and gave a proof based on the Pluecker relations. Here we show that this identity is in fact a special case of a quite general Schur function identity, which was stated and proved in a paper by Fulmek and Kleber, where it was used to prove bijectively Dodgsons condensation formula and the Pluecker relations, but was not paid further attention: So we take the opportunity to make obvious the range of applicability of this identity by giving concrete examples, accompanied by many graphical illustratio","authors_text":"Markus Fulmek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-09-29T13:14:39Z","title":"Bijective proofs for Schur function identities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.5334","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":"sha256:603d37c30ac03b13904308e52b48096eb695548e15380621a60ba76f2dad667a","target":"record","created_at":"2026-07-04T15:53:16Z","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":"66456d7f599b0e8986253e0565a1e4bbb8dd71a700ab9bde64535630448ff536","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-09-29T13:14:39Z","title_canon_sha256":"98c8c6e0e825ecda956a360d6fb0c2d9b32595c29159a8208fc3322df15acd05"},"schema_version":"1.0","source":{"id":"0909.5334","kind":"arxiv","version":1}},"canonical_sha256":"6144e281a707b8a7fad9a466d5e3e7f8015cf514d7f9f0ea7f807af75b9b8e15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6144e281a707b8a7fad9a466d5e3e7f8015cf514d7f9f0ea7f807af75b9b8e15","first_computed_at":"2026-07-04T15:53:16.679907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:53:16.679907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iv+LAWzOXZ+quwS/IzUPkID1vGrjDsq5mniGcH8ypH+F3SBuJV5oukMWgXclIEs9JWYqSd2oyZzcOqExM6CrCg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:53:16.680293Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.5334","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:603d37c30ac03b13904308e52b48096eb695548e15380621a60ba76f2dad667a","sha256:ff0634606f86ecac43f3c30ee1c67acbca464f383ff20a0884e05634497279c3"],"state_sha256":"02d5ed44fd4e6bba7fbb0a70770ddfc349a591398d5c9db815f0b0fa4663cbe5"}