{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:B6H6QDSPUU4IPF3S7A63QKWCOA","short_pith_number":"pith:B6H6QDSP","schema_version":"1.0","canonical_sha256":"0f8fe80e4fa538879772f83db82ac27012cc903c315fc8ef1c7db4262cb71e50","source":{"kind":"arxiv","id":"1510.01657","version":1},"attestation_state":"computed","paper":{"title":"A new generalization of Hermite's reciprocity law","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Daniel Penazzi, Leandro Cagliero","submitted_at":"2015-10-06T16:44:10Z","abstract_excerpt":"Given a partition $\\lambda$ of $n$, the {\\it Schur functor} $\\mathbb{S}_\\lambda$ associates to any complex vector space $V$, a subspace $\\mathbb{S}_\\lambda(V)$ of $V^{\\otimes n}$. Hermite's reciprocity law, in terms of the Schur functor, states that $\n  \\mathbb{S}_{(p)}\\left(\\mathbb{S}_{(q)}(\\mathbb{C}^2)\\right)\\simeq \\mathbb{S}_{(q)}\\left(\\mathbb{S}_{(p)}(\\mathbb{C}^2)\\right). $\nWe extend this identity to many other identities of the type $\\mathbb{S}_{\\lambda}\\left(\\mathbb{S}_{\\delta}(\\mathbb{C}^2)\\right)\\simeq \\mathbb{S}_{\\mu}\\left(\\mathbb{S}_{\\epsilon}(\\mathbb{C}^2)\\right)$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1510.01657","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-06T16:44:10Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"5920d69be469048ad53f832419b22bc75746a4e61b2c2944c9eb449ad12a6cd4","abstract_canon_sha256":"aa9b5387fc3f36268454dc127ddd0c2ae835e9ca7205f2d4ff83366bf20213cf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:56.344173Z","signature_b64":"YUlza2wxDA4HsEBtJCMRTPCuHYuMMqD6WIVrJoaxV+l4LamQz7vPrAGntx77LWtPk95EBK33LoTYZkVl8IsIAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f8fe80e4fa538879772f83db82ac27012cc903c315fc8ef1c7db4262cb71e50","last_reissued_at":"2026-05-18T01:30:56.343701Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:56.343701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A new generalization of Hermite's reciprocity law","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Daniel Penazzi, Leandro Cagliero","submitted_at":"2015-10-06T16:44:10Z","abstract_excerpt":"Given a partition $\\lambda$ of $n$, the {\\it Schur functor} $\\mathbb{S}_\\lambda$ associates to any complex vector space $V$, a subspace $\\mathbb{S}_\\lambda(V)$ of $V^{\\otimes n}$. Hermite's reciprocity law, in terms of the Schur functor, states that $\n  \\mathbb{S}_{(p)}\\left(\\mathbb{S}_{(q)}(\\mathbb{C}^2)\\right)\\simeq \\mathbb{S}_{(q)}\\left(\\mathbb{S}_{(p)}(\\mathbb{C}^2)\\right). $\nWe extend this identity to many other identities of the type $\\mathbb{S}_{\\lambda}\\left(\\mathbb{S}_{\\delta}(\\mathbb{C}^2)\\right)\\simeq \\mathbb{S}_{\\mu}\\left(\\mathbb{S}_{\\epsilon}(\\mathbb{C}^2)\\right)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01657","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1510.01657","created_at":"2026-05-18T01:30:56.343770+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.01657v1","created_at":"2026-05-18T01:30:56.343770+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01657","created_at":"2026-05-18T01:30:56.343770+00:00"},{"alias_kind":"pith_short_12","alias_value":"B6H6QDSPUU4I","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"B6H6QDSPUU4IPF3S","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"B6H6QDSP","created_at":"2026-05-18T12:29:14.074870+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/B6H6QDSPUU4IPF3S7A63QKWCOA","json":"https://pith.science/pith/B6H6QDSPUU4IPF3S7A63QKWCOA.json","graph_json":"https://pith.science/api/pith-number/B6H6QDSPUU4IPF3S7A63QKWCOA/graph.json","events_json":"https://pith.science/api/pith-number/B6H6QDSPUU4IPF3S7A63QKWCOA/events.json","paper":"https://pith.science/paper/B6H6QDSP"},"agent_actions":{"view_html":"https://pith.science/pith/B6H6QDSPUU4IPF3S7A63QKWCOA","download_json":"https://pith.science/pith/B6H6QDSPUU4IPF3S7A63QKWCOA.json","view_paper":"https://pith.science/paper/B6H6QDSP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.01657&json=true","fetch_graph":"https://pith.science/api/pith-number/B6H6QDSPUU4IPF3S7A63QKWCOA/graph.json","fetch_events":"https://pith.science/api/pith-number/B6H6QDSPUU4IPF3S7A63QKWCOA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B6H6QDSPUU4IPF3S7A63QKWCOA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B6H6QDSPUU4IPF3S7A63QKWCOA/action/storage_attestation","attest_author":"https://pith.science/pith/B6H6QDSPUU4IPF3S7A63QKWCOA/action/author_attestation","sign_citation":"https://pith.science/pith/B6H6QDSPUU4IPF3S7A63QKWCOA/action/citation_signature","submit_replication":"https://pith.science/pith/B6H6QDSPUU4IPF3S7A63QKWCOA/action/replication_record"}},"created_at":"2026-05-18T01:30:56.343770+00:00","updated_at":"2026-05-18T01:30:56.343770+00:00"}