{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:B6H6QDSPUU4IPF3S7A63QKWCOA","short_pith_number":"pith:B6H6QDSP","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"},"canonical_sha256":"0f8fe80e4fa538879772f83db82ac27012cc903c315fc8ef1c7db4262cb71e50","source":{"kind":"arxiv","id":"1510.01657","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.01657","created_at":"2026-05-18T01:30:56Z"},{"alias_kind":"arxiv_version","alias_value":"1510.01657v1","created_at":"2026-05-18T01:30:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01657","created_at":"2026-05-18T01:30:56Z"},{"alias_kind":"pith_short_12","alias_value":"B6H6QDSPUU4I","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"B6H6QDSPUU4IPF3S","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"B6H6QDSP","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:B6H6QDSPUU4IPF3S7A63QKWCOA","target":"record","payload":{"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"},"canonical_sha256":"0f8fe80e4fa538879772f83db82ac27012cc903c315fc8ef1c7db4262cb71e50","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"},"source_kind":"arxiv","source_id":"1510.01657","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ncTGGI5XtgR5jLy1bFUaOZm1nl5/aJ3S2KGOOjkuwb07gXeO/ieQf1ZTdcSSUtkp24V6dobo836+97ni5N/4Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T09:47:41.396946Z"},"content_sha256":"972ad6ea7d5d85e8c5f811bc4eb55c63d6f10b7634bc06b87395c051c41894e1","schema_version":"1.0","event_id":"sha256:972ad6ea7d5d85e8c5f811bc4eb55c63d6f10b7634bc06b87395c051c41894e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:B6H6QDSPUU4IPF3S7A63QKWCOA","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BGlIT9XCUjk2pONr7cltK8KeGHAgt3VIcFCQLj9DD9jYss3rw5EAXTs1EqBFcr29tRG9QpN4d6dZ9pyC2tKLAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T09:47:41.397296Z"},"content_sha256":"687cdb4a4ed6344256780bc0b67a4fa9cd4faf10bd9c99529e31ee646c75ed50","schema_version":"1.0","event_id":"sha256:687cdb4a4ed6344256780bc0b67a4fa9cd4faf10bd9c99529e31ee646c75ed50"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B6H6QDSPUU4IPF3S7A63QKWCOA/bundle.json","state_url":"https://pith.science/pith/B6H6QDSPUU4IPF3S7A63QKWCOA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B6H6QDSPUU4IPF3S7A63QKWCOA/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":"2026-06-27T09:47:41Z","links":{"resolver":"https://pith.science/pith/B6H6QDSPUU4IPF3S7A63QKWCOA","bundle":"https://pith.science/pith/B6H6QDSPUU4IPF3S7A63QKWCOA/bundle.json","state":"https://pith.science/pith/B6H6QDSPUU4IPF3S7A63QKWCOA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B6H6QDSPUU4IPF3S7A63QKWCOA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:B6H6QDSPUU4IPF3S7A63QKWCOA","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":"aa9b5387fc3f36268454dc127ddd0c2ae835e9ca7205f2d4ff83366bf20213cf","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-06T16:44:10Z","title_canon_sha256":"5920d69be469048ad53f832419b22bc75746a4e61b2c2944c9eb449ad12a6cd4"},"schema_version":"1.0","source":{"id":"1510.01657","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.01657","created_at":"2026-05-18T01:30:56Z"},{"alias_kind":"arxiv_version","alias_value":"1510.01657v1","created_at":"2026-05-18T01:30:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01657","created_at":"2026-05-18T01:30:56Z"},{"alias_kind":"pith_short_12","alias_value":"B6H6QDSPUU4I","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"B6H6QDSPUU4IPF3S","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"B6H6QDSP","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:687cdb4a4ed6344256780bc0b67a4fa9cd4faf10bd9c99529e31ee646c75ed50","target":"graph","created_at":"2026-05-18T01:30:56Z","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":"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 $\\mathbb{S}_{\\lambda}\\left(\\mathbb{S}_{\\delta}(\\mathbb{C}^2)\\right)\\simeq \\mathbb{S}_{\\mu}\\left(\\mathbb{S}_{\\epsilon}(\\mathbb{C}^2)\\right)$.","authors_text":"Daniel Penazzi, Leandro Cagliero","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-06T16:44:10Z","title":"A new generalization of Hermite's reciprocity law"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01657","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":"sha256:972ad6ea7d5d85e8c5f811bc4eb55c63d6f10b7634bc06b87395c051c41894e1","target":"record","created_at":"2026-05-18T01:30:56Z","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":"aa9b5387fc3f36268454dc127ddd0c2ae835e9ca7205f2d4ff83366bf20213cf","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-06T16:44:10Z","title_canon_sha256":"5920d69be469048ad53f832419b22bc75746a4e61b2c2944c9eb449ad12a6cd4"},"schema_version":"1.0","source":{"id":"1510.01657","kind":"arxiv","version":1}},"canonical_sha256":"0f8fe80e4fa538879772f83db82ac27012cc903c315fc8ef1c7db4262cb71e50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f8fe80e4fa538879772f83db82ac27012cc903c315fc8ef1c7db4262cb71e50","first_computed_at":"2026-05-18T01:30:56.343701Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:56.343701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YUlza2wxDA4HsEBtJCMRTPCuHYuMMqD6WIVrJoaxV+l4LamQz7vPrAGntx77LWtPk95EBK33LoTYZkVl8IsIAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:56.344173Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.01657","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:972ad6ea7d5d85e8c5f811bc4eb55c63d6f10b7634bc06b87395c051c41894e1","sha256:687cdb4a4ed6344256780bc0b67a4fa9cd4faf10bd9c99529e31ee646c75ed50"],"state_sha256":"e7537dd34a31f9bcb2bd42f4e4232f6406b02968eb4ee323c5823b8cf0a3acc3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6HDAzTvHUMZ/vBZqguaLt7tyfhEKwIRoUer+8fzk4FFexJTgEv4vtkET5S2pJfI4u6iSx+JqZqlKIhQiT2U2CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T09:47:41.399251Z","bundle_sha256":"3ca2a587ed3b3bd6c8a489fba51e54bc099368b37524e4e688c83d36c5c5d992"}}