{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:NFGB3WC6W5IH4I4YOO5SCTNK5R","short_pith_number":"pith:NFGB3WC6","canonical_record":{"source":{"id":"1409.0734","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-02T14:47:05Z","cross_cats_sorted":[],"title_canon_sha256":"588ff502ab342bdad8aa99ce73f38cd3f1f7b879385c5c58488b3d6bf4c2b5d8","abstract_canon_sha256":"abfc26a98e823e80e6dc50ca0f4bc176e2e58df1145a5ede7fe7ec65c2dc370e"},"schema_version":"1.0"},"canonical_sha256":"694c1dd85eb7507e239873bb214daaec4d6958a8fe033ab88c4fa147b01a8fab","source":{"kind":"arxiv","id":"1409.0734","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0734","created_at":"2026-05-18T01:20:17Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0734v2","created_at":"2026-05-18T01:20:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0734","created_at":"2026-05-18T01:20:17Z"},{"alias_kind":"pith_short_12","alias_value":"NFGB3WC6W5IH","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NFGB3WC6W5IH4I4Y","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NFGB3WC6","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:NFGB3WC6W5IH4I4YOO5SCTNK5R","target":"record","payload":{"canonical_record":{"source":{"id":"1409.0734","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-02T14:47:05Z","cross_cats_sorted":[],"title_canon_sha256":"588ff502ab342bdad8aa99ce73f38cd3f1f7b879385c5c58488b3d6bf4c2b5d8","abstract_canon_sha256":"abfc26a98e823e80e6dc50ca0f4bc176e2e58df1145a5ede7fe7ec65c2dc370e"},"schema_version":"1.0"},"canonical_sha256":"694c1dd85eb7507e239873bb214daaec4d6958a8fe033ab88c4fa147b01a8fab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:17.611942Z","signature_b64":"3kAdPRBCcJ2G6U5DCCAesKBfdl9jsbyZwBUWmyEJ8TitPZyWYZzoiqo9g4wvaD786LnxnF351yZ7cK5uI2f8BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"694c1dd85eb7507e239873bb214daaec4d6958a8fe033ab88c4fa147b01a8fab","last_reissued_at":"2026-05-18T01:20:17.611446Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:17.611446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.0734","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":"2026-05-18T01:20:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tpTgCO70umNj6P6yD1T7/owFZammAzjQezLTqyxUvBC+4UrphNkPgjgUCOujVGi3v0ugLAbGIyux87VCpMe8Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:26:48.512632Z"},"content_sha256":"f0f47d9ef500f02379852a1f53bfb077fe9235dfd2d9adb86d64e4683076a7d4","schema_version":"1.0","event_id":"sha256:f0f47d9ef500f02379852a1f53bfb077fe9235dfd2d9adb86d64e4683076a7d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:NFGB3WC6W5IH4I4YOO5SCTNK5R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relationships between plethysm coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Melanie de Boeck","submitted_at":"2014-09-02T14:47:05Z","abstract_excerpt":"We consider the plethysm problem stated for representations of symmetric groups. In particular, we prove new relationships between composition multiplicities of twisted Foulkes modules. Expressed in terms of symmetric functions, our results establish relationships between plethysm coefficients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0734","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":"2026-05-18T01:20:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ZACsbwxayL3DD+BxBakk3rw+wDJ7jEj5xvVB9itOBq/uZomu3x2QMwi/b20/9Q5zEmg8iPXY2q+kEzn7nGDAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:26:48.512983Z"},"content_sha256":"4e4d89bd623a83fd8db77afd9d1621249ad2c6fe0e3ed1cbf5d53e96c072cd60","schema_version":"1.0","event_id":"sha256:4e4d89bd623a83fd8db77afd9d1621249ad2c6fe0e3ed1cbf5d53e96c072cd60"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NFGB3WC6W5IH4I4YOO5SCTNK5R/bundle.json","state_url":"https://pith.science/pith/NFGB3WC6W5IH4I4YOO5SCTNK5R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NFGB3WC6W5IH4I4YOO5SCTNK5R/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":"2026-06-05T10:26:48Z","links":{"resolver":"https://pith.science/pith/NFGB3WC6W5IH4I4YOO5SCTNK5R","bundle":"https://pith.science/pith/NFGB3WC6W5IH4I4YOO5SCTNK5R/bundle.json","state":"https://pith.science/pith/NFGB3WC6W5IH4I4YOO5SCTNK5R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NFGB3WC6W5IH4I4YOO5SCTNK5R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NFGB3WC6W5IH4I4YOO5SCTNK5R","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":"abfc26a98e823e80e6dc50ca0f4bc176e2e58df1145a5ede7fe7ec65c2dc370e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-02T14:47:05Z","title_canon_sha256":"588ff502ab342bdad8aa99ce73f38cd3f1f7b879385c5c58488b3d6bf4c2b5d8"},"schema_version":"1.0","source":{"id":"1409.0734","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0734","created_at":"2026-05-18T01:20:17Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0734v2","created_at":"2026-05-18T01:20:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0734","created_at":"2026-05-18T01:20:17Z"},{"alias_kind":"pith_short_12","alias_value":"NFGB3WC6W5IH","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NFGB3WC6W5IH4I4Y","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NFGB3WC6","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:4e4d89bd623a83fd8db77afd9d1621249ad2c6fe0e3ed1cbf5d53e96c072cd60","target":"graph","created_at":"2026-05-18T01:20:17Z","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 the plethysm problem stated for representations of symmetric groups. In particular, we prove new relationships between composition multiplicities of twisted Foulkes modules. Expressed in terms of symmetric functions, our results establish relationships between plethysm coefficients.","authors_text":"Melanie de Boeck","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-02T14:47:05Z","title":"Relationships between plethysm coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0734","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:f0f47d9ef500f02379852a1f53bfb077fe9235dfd2d9adb86d64e4683076a7d4","target":"record","created_at":"2026-05-18T01:20:17Z","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":"abfc26a98e823e80e6dc50ca0f4bc176e2e58df1145a5ede7fe7ec65c2dc370e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-02T14:47:05Z","title_canon_sha256":"588ff502ab342bdad8aa99ce73f38cd3f1f7b879385c5c58488b3d6bf4c2b5d8"},"schema_version":"1.0","source":{"id":"1409.0734","kind":"arxiv","version":2}},"canonical_sha256":"694c1dd85eb7507e239873bb214daaec4d6958a8fe033ab88c4fa147b01a8fab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"694c1dd85eb7507e239873bb214daaec4d6958a8fe033ab88c4fa147b01a8fab","first_computed_at":"2026-05-18T01:20:17.611446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:17.611446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3kAdPRBCcJ2G6U5DCCAesKBfdl9jsbyZwBUWmyEJ8TitPZyWYZzoiqo9g4wvaD786LnxnF351yZ7cK5uI2f8BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:17.611942Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.0734","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0f47d9ef500f02379852a1f53bfb077fe9235dfd2d9adb86d64e4683076a7d4","sha256:4e4d89bd623a83fd8db77afd9d1621249ad2c6fe0e3ed1cbf5d53e96c072cd60"],"state_sha256":"39df434bcd0f7c9cb85160c6c44486eafbfabab01d156489827cc58c40120a7b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v3zXWMYniJhzTvAuedRMt5P+Wv4gSIOl+wzk4ERra3YwLUYGHavZVDzZfCthiNwJfqF88PpOd5a0r4koHJoRAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T10:26:48.515263Z","bundle_sha256":"1cd407c3d821935409798bd0e2d186032505549c6955c758460f927453fc3d1b"}}