{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:FVAQIBKG2YILMAVAOIP2YPCUER","short_pith_number":"pith:FVAQIBKG","canonical_record":{"source":{"id":"2505.17904","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-05-23T13:51:25Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"fb49ee723e096be8bb33e79a8c68ce2f3da7b2a3e62d214e92fc18ebbf52896d","abstract_canon_sha256":"c074fde29cf491d0f8bc0d47b03d86263f26e9f0e665a024c94a9a68b6042058"},"schema_version":"1.0"},"canonical_sha256":"2d41040546d610b602a0721fac3c54245a472894860a508cd162b3c70389670f","source":{"kind":"arxiv","id":"2505.17904","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.17904","created_at":"2026-07-05T11:08:33Z"},{"alias_kind":"arxiv_version","alias_value":"2505.17904v1","created_at":"2026-07-05T11:08:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.17904","created_at":"2026-07-05T11:08:33Z"},{"alias_kind":"pith_short_12","alias_value":"FVAQIBKG2YIL","created_at":"2026-07-05T11:08:33Z"},{"alias_kind":"pith_short_16","alias_value":"FVAQIBKG2YILMAVA","created_at":"2026-07-05T11:08:33Z"},{"alias_kind":"pith_short_8","alias_value":"FVAQIBKG","created_at":"2026-07-05T11:08:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:FVAQIBKG2YILMAVAOIP2YPCUER","target":"record","payload":{"canonical_record":{"source":{"id":"2505.17904","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-05-23T13:51:25Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"fb49ee723e096be8bb33e79a8c68ce2f3da7b2a3e62d214e92fc18ebbf52896d","abstract_canon_sha256":"c074fde29cf491d0f8bc0d47b03d86263f26e9f0e665a024c94a9a68b6042058"},"schema_version":"1.0"},"canonical_sha256":"2d41040546d610b602a0721fac3c54245a472894860a508cd162b3c70389670f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:08:33.519024Z","signature_b64":"EsBXnQZ03q0t9OfoIqTgidCrgfHKRwceIvEpNbJDCUtCHShTvn+bVdcKtQDake/KCwq99aVKdc8NxOULlU2eDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d41040546d610b602a0721fac3c54245a472894860a508cd162b3c70389670f","last_reissued_at":"2026-07-05T11:08:33.518570Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:08:33.518570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.17904","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":"2026-07-05T11:08:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"McFkhdiBTwBpVrA3nkTSOENXK+1x2P0m4TMKWudQtrKHB5nXaoJFgOZ+G30CZEFOlctEaQOQy7qptekZI5RnAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T02:02:52.262822Z"},"content_sha256":"75df3077d498129b39162b77354345be4d442fea777b23e7ed882b87305aabf8","schema_version":"1.0","event_id":"sha256:75df3077d498129b39162b77354345be4d442fea777b23e7ed882b87305aabf8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:FVAQIBKG2YILMAVAOIP2YPCUER","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimal numbers of linear constituents in Sylow restrictions for symmetric groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Bim Gustavsson, Stacey Law","submitted_at":"2025-05-23T13:51:25Z","abstract_excerpt":"Let $p$ be any prime. We determine precisely those irreducible characters of symmetric groups which contain at most $p$ distinct linear constituents in their restriction to a Sylow $p$-subgroup, answering a question of Giannelli and Navarro. Moreover, we identify all of the linear constituents of such characters, and in the case $p = 2$ explicitly calculate a new class of Sylow branching coefficients for symmetric groups indexed by so-called almost hook partitions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.17904","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.17904/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:08:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v4bvFZQ/sg/vP6OQdz/eEkz1IqheHTwSU5QIFkLMa6Dz8H7BcbCf2Jk/Sf8Qf4Pn9+o69GTI8k605VONYJrMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T02:02:52.263198Z"},"content_sha256":"2586497d9e96e478b6dd3398361c0bcbef066299116e7ef0a107d73e8927262e","schema_version":"1.0","event_id":"sha256:2586497d9e96e478b6dd3398361c0bcbef066299116e7ef0a107d73e8927262e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FVAQIBKG2YILMAVAOIP2YPCUER/bundle.json","state_url":"https://pith.science/pith/FVAQIBKG2YILMAVAOIP2YPCUER/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FVAQIBKG2YILMAVAOIP2YPCUER/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":"2026-07-11T02:02:52Z","links":{"resolver":"https://pith.science/pith/FVAQIBKG2YILMAVAOIP2YPCUER","bundle":"https://pith.science/pith/FVAQIBKG2YILMAVAOIP2YPCUER/bundle.json","state":"https://pith.science/pith/FVAQIBKG2YILMAVAOIP2YPCUER/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FVAQIBKG2YILMAVAOIP2YPCUER/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FVAQIBKG2YILMAVAOIP2YPCUER","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":"c074fde29cf491d0f8bc0d47b03d86263f26e9f0e665a024c94a9a68b6042058","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-05-23T13:51:25Z","title_canon_sha256":"fb49ee723e096be8bb33e79a8c68ce2f3da7b2a3e62d214e92fc18ebbf52896d"},"schema_version":"1.0","source":{"id":"2505.17904","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.17904","created_at":"2026-07-05T11:08:33Z"},{"alias_kind":"arxiv_version","alias_value":"2505.17904v1","created_at":"2026-07-05T11:08:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.17904","created_at":"2026-07-05T11:08:33Z"},{"alias_kind":"pith_short_12","alias_value":"FVAQIBKG2YIL","created_at":"2026-07-05T11:08:33Z"},{"alias_kind":"pith_short_16","alias_value":"FVAQIBKG2YILMAVA","created_at":"2026-07-05T11:08:33Z"},{"alias_kind":"pith_short_8","alias_value":"FVAQIBKG","created_at":"2026-07-05T11:08:33Z"}],"graph_snapshots":[{"event_id":"sha256:2586497d9e96e478b6dd3398361c0bcbef066299116e7ef0a107d73e8927262e","target":"graph","created_at":"2026-07-05T11:08:33Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.17904/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $p$ be any prime. We determine precisely those irreducible characters of symmetric groups which contain at most $p$ distinct linear constituents in their restriction to a Sylow $p$-subgroup, answering a question of Giannelli and Navarro. Moreover, we identify all of the linear constituents of such characters, and in the case $p = 2$ explicitly calculate a new class of Sylow branching coefficients for symmetric groups indexed by so-called almost hook partitions.","authors_text":"Bim Gustavsson, Stacey Law","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-05-23T13:51:25Z","title":"Minimal numbers of linear constituents in Sylow restrictions for symmetric groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.17904","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":"sha256:75df3077d498129b39162b77354345be4d442fea777b23e7ed882b87305aabf8","target":"record","created_at":"2026-07-05T11:08:33Z","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":"c074fde29cf491d0f8bc0d47b03d86263f26e9f0e665a024c94a9a68b6042058","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-05-23T13:51:25Z","title_canon_sha256":"fb49ee723e096be8bb33e79a8c68ce2f3da7b2a3e62d214e92fc18ebbf52896d"},"schema_version":"1.0","source":{"id":"2505.17904","kind":"arxiv","version":1}},"canonical_sha256":"2d41040546d610b602a0721fac3c54245a472894860a508cd162b3c70389670f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d41040546d610b602a0721fac3c54245a472894860a508cd162b3c70389670f","first_computed_at":"2026-07-05T11:08:33.518570Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:08:33.518570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EsBXnQZ03q0t9OfoIqTgidCrgfHKRwceIvEpNbJDCUtCHShTvn+bVdcKtQDake/KCwq99aVKdc8NxOULlU2eDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:08:33.519024Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.17904","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75df3077d498129b39162b77354345be4d442fea777b23e7ed882b87305aabf8","sha256:2586497d9e96e478b6dd3398361c0bcbef066299116e7ef0a107d73e8927262e"],"state_sha256":"94a44f488788b15da1fed0e48b69222a8dc8c9feeb2a2ac5e8649912b80bd2dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rof0FV+gFoye7mGZLseB1+zXQmMEoeq60rKjnb2P9b6h4hkn1SRSuvcO3MnoTvNLKjDwqs2GvqGn4WMf9MxSCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-11T02:02:52.265852Z","bundle_sha256":"c3fe692af64eb6797e7f33f42cdef74dbf0ec120eb18a374d4eb96d447eaaa0a"}}