{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GEGBIH7YFXAEVK4RTDLDQ3242Y","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":"880d912a5771ed86df18172d592dc0652784abfa0b83805dcc298ddbdd85804c","cross_cats_sorted":["math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-07-28T00:24:32Z","title_canon_sha256":"6545edb942ce9fedce27d740a0e8620370b25cb4dbc9d0775dac451205de7f30"},"schema_version":"1.0","source":{"id":"1107.5610","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.5610","created_at":"2026-05-18T03:13:00Z"},{"alias_kind":"arxiv_version","alias_value":"1107.5610v2","created_at":"2026-05-18T03:13:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5610","created_at":"2026-05-18T03:13:00Z"},{"alias_kind":"pith_short_12","alias_value":"GEGBIH7YFXAE","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GEGBIH7YFXAEVK4R","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GEGBIH7Y","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:dc3f5e2c9ef0ff37133366f622fcf7f8112d40ad5ef95a07b3eb881c3ef282f2","target":"graph","created_at":"2026-05-18T03:13:00Z","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":"We consider a q-analogue of the standard bilinear form on the commutative ring of symmetric functions. The q=-1 case leads to a Z-graded Hopf superalgebra which we call the algebra of odd symmetric functions. In the odd setting we describe counterparts of the elementary and complete symmetric functions, power sums, Schur functions, and combinatorial interpretations of associated change of basis relations.","authors_text":"Alexander P. Ellis, Mikhail Khovanov","cross_cats":["math.CO","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-07-28T00:24:32Z","title":"The Hopf algebra of odd symmetric functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5610","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:ee1eeaef8cd91d042f186056677a2710e09b2a16e9998b02340f8397fe59f6af","target":"record","created_at":"2026-05-18T03:13:00Z","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":"880d912a5771ed86df18172d592dc0652784abfa0b83805dcc298ddbdd85804c","cross_cats_sorted":["math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-07-28T00:24:32Z","title_canon_sha256":"6545edb942ce9fedce27d740a0e8620370b25cb4dbc9d0775dac451205de7f30"},"schema_version":"1.0","source":{"id":"1107.5610","kind":"arxiv","version":2}},"canonical_sha256":"310c141ff82dc04aab9198d6386f5cd619dd6f1bf4b3bf705c4d0023450e2d18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"310c141ff82dc04aab9198d6386f5cd619dd6f1bf4b3bf705c4d0023450e2d18","first_computed_at":"2026-05-18T03:13:00.606352Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:00.606352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VsP9XSEamOxhD4VpCttL3BLswjyciEhralUdMdZfD4IxfjG0T3Wu2cuNTZmdwknjs9OfxtT08/DxiiPzWCi2CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:00.606992Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.5610","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee1eeaef8cd91d042f186056677a2710e09b2a16e9998b02340f8397fe59f6af","sha256:dc3f5e2c9ef0ff37133366f622fcf7f8112d40ad5ef95a07b3eb881c3ef282f2"],"state_sha256":"9aa9abba5725ce94772248b298cf2aff26694414ea2a1c50c879c1e1f5d0ef63"}