{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2AVQIT3KT7PZ5XKQJBXU2ZGYGF","short_pith_number":"pith:2AVQIT3K","canonical_record":{"source":{"id":"1602.02168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-05T21:23:52Z","cross_cats_sorted":[],"title_canon_sha256":"e822d579407f263733ac5835f4be4e0d5848a6ff672bc29d85fcd0ed4b3088c9","abstract_canon_sha256":"1241ba397c252cdd5e42c775703175eba7510ad532a756ae5158c57099a5711d"},"schema_version":"1.0"},"canonical_sha256":"d02b044f6a9fdf9edd50486f4d64d831683747b3096727c2f5e0407e0a0a4c2a","source":{"kind":"arxiv","id":"1602.02168","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02168","created_at":"2026-05-18T01:21:10Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02168v1","created_at":"2026-05-18T01:21:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02168","created_at":"2026-05-18T01:21:10Z"},{"alias_kind":"pith_short_12","alias_value":"2AVQIT3KT7PZ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"2AVQIT3KT7PZ5XKQ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"2AVQIT3K","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2AVQIT3KT7PZ5XKQJBXU2ZGYGF","target":"record","payload":{"canonical_record":{"source":{"id":"1602.02168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-05T21:23:52Z","cross_cats_sorted":[],"title_canon_sha256":"e822d579407f263733ac5835f4be4e0d5848a6ff672bc29d85fcd0ed4b3088c9","abstract_canon_sha256":"1241ba397c252cdd5e42c775703175eba7510ad532a756ae5158c57099a5711d"},"schema_version":"1.0"},"canonical_sha256":"d02b044f6a9fdf9edd50486f4d64d831683747b3096727c2f5e0407e0a0a4c2a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:10.763360Z","signature_b64":"87buBRgVrxu2FSW2U10oHPMShMiGvnr6oJaRPAP4J+t3NuIC3GRHqXJrFovKTeyY6hV7UtycJYI+GEnrW6PhDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d02b044f6a9fdf9edd50486f4d64d831683747b3096727c2f5e0407e0a0a4c2a","last_reissued_at":"2026-05-18T01:21:10.762786Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:10.762786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.02168","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":"2026-05-18T01:21:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u0K+t80LC8C3j76mmBjepOqIGLL82nmykGPtmk81QBvViBLeiB98A0bS4M+/3llRJ3sMIfSihiRGTsRbtOM/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:24:57.632084Z"},"content_sha256":"84081aade8f2063216210ca349b83e539602fd538ef0b73789416020260ebbe5","schema_version":"1.0","event_id":"sha256:84081aade8f2063216210ca349b83e539602fd538ef0b73789416020260ebbe5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2AVQIT3KT7PZ5XKQJBXU2ZGYGF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dimensions of the irreducible representations of the symmetric and alternating group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Korneel Debaene","submitted_at":"2016-02-05T21:23:52Z","abstract_excerpt":"We establish the existence of an irreducible representation of $A_n$ whose dimension does not occur as the dimension of an irreducible representation of $S_n$, and vice versa. This proves a conjecture by Tong-Viet. The main ingredient in the proof is a result on large prime factors in short intervals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02168","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":"2026-05-18T01:21:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ib0HjKnizyCVakBFPrG+XcDyNGl7KjkeUAOaMqU+W52z5FsXCvm3yscEmiV43rKgJw9vK2RUslNMko8SUSdHAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:24:57.632442Z"},"content_sha256":"0f1bf260bcc8dc1f4db85760aa5f503dfb7ce3c4f41db333b1aba437e2c5bb7c","schema_version":"1.0","event_id":"sha256:0f1bf260bcc8dc1f4db85760aa5f503dfb7ce3c4f41db333b1aba437e2c5bb7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2AVQIT3KT7PZ5XKQJBXU2ZGYGF/bundle.json","state_url":"https://pith.science/pith/2AVQIT3KT7PZ5XKQJBXU2ZGYGF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2AVQIT3KT7PZ5XKQJBXU2ZGYGF/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":"2026-06-05T09:24:57Z","links":{"resolver":"https://pith.science/pith/2AVQIT3KT7PZ5XKQJBXU2ZGYGF","bundle":"https://pith.science/pith/2AVQIT3KT7PZ5XKQJBXU2ZGYGF/bundle.json","state":"https://pith.science/pith/2AVQIT3KT7PZ5XKQJBXU2ZGYGF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2AVQIT3KT7PZ5XKQJBXU2ZGYGF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2AVQIT3KT7PZ5XKQJBXU2ZGYGF","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":"1241ba397c252cdd5e42c775703175eba7510ad532a756ae5158c57099a5711d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-05T21:23:52Z","title_canon_sha256":"e822d579407f263733ac5835f4be4e0d5848a6ff672bc29d85fcd0ed4b3088c9"},"schema_version":"1.0","source":{"id":"1602.02168","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02168","created_at":"2026-05-18T01:21:10Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02168v1","created_at":"2026-05-18T01:21:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02168","created_at":"2026-05-18T01:21:10Z"},{"alias_kind":"pith_short_12","alias_value":"2AVQIT3KT7PZ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"2AVQIT3KT7PZ5XKQ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"2AVQIT3K","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:0f1bf260bcc8dc1f4db85760aa5f503dfb7ce3c4f41db333b1aba437e2c5bb7c","target":"graph","created_at":"2026-05-18T01:21:10Z","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 establish the existence of an irreducible representation of $A_n$ whose dimension does not occur as the dimension of an irreducible representation of $S_n$, and vice versa. This proves a conjecture by Tong-Viet. The main ingredient in the proof is a result on large prime factors in short intervals.","authors_text":"Korneel Debaene","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-05T21:23:52Z","title":"Dimensions of the irreducible representations of the symmetric and alternating group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02168","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":"sha256:84081aade8f2063216210ca349b83e539602fd538ef0b73789416020260ebbe5","target":"record","created_at":"2026-05-18T01:21:10Z","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":"1241ba397c252cdd5e42c775703175eba7510ad532a756ae5158c57099a5711d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-05T21:23:52Z","title_canon_sha256":"e822d579407f263733ac5835f4be4e0d5848a6ff672bc29d85fcd0ed4b3088c9"},"schema_version":"1.0","source":{"id":"1602.02168","kind":"arxiv","version":1}},"canonical_sha256":"d02b044f6a9fdf9edd50486f4d64d831683747b3096727c2f5e0407e0a0a4c2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d02b044f6a9fdf9edd50486f4d64d831683747b3096727c2f5e0407e0a0a4c2a","first_computed_at":"2026-05-18T01:21:10.762786Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:10.762786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"87buBRgVrxu2FSW2U10oHPMShMiGvnr6oJaRPAP4J+t3NuIC3GRHqXJrFovKTeyY6hV7UtycJYI+GEnrW6PhDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:10.763360Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.02168","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84081aade8f2063216210ca349b83e539602fd538ef0b73789416020260ebbe5","sha256:0f1bf260bcc8dc1f4db85760aa5f503dfb7ce3c4f41db333b1aba437e2c5bb7c"],"state_sha256":"f232f301c6a0605ebf0337e7a41dc09c40f212349b0875ee8800f6d207d95104"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8vbMEqux71NQu/ehgVg1Ylbx8QI9Ngh9ej1q/O5XvOVtENydIXUEzN62D0uU6+USacV+eO21RK/2tFhdtulWBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T09:24:57.634406Z","bundle_sha256":"d6b3b53bf1653431734ba653b636f549dc2de92fc7ed053896c6a9e8e3ac1f9f"}}