{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:E4H475IOZ7CGYEPZ75TFLWFLVH","short_pith_number":"pith:E4H475IO","canonical_record":{"source":{"id":"1706.02860","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-09T08:03:37Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"f14faf0afc459402878dad0e06bfb608edf104fe75d147710530f09059dca45e","abstract_canon_sha256":"4e4950fe6388f0db98736d4480e611b981237262cec9b6bcbbd68c3e3c5ebc14"},"schema_version":"1.0"},"canonical_sha256":"270fcff50ecfc46c11f9ff6655d8aba9df23792468fb8c3a7215a3695c08e2b5","source":{"kind":"arxiv","id":"1706.02860","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02860","created_at":"2026-05-18T00:06:16Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02860v2","created_at":"2026-05-18T00:06:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02860","created_at":"2026-05-18T00:06:16Z"},{"alias_kind":"pith_short_12","alias_value":"E4H475IOZ7CG","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"E4H475IOZ7CGYEPZ","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"E4H475IO","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:E4H475IOZ7CGYEPZ75TFLWFLVH","target":"record","payload":{"canonical_record":{"source":{"id":"1706.02860","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-09T08:03:37Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"f14faf0afc459402878dad0e06bfb608edf104fe75d147710530f09059dca45e","abstract_canon_sha256":"4e4950fe6388f0db98736d4480e611b981237262cec9b6bcbbd68c3e3c5ebc14"},"schema_version":"1.0"},"canonical_sha256":"270fcff50ecfc46c11f9ff6655d8aba9df23792468fb8c3a7215a3695c08e2b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:16.391890Z","signature_b64":"Mh8GCTTyhzv/U5FRuBwwrsAGVJpc6joopSdB670rTTf02WwNhJ1UfaWPK/Uj8Pc4cVSR4AGL1coK/ZM7RQdgDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"270fcff50ecfc46c11f9ff6655d8aba9df23792468fb8c3a7215a3695c08e2b5","last_reissued_at":"2026-05-18T00:06:16.391455Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:16.391455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.02860","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":"2026-05-18T00:06:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xPk6un/0p1KEXjf7gA32yA/rEbYfg97YJgN0oN7udebWBRvMiOAlFEafTeAg1xLpYFD6jbQDU5x42JW/UWtaDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:20:03.926389Z"},"content_sha256":"6cec8206a82e198bee7242cd3e4e5e51f45409fe2d65800e4510344bf84bb2b5","schema_version":"1.0","event_id":"sha256:6cec8206a82e198bee7242cd3e4e5e51f45409fe2d65800e4510344bf84bb2b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:E4H475IOZ7CGYEPZ75TFLWFLVH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Integral Forms of Specht Modules Labelled by Hook Partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Susanne Danz, Tommy Hofmann","submitted_at":"2017-06-09T08:03:37Z","abstract_excerpt":"We investigate integral forms of simple modules of symmetric groups over fields of characteristic $0$ labelled by hook partitions. Building on work of Plesken and Craig, for every odd prime $p$, we give a set of representatives of the isomorphism classes of $\\mathbb{Z}_p$-forms of the simple $\\mathbb{Q}_p \\mathfrak{S}_n$-module labelled by the partition $(n-k,1^k)$, where $n\\in\\mathbb{N}$ and $0\\leq k\\leq n-1$. We also settle the analogous question for $p=2$, assuming that $n\\not\\equiv 0\\pmod{4}$ and $k\\in\\{2,n-3\\}$. As a consequence this leads to a set of representatives of the isomorphism cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02860","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":"2026-05-18T00:06:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J154VOIILw4HMz4J1+rjzVZwZttFMAqCeM71qrgFMxVzZIVC7/Hf+LK5BZxRW5x92KzUA7aftGkEw9YeIYlYBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:20:03.926994Z"},"content_sha256":"a950b32daa5655d8dc0f1b57ac9c6740a0a437ace8dd2e76f831f7ca2b440065","schema_version":"1.0","event_id":"sha256:a950b32daa5655d8dc0f1b57ac9c6740a0a437ace8dd2e76f831f7ca2b440065"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E4H475IOZ7CGYEPZ75TFLWFLVH/bundle.json","state_url":"https://pith.science/pith/E4H475IOZ7CGYEPZ75TFLWFLVH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E4H475IOZ7CGYEPZ75TFLWFLVH/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":"2026-06-04T18:20:03Z","links":{"resolver":"https://pith.science/pith/E4H475IOZ7CGYEPZ75TFLWFLVH","bundle":"https://pith.science/pith/E4H475IOZ7CGYEPZ75TFLWFLVH/bundle.json","state":"https://pith.science/pith/E4H475IOZ7CGYEPZ75TFLWFLVH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E4H475IOZ7CGYEPZ75TFLWFLVH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:E4H475IOZ7CGYEPZ75TFLWFLVH","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":"4e4950fe6388f0db98736d4480e611b981237262cec9b6bcbbd68c3e3c5ebc14","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-09T08:03:37Z","title_canon_sha256":"f14faf0afc459402878dad0e06bfb608edf104fe75d147710530f09059dca45e"},"schema_version":"1.0","source":{"id":"1706.02860","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02860","created_at":"2026-05-18T00:06:16Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02860v2","created_at":"2026-05-18T00:06:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02860","created_at":"2026-05-18T00:06:16Z"},{"alias_kind":"pith_short_12","alias_value":"E4H475IOZ7CG","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"E4H475IOZ7CGYEPZ","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"E4H475IO","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:a950b32daa5655d8dc0f1b57ac9c6740a0a437ace8dd2e76f831f7ca2b440065","target":"graph","created_at":"2026-05-18T00:06:16Z","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 investigate integral forms of simple modules of symmetric groups over fields of characteristic $0$ labelled by hook partitions. Building on work of Plesken and Craig, for every odd prime $p$, we give a set of representatives of the isomorphism classes of $\\mathbb{Z}_p$-forms of the simple $\\mathbb{Q}_p \\mathfrak{S}_n$-module labelled by the partition $(n-k,1^k)$, where $n\\in\\mathbb{N}$ and $0\\leq k\\leq n-1$. We also settle the analogous question for $p=2$, assuming that $n\\not\\equiv 0\\pmod{4}$ and $k\\in\\{2,n-3\\}$. As a consequence this leads to a set of representatives of the isomorphism cl","authors_text":"Susanne Danz, Tommy Hofmann","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-09T08:03:37Z","title":"On Integral Forms of Specht Modules Labelled by Hook Partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02860","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":"sha256:6cec8206a82e198bee7242cd3e4e5e51f45409fe2d65800e4510344bf84bb2b5","target":"record","created_at":"2026-05-18T00:06:16Z","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":"4e4950fe6388f0db98736d4480e611b981237262cec9b6bcbbd68c3e3c5ebc14","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-09T08:03:37Z","title_canon_sha256":"f14faf0afc459402878dad0e06bfb608edf104fe75d147710530f09059dca45e"},"schema_version":"1.0","source":{"id":"1706.02860","kind":"arxiv","version":2}},"canonical_sha256":"270fcff50ecfc46c11f9ff6655d8aba9df23792468fb8c3a7215a3695c08e2b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"270fcff50ecfc46c11f9ff6655d8aba9df23792468fb8c3a7215a3695c08e2b5","first_computed_at":"2026-05-18T00:06:16.391455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:16.391455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mh8GCTTyhzv/U5FRuBwwrsAGVJpc6joopSdB670rTTf02WwNhJ1UfaWPK/Uj8Pc4cVSR4AGL1coK/ZM7RQdgDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:16.391890Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.02860","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6cec8206a82e198bee7242cd3e4e5e51f45409fe2d65800e4510344bf84bb2b5","sha256:a950b32daa5655d8dc0f1b57ac9c6740a0a437ace8dd2e76f831f7ca2b440065"],"state_sha256":"a16cbad6d66c9d48ab476eecbc8d2d22ad985fdcb60e7e5ad4f1ce9f6af6af25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tMS0oKKu1ODycjeY6ozUCLDvvbAy1ebTdKhn/F6V+gW3QDjZXtsGh40A/46kimazqtSpY30PYFIg4uz2rsA/Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T18:20:03.931116Z","bundle_sha256":"14f1410b4e24bc7339a3522704d97f6a5f51254c91eac96420f03492a9208257"}}