{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:JPQKZQEMISRTAWFW5TFUJA2547","short_pith_number":"pith:JPQKZQEM","canonical_record":{"source":{"id":"2306.17511","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-06-30T09:56:05Z","cross_cats_sorted":["cs.CC","math.RT"],"title_canon_sha256":"d3669ed6db4fbe6c430a5d944db22f0f5c92f141ed2c75106875581d9a3f4662","abstract_canon_sha256":"2f0ec8398196766e89763dc171d7392022ee3cfc57f3c1d5241df11706959a9a"},"schema_version":"1.0"},"canonical_sha256":"4be0acc08c44a33058b6eccb44835de7e3793faa8ad3a7f2efae4c5488675570","source":{"kind":"arxiv","id":"2306.17511","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.17511","created_at":"2026-07-05T06:26:28Z"},{"alias_kind":"arxiv_version","alias_value":"2306.17511v1","created_at":"2026-07-05T06:26:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.17511","created_at":"2026-07-05T06:26:28Z"},{"alias_kind":"pith_short_12","alias_value":"JPQKZQEMISRT","created_at":"2026-07-05T06:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"JPQKZQEMISRTAWFW","created_at":"2026-07-05T06:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"JPQKZQEM","created_at":"2026-07-05T06:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:JPQKZQEMISRTAWFW5TFUJA2547","target":"record","payload":{"canonical_record":{"source":{"id":"2306.17511","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-06-30T09:56:05Z","cross_cats_sorted":["cs.CC","math.RT"],"title_canon_sha256":"d3669ed6db4fbe6c430a5d944db22f0f5c92f141ed2c75106875581d9a3f4662","abstract_canon_sha256":"2f0ec8398196766e89763dc171d7392022ee3cfc57f3c1d5241df11706959a9a"},"schema_version":"1.0"},"canonical_sha256":"4be0acc08c44a33058b6eccb44835de7e3793faa8ad3a7f2efae4c5488675570","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:26:28.064583Z","signature_b64":"N/FisDfNZwGWRcbtKOEEv4YM9yZZCDwjqeIrF1oan6YnagG8pPVQRJ5o0+aWZBrnAwyoANt5J+qa8OFPZ51EDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4be0acc08c44a33058b6eccb44835de7e3793faa8ad3a7f2efae4c5488675570","last_reissued_at":"2026-07-05T06:26:28.063988Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:26:28.063988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2306.17511","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":"2026-07-05T06:26:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hMn5mYxjs6Xvxjipok1arC2pszZsQ5rWUhf96s5Z0HN4ip7IpKBSvOo8C9bRLqSA3Ziu4RK4bIPV9/dh2sOADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:51:03.653165Z"},"content_sha256":"aab9aab823a94c6c1fad7928c01126166658bca9d26fed04f7e13621c1e59261","schema_version":"1.0","event_id":"sha256:aab9aab823a94c6c1fad7928c01126166658bca9d26fed04f7e13621c1e59261"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:JPQKZQEMISRTAWFW5TFUJA2547","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computational Complexity in Algebraic Combinatorics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","math.RT"],"primary_cat":"math.CO","authors_text":"Greta Panova","submitted_at":"2023-06-30T09:56:05Z","abstract_excerpt":"Algebraic Combinatorics originated in Algebra and Representation Theory, studying their discrete objects and integral quantities via combinatorial methods which have since developed independent and self-contained lives and brought us some beautiful formulas and combinatorial interpretations. The flagship hook-length formula counts the number of Standard Young Tableaux, which also gives the dimension of the irreducible Specht modules of the Symmetric group. The elegant Littlewood-Richardson rule gives the multiplicities of irreducible GL-modules in the tensor products of GL-modules. Such formul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.17511","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/2306.17511/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":"2026-07-05T06:26:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AMuYT9S7B6kXqtS14BsYXk6R68m+74AxLKufDdgpP5SNRJXJkPFXnZ9E47wLoq1oEge9rPbO+zpbgl3f7k2PBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:51:03.653667Z"},"content_sha256":"7cb699fd719c35f3875c0eeb5636d052170ee56aea824c2f0a1f416c95d4f2ed","schema_version":"1.0","event_id":"sha256:7cb699fd719c35f3875c0eeb5636d052170ee56aea824c2f0a1f416c95d4f2ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JPQKZQEMISRTAWFW5TFUJA2547/bundle.json","state_url":"https://pith.science/pith/JPQKZQEMISRTAWFW5TFUJA2547/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JPQKZQEMISRTAWFW5TFUJA2547/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":"2026-08-03T17:51:03Z","links":{"resolver":"https://pith.science/pith/JPQKZQEMISRTAWFW5TFUJA2547","bundle":"https://pith.science/pith/JPQKZQEMISRTAWFW5TFUJA2547/bundle.json","state":"https://pith.science/pith/JPQKZQEMISRTAWFW5TFUJA2547/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JPQKZQEMISRTAWFW5TFUJA2547/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:JPQKZQEMISRTAWFW5TFUJA2547","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":"2f0ec8398196766e89763dc171d7392022ee3cfc57f3c1d5241df11706959a9a","cross_cats_sorted":["cs.CC","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-06-30T09:56:05Z","title_canon_sha256":"d3669ed6db4fbe6c430a5d944db22f0f5c92f141ed2c75106875581d9a3f4662"},"schema_version":"1.0","source":{"id":"2306.17511","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.17511","created_at":"2026-07-05T06:26:28Z"},{"alias_kind":"arxiv_version","alias_value":"2306.17511v1","created_at":"2026-07-05T06:26:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.17511","created_at":"2026-07-05T06:26:28Z"},{"alias_kind":"pith_short_12","alias_value":"JPQKZQEMISRT","created_at":"2026-07-05T06:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"JPQKZQEMISRTAWFW","created_at":"2026-07-05T06:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"JPQKZQEM","created_at":"2026-07-05T06:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:7cb699fd719c35f3875c0eeb5636d052170ee56aea824c2f0a1f416c95d4f2ed","target":"graph","created_at":"2026-07-05T06:26:28Z","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/2306.17511/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Algebraic Combinatorics originated in Algebra and Representation Theory, studying their discrete objects and integral quantities via combinatorial methods which have since developed independent and self-contained lives and brought us some beautiful formulas and combinatorial interpretations. The flagship hook-length formula counts the number of Standard Young Tableaux, which also gives the dimension of the irreducible Specht modules of the Symmetric group. The elegant Littlewood-Richardson rule gives the multiplicities of irreducible GL-modules in the tensor products of GL-modules. Such formul","authors_text":"Greta Panova","cross_cats":["cs.CC","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-06-30T09:56:05Z","title":"Computational Complexity in Algebraic Combinatorics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.17511","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:aab9aab823a94c6c1fad7928c01126166658bca9d26fed04f7e13621c1e59261","target":"record","created_at":"2026-07-05T06:26:28Z","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":"2f0ec8398196766e89763dc171d7392022ee3cfc57f3c1d5241df11706959a9a","cross_cats_sorted":["cs.CC","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-06-30T09:56:05Z","title_canon_sha256":"d3669ed6db4fbe6c430a5d944db22f0f5c92f141ed2c75106875581d9a3f4662"},"schema_version":"1.0","source":{"id":"2306.17511","kind":"arxiv","version":1}},"canonical_sha256":"4be0acc08c44a33058b6eccb44835de7e3793faa8ad3a7f2efae4c5488675570","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4be0acc08c44a33058b6eccb44835de7e3793faa8ad3a7f2efae4c5488675570","first_computed_at":"2026-07-05T06:26:28.063988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:26:28.063988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N/FisDfNZwGWRcbtKOEEv4YM9yZZCDwjqeIrF1oan6YnagG8pPVQRJ5o0+aWZBrnAwyoANt5J+qa8OFPZ51EDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:26:28.064583Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.17511","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aab9aab823a94c6c1fad7928c01126166658bca9d26fed04f7e13621c1e59261","sha256:7cb699fd719c35f3875c0eeb5636d052170ee56aea824c2f0a1f416c95d4f2ed"],"state_sha256":"04f974ad311f2b9ca12e18230c813f4b0a7cd223ff811aaa819593067fd88320"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fsXenq61qbhezbWfMwerv/qsv/K0nLD1DnUvqOc2WbANwmQfyn5MCvtUspwRJJ0LLQuwd9DtS59hSp8HF6fOBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T17:51:03.657637Z","bundle_sha256":"f435506dc3d11f097e4a07e73f486483cd45f208a12f885537227e180583f5b1"}}