{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:UDHGCBGFAD2KWOFAABYJOQIS4S","short_pith_number":"pith:UDHGCBGF","canonical_record":{"source":{"id":"2503.17552","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-03-21T21:55:36Z","cross_cats_sorted":[],"title_canon_sha256":"e1e33d7c7ea3f3cb98f7ad60feb61d4e5a526d9b6d06b62c23c7ec40e1516519","abstract_canon_sha256":"7af99b176be97fc8ed9b9614a1184938bcb14b2c440f8eec74809ae460d439b2"},"schema_version":"1.0"},"canonical_sha256":"a0ce6104c500f4ab38a00070974112e4ad8a18427fcf1cc54341bb25a34b7e1f","source":{"kind":"arxiv","id":"2503.17552","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.17552","created_at":"2026-07-05T10:37:11Z"},{"alias_kind":"arxiv_version","alias_value":"2503.17552v1","created_at":"2026-07-05T10:37:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.17552","created_at":"2026-07-05T10:37:11Z"},{"alias_kind":"pith_short_12","alias_value":"UDHGCBGFAD2K","created_at":"2026-07-05T10:37:11Z"},{"alias_kind":"pith_short_16","alias_value":"UDHGCBGFAD2KWOFA","created_at":"2026-07-05T10:37:11Z"},{"alias_kind":"pith_short_8","alias_value":"UDHGCBGF","created_at":"2026-07-05T10:37:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:UDHGCBGFAD2KWOFAABYJOQIS4S","target":"record","payload":{"canonical_record":{"source":{"id":"2503.17552","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-03-21T21:55:36Z","cross_cats_sorted":[],"title_canon_sha256":"e1e33d7c7ea3f3cb98f7ad60feb61d4e5a526d9b6d06b62c23c7ec40e1516519","abstract_canon_sha256":"7af99b176be97fc8ed9b9614a1184938bcb14b2c440f8eec74809ae460d439b2"},"schema_version":"1.0"},"canonical_sha256":"a0ce6104c500f4ab38a00070974112e4ad8a18427fcf1cc54341bb25a34b7e1f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:37:11.799033Z","signature_b64":"0I06UrGKTkxrSkjQbYe4HY3scGXDsFLeNQA9hUwQR0mx7H3zfV8zTrluBDs3MRE1LwA5Rc7zjHfzCEyq+/R/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0ce6104c500f4ab38a00070974112e4ad8a18427fcf1cc54341bb25a34b7e1f","last_reissued_at":"2026-07-05T10:37:11.798545Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:37:11.798545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.17552","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":"2026-07-05T10:37:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yzf1389a2LOgpUPCMNp1oWmoS7DETn0FR9+CGTU4xkIm6/5+vhEMOrJFC6GVw+BY2Fj2tEI2/QY9xIpdEw1gBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T19:56:43.838243Z"},"content_sha256":"894be8d79d62000a80a5e12b0562b834523b37c1915f9f1c17907f89dff5ce52","schema_version":"1.0","event_id":"sha256:894be8d79d62000a80a5e12b0562b834523b37c1915f9f1c17907f89dff5ce52"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:UDHGCBGFAD2KWOFAABYJOQIS4S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Partial permutations and character evaluations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brendon Rhoades, Zachary Hamaker","submitted_at":"2025-03-21T21:55:36Z","abstract_excerpt":"Let $I = (i_1, \\dots, i_k)$ and $J = (j_1, \\dots, j_k)$ be two length $k$ sequences drawn from $\\{1, \\dots, n \\}$. We have the group algebra element $[I,J] := \\sum_{w(I) = J} w \\in \\mathbb{C}[\\mathfrak{S}_n]$ where the sum is over permutations $w \\in \\mathfrak{S}_n$ which satisfy $w(i_p) = j_p$ for $p = 1, \\dots, k$. We give an algorithm for evaluating irreducible characters $\\chi^\\lambda: \\mathbb{C}[\\mathfrak{S}_n] \\to \\mathbb{C}$ of the symmetric group on the elements $[I,J]$. This algorithm is a hybrid of the classical Murnaghan--Nakayama rule and a new path Murnaghan--Nakayama rule which r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.17552","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/2503.17552/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":"2026-07-05T10:37:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lHpiDBa4J85TssYm8N1sHK3FT7nrpURqqPImmASKElTKvHcJ/k6ae68yjkfBg+C+M9jPr1Y401m3gVVb65oLAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T19:56:43.838844Z"},"content_sha256":"4f4c515eec3e5c21a2435b53d0a30bb13cb996ab656b7e96ff649f22e3a4d323","schema_version":"1.0","event_id":"sha256:4f4c515eec3e5c21a2435b53d0a30bb13cb996ab656b7e96ff649f22e3a4d323"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UDHGCBGFAD2KWOFAABYJOQIS4S/bundle.json","state_url":"https://pith.science/pith/UDHGCBGFAD2KWOFAABYJOQIS4S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UDHGCBGFAD2KWOFAABYJOQIS4S/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":"2026-08-08T19:56:43Z","links":{"resolver":"https://pith.science/pith/UDHGCBGFAD2KWOFAABYJOQIS4S","bundle":"https://pith.science/pith/UDHGCBGFAD2KWOFAABYJOQIS4S/bundle.json","state":"https://pith.science/pith/UDHGCBGFAD2KWOFAABYJOQIS4S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UDHGCBGFAD2KWOFAABYJOQIS4S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:UDHGCBGFAD2KWOFAABYJOQIS4S","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":"7af99b176be97fc8ed9b9614a1184938bcb14b2c440f8eec74809ae460d439b2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-03-21T21:55:36Z","title_canon_sha256":"e1e33d7c7ea3f3cb98f7ad60feb61d4e5a526d9b6d06b62c23c7ec40e1516519"},"schema_version":"1.0","source":{"id":"2503.17552","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.17552","created_at":"2026-07-05T10:37:11Z"},{"alias_kind":"arxiv_version","alias_value":"2503.17552v1","created_at":"2026-07-05T10:37:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.17552","created_at":"2026-07-05T10:37:11Z"},{"alias_kind":"pith_short_12","alias_value":"UDHGCBGFAD2K","created_at":"2026-07-05T10:37:11Z"},{"alias_kind":"pith_short_16","alias_value":"UDHGCBGFAD2KWOFA","created_at":"2026-07-05T10:37:11Z"},{"alias_kind":"pith_short_8","alias_value":"UDHGCBGF","created_at":"2026-07-05T10:37:11Z"}],"graph_snapshots":[{"event_id":"sha256:4f4c515eec3e5c21a2435b53d0a30bb13cb996ab656b7e96ff649f22e3a4d323","target":"graph","created_at":"2026-07-05T10:37:11Z","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/2503.17552/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $I = (i_1, \\dots, i_k)$ and $J = (j_1, \\dots, j_k)$ be two length $k$ sequences drawn from $\\{1, \\dots, n \\}$. We have the group algebra element $[I,J] := \\sum_{w(I) = J} w \\in \\mathbb{C}[\\mathfrak{S}_n]$ where the sum is over permutations $w \\in \\mathfrak{S}_n$ which satisfy $w(i_p) = j_p$ for $p = 1, \\dots, k$. We give an algorithm for evaluating irreducible characters $\\chi^\\lambda: \\mathbb{C}[\\mathfrak{S}_n] \\to \\mathbb{C}$ of the symmetric group on the elements $[I,J]$. This algorithm is a hybrid of the classical Murnaghan--Nakayama rule and a new path Murnaghan--Nakayama rule which r","authors_text":"Brendon Rhoades, Zachary Hamaker","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-03-21T21:55:36Z","title":"Partial permutations and character evaluations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.17552","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":"sha256:894be8d79d62000a80a5e12b0562b834523b37c1915f9f1c17907f89dff5ce52","target":"record","created_at":"2026-07-05T10:37:11Z","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":"7af99b176be97fc8ed9b9614a1184938bcb14b2c440f8eec74809ae460d439b2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-03-21T21:55:36Z","title_canon_sha256":"e1e33d7c7ea3f3cb98f7ad60feb61d4e5a526d9b6d06b62c23c7ec40e1516519"},"schema_version":"1.0","source":{"id":"2503.17552","kind":"arxiv","version":1}},"canonical_sha256":"a0ce6104c500f4ab38a00070974112e4ad8a18427fcf1cc54341bb25a34b7e1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0ce6104c500f4ab38a00070974112e4ad8a18427fcf1cc54341bb25a34b7e1f","first_computed_at":"2026-07-05T10:37:11.798545Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:37:11.798545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0I06UrGKTkxrSkjQbYe4HY3scGXDsFLeNQA9hUwQR0mx7H3zfV8zTrluBDs3MRE1LwA5Rc7zjHfzCEyq+/R/Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:37:11.799033Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.17552","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:894be8d79d62000a80a5e12b0562b834523b37c1915f9f1c17907f89dff5ce52","sha256:4f4c515eec3e5c21a2435b53d0a30bb13cb996ab656b7e96ff649f22e3a4d323"],"state_sha256":"cab646a0c56169e56e2e4749bef189320b655e198ec5f0725c90a1efc6ac38d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9C9WEoVwzq2InHJwhGkFQQ0H6JSE4GvBECty7nJBaCTgAvX3TEfbCHCBaqhObDxfzzj97x4VbkX6APO0hEOkBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T19:56:43.844447Z","bundle_sha256":"e594a0d4e4bd6c6bb8aa1c4719ffcff7bd96b1d888249b19e2408bcc5f61d23e"}}