{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:Q6ZMDUJ5H2DWBGWY7ZBOWCXSRW","short_pith_number":"pith:Q6ZMDUJ5","canonical_record":{"source":{"id":"1705.05454","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-15T21:11:30Z","cross_cats_sorted":["math.PR","math.RT"],"title_canon_sha256":"8ed3d535b4d9676a920a151d942989ca4baeeb744f7d39d05fe10ecf5987d630","abstract_canon_sha256":"91b989f97511d32dbc5b31bc857c64af191ef549f0f2d5c5358292af696eef50"},"schema_version":"1.0"},"canonical_sha256":"87b2c1d13d3e87609ad8fe42eb0af28d97f6be6fb91cccf8245b74e9e3765a88","source":{"kind":"arxiv","id":"1705.05454","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05454","created_at":"2026-05-18T00:38:02Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05454v2","created_at":"2026-05-18T00:38:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05454","created_at":"2026-05-18T00:38:02Z"},{"alias_kind":"pith_short_12","alias_value":"Q6ZMDUJ5H2DW","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q6ZMDUJ5H2DWBGWY","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q6ZMDUJ5","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:Q6ZMDUJ5H2DWBGWY7ZBOWCXSRW","target":"record","payload":{"canonical_record":{"source":{"id":"1705.05454","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-15T21:11:30Z","cross_cats_sorted":["math.PR","math.RT"],"title_canon_sha256":"8ed3d535b4d9676a920a151d942989ca4baeeb744f7d39d05fe10ecf5987d630","abstract_canon_sha256":"91b989f97511d32dbc5b31bc857c64af191ef549f0f2d5c5358292af696eef50"},"schema_version":"1.0"},"canonical_sha256":"87b2c1d13d3e87609ad8fe42eb0af28d97f6be6fb91cccf8245b74e9e3765a88","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:02.631506Z","signature_b64":"Noi8ukCxVTVEC3FMlpjXjQxeiavSyOzPRHJ7NhH1YjiF/tZTDZ4cyE6sYhG4NP4T16AP/hYLxFTy22/zeYkSBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87b2c1d13d3e87609ad8fe42eb0af28d97f6be6fb91cccf8245b74e9e3765a88","last_reissued_at":"2026-05-18T00:38:02.630893Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:02.630893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.05454","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:38:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IW3o9Uuj1/rz+/LkbmVqbkfz7C8M+W9q+1iVBflzcOO7TaiWVOGrjiOrvDgZU9m1+BU5a1ctj/yrmvwbDtjZAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T20:34:34.990098Z"},"content_sha256":"2e3cec5cab966ab897202055b53bb5418102125bd28ee6ebca6592a424820c65","schema_version":"1.0","event_id":"sha256:2e3cec5cab966ab897202055b53bb5418102125bd28ee6ebca6592a424820c65"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:Q6ZMDUJ5H2DWBGWY7ZBOWCXSRW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A $q$-deformation of the symplectic Schur functions and the Berele insertion algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","math.RT"],"primary_cat":"math.CO","authors_text":"Ioanna Nteka","submitted_at":"2017-05-15T21:11:30Z","abstract_excerpt":"A randomisation of the Berele insertion algorithm is proposed, where the insertion of a letter to a symplectic Young tableau leads to a distribution over the set of symplectic Young tableaux. Berele's algorithm provides a bijection between words from an alphabet and a symplectic Young tableau along with a recording oscillating tableau. The randomised version of the algorithm is achieved by introducing a parameter $0 < q < 1$. The classic Berele algorithm corresponds to letting the parameter $q \\to 0$. The new version provides a probabilistic framework that allows to prove Littlewood-type ident"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05454","kind":"arxiv","version":2},"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":"2026-05-18T00:38:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yjym8gNiRteRQUzSeI48qDvQIkLnyiYKctYpJrhNeFOvH0P/j8rCoZ2EWL3WeFsZXBa4+xWX4yQSQ08Xg1uQBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T20:34:34.990450Z"},"content_sha256":"025e17f0b840542efbbe1f20bcb741ad61b81e339b25f16d5b5707f2ae30ba88","schema_version":"1.0","event_id":"sha256:025e17f0b840542efbbe1f20bcb741ad61b81e339b25f16d5b5707f2ae30ba88"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q6ZMDUJ5H2DWBGWY7ZBOWCXSRW/bundle.json","state_url":"https://pith.science/pith/Q6ZMDUJ5H2DWBGWY7ZBOWCXSRW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q6ZMDUJ5H2DWBGWY7ZBOWCXSRW/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":"2026-06-26T20:34:34Z","links":{"resolver":"https://pith.science/pith/Q6ZMDUJ5H2DWBGWY7ZBOWCXSRW","bundle":"https://pith.science/pith/Q6ZMDUJ5H2DWBGWY7ZBOWCXSRW/bundle.json","state":"https://pith.science/pith/Q6ZMDUJ5H2DWBGWY7ZBOWCXSRW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q6ZMDUJ5H2DWBGWY7ZBOWCXSRW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Q6ZMDUJ5H2DWBGWY7ZBOWCXSRW","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":"91b989f97511d32dbc5b31bc857c64af191ef549f0f2d5c5358292af696eef50","cross_cats_sorted":["math.PR","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-15T21:11:30Z","title_canon_sha256":"8ed3d535b4d9676a920a151d942989ca4baeeb744f7d39d05fe10ecf5987d630"},"schema_version":"1.0","source":{"id":"1705.05454","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05454","created_at":"2026-05-18T00:38:02Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05454v2","created_at":"2026-05-18T00:38:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05454","created_at":"2026-05-18T00:38:02Z"},{"alias_kind":"pith_short_12","alias_value":"Q6ZMDUJ5H2DW","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q6ZMDUJ5H2DWBGWY","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q6ZMDUJ5","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:025e17f0b840542efbbe1f20bcb741ad61b81e339b25f16d5b5707f2ae30ba88","target":"graph","created_at":"2026-05-18T00:38:02Z","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":"A randomisation of the Berele insertion algorithm is proposed, where the insertion of a letter to a symplectic Young tableau leads to a distribution over the set of symplectic Young tableaux. Berele's algorithm provides a bijection between words from an alphabet and a symplectic Young tableau along with a recording oscillating tableau. The randomised version of the algorithm is achieved by introducing a parameter $0 < q < 1$. The classic Berele algorithm corresponds to letting the parameter $q \\to 0$. The new version provides a probabilistic framework that allows to prove Littlewood-type ident","authors_text":"Ioanna Nteka","cross_cats":["math.PR","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-15T21:11:30Z","title":"A $q$-deformation of the symplectic Schur functions and the Berele insertion algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05454","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":"sha256:2e3cec5cab966ab897202055b53bb5418102125bd28ee6ebca6592a424820c65","target":"record","created_at":"2026-05-18T00:38:02Z","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":"91b989f97511d32dbc5b31bc857c64af191ef549f0f2d5c5358292af696eef50","cross_cats_sorted":["math.PR","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-15T21:11:30Z","title_canon_sha256":"8ed3d535b4d9676a920a151d942989ca4baeeb744f7d39d05fe10ecf5987d630"},"schema_version":"1.0","source":{"id":"1705.05454","kind":"arxiv","version":2}},"canonical_sha256":"87b2c1d13d3e87609ad8fe42eb0af28d97f6be6fb91cccf8245b74e9e3765a88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87b2c1d13d3e87609ad8fe42eb0af28d97f6be6fb91cccf8245b74e9e3765a88","first_computed_at":"2026-05-18T00:38:02.630893Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:02.630893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Noi8ukCxVTVEC3FMlpjXjQxeiavSyOzPRHJ7NhH1YjiF/tZTDZ4cyE6sYhG4NP4T16AP/hYLxFTy22/zeYkSBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:02.631506Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.05454","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e3cec5cab966ab897202055b53bb5418102125bd28ee6ebca6592a424820c65","sha256:025e17f0b840542efbbe1f20bcb741ad61b81e339b25f16d5b5707f2ae30ba88"],"state_sha256":"53f44636c045ad4812ac44c574dba667638becc02f7a1aadd8e3286a01051075"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XcdDenyGGX4STJeN1rUjG/RzR8QowtDgWtp+R3ZA/fHYWlqG/C8rTjW15abrk1LsPJLa2vWl9Yekpi8lc0FsBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T20:34:34.992219Z","bundle_sha256":"0e4f356902f14b725fdc3423241434b53f375d52d2a62f32eb489130f7a9b110"}}