{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:VDDYJFF3MHMLRNR6UCNPGLEVX7","short_pith_number":"pith:VDDYJFF3","canonical_record":{"source":{"id":"0907.4505","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-07-26T18:50:04Z","cross_cats_sorted":["math.CO","math.RT"],"title_canon_sha256":"db82c0bafc570f1669098bfbde3f88dac2cb59d35bd44c7f665a938cbc6d8731","abstract_canon_sha256":"67793ab1eac5a7ebe936912fb91c9a429078e4d19e8d423e825ad579094f0c84"},"schema_version":"1.0"},"canonical_sha256":"a8c78494bb61d8b8b63ea09af32c95bfd33a6628ae58d0cf00f210382326f0de","source":{"kind":"arxiv","id":"0907.4505","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.4505","created_at":"2026-05-18T03:54:50Z"},{"alias_kind":"arxiv_version","alias_value":"0907.4505v5","created_at":"2026-05-18T03:54:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.4505","created_at":"2026-05-18T03:54:50Z"},{"alias_kind":"pith_short_12","alias_value":"VDDYJFF3MHML","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VDDYJFF3MHMLRNR6","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VDDYJFF3","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:VDDYJFF3MHMLRNR6UCNPGLEVX7","target":"record","payload":{"canonical_record":{"source":{"id":"0907.4505","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-07-26T18:50:04Z","cross_cats_sorted":["math.CO","math.RT"],"title_canon_sha256":"db82c0bafc570f1669098bfbde3f88dac2cb59d35bd44c7f665a938cbc6d8731","abstract_canon_sha256":"67793ab1eac5a7ebe936912fb91c9a429078e4d19e8d423e825ad579094f0c84"},"schema_version":"1.0"},"canonical_sha256":"a8c78494bb61d8b8b63ea09af32c95bfd33a6628ae58d0cf00f210382326f0de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:50.242156Z","signature_b64":"2ireNRoBu7pBCcE3SStlT0ZWVQgF5sB1ZtZIhztzNB7CjoTKpP/Tubc89tBqR2THwNPHdNeGc3x8UQdIBX/5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8c78494bb61d8b8b63ea09af32c95bfd33a6628ae58d0cf00f210382326f0de","last_reissued_at":"2026-05-18T03:54:50.241590Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:50.241590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.4505","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:54:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yoM42nKPLGDSxvDUJjqb6KGc3URMcE1WTI+gRQWhJpPdb6zhCa2SOb2kSG0ELvLZDGQpJY28LJubIb7dlIr8CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T07:43:26.632589Z"},"content_sha256":"d7f93bf9c35ec98e128a93b3d4722e1dea6829e7f0b9475a2265761c7ddf946a","schema_version":"1.0","event_id":"sha256:d7f93bf9c35ec98e128a93b3d4722e1dea6829e7f0b9475a2265761c7ddf946a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:VDDYJFF3MHMLRNR6UCNPGLEVX7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pieri resolutions for classical groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.AC","authors_text":"Jerzy Weyman, Steven V Sam","submitted_at":"2009-07-26T18:50:04Z","abstract_excerpt":"We generalize the constructions of Eisenbud, Fl{\\o}ystad, and Weyman for equivariant minimal free resolutions over the general linear group, and we construct equivariant resolutions over the orthogonal and symplectic groups. We also conjecture and provide some partial results for the existence of an equivariant analogue of Boij-S\\\"oderberg decompositions for Betti tables, which were proven to exist in the non-equivariant setting by Eisenbud and Schreyer. Many examples are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.4505","kind":"arxiv","version":5},"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":"2026-05-18T03:54:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sjw99w3Gm8+r/RF6/ItKcPuGlRQUlNPZkgpbnnvshPrKYzqSyflcyGsZXy6kBlIJYrFdY+qOxTuPU10OaQsYCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T07:43:26.632994Z"},"content_sha256":"ee6b4b76a15ef952f1430dc4ab06c134ec974da9ddb9d27e952b30a52fd229a5","schema_version":"1.0","event_id":"sha256:ee6b4b76a15ef952f1430dc4ab06c134ec974da9ddb9d27e952b30a52fd229a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VDDYJFF3MHMLRNR6UCNPGLEVX7/bundle.json","state_url":"https://pith.science/pith/VDDYJFF3MHMLRNR6UCNPGLEVX7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VDDYJFF3MHMLRNR6UCNPGLEVX7/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":"2026-07-05T07:43:26Z","links":{"resolver":"https://pith.science/pith/VDDYJFF3MHMLRNR6UCNPGLEVX7","bundle":"https://pith.science/pith/VDDYJFF3MHMLRNR6UCNPGLEVX7/bundle.json","state":"https://pith.science/pith/VDDYJFF3MHMLRNR6UCNPGLEVX7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VDDYJFF3MHMLRNR6UCNPGLEVX7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:VDDYJFF3MHMLRNR6UCNPGLEVX7","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":"67793ab1eac5a7ebe936912fb91c9a429078e4d19e8d423e825ad579094f0c84","cross_cats_sorted":["math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-07-26T18:50:04Z","title_canon_sha256":"db82c0bafc570f1669098bfbde3f88dac2cb59d35bd44c7f665a938cbc6d8731"},"schema_version":"1.0","source":{"id":"0907.4505","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.4505","created_at":"2026-05-18T03:54:50Z"},{"alias_kind":"arxiv_version","alias_value":"0907.4505v5","created_at":"2026-05-18T03:54:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.4505","created_at":"2026-05-18T03:54:50Z"},{"alias_kind":"pith_short_12","alias_value":"VDDYJFF3MHML","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VDDYJFF3MHMLRNR6","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VDDYJFF3","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:ee6b4b76a15ef952f1430dc4ab06c134ec974da9ddb9d27e952b30a52fd229a5","target":"graph","created_at":"2026-05-18T03:54:50Z","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 generalize the constructions of Eisenbud, Fl{\\o}ystad, and Weyman for equivariant minimal free resolutions over the general linear group, and we construct equivariant resolutions over the orthogonal and symplectic groups. We also conjecture and provide some partial results for the existence of an equivariant analogue of Boij-S\\\"oderberg decompositions for Betti tables, which were proven to exist in the non-equivariant setting by Eisenbud and Schreyer. Many examples are given.","authors_text":"Jerzy Weyman, Steven V Sam","cross_cats":["math.CO","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-07-26T18:50:04Z","title":"Pieri resolutions for classical groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.4505","kind":"arxiv","version":5},"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:d7f93bf9c35ec98e128a93b3d4722e1dea6829e7f0b9475a2265761c7ddf946a","target":"record","created_at":"2026-05-18T03:54:50Z","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":"67793ab1eac5a7ebe936912fb91c9a429078e4d19e8d423e825ad579094f0c84","cross_cats_sorted":["math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-07-26T18:50:04Z","title_canon_sha256":"db82c0bafc570f1669098bfbde3f88dac2cb59d35bd44c7f665a938cbc6d8731"},"schema_version":"1.0","source":{"id":"0907.4505","kind":"arxiv","version":5}},"canonical_sha256":"a8c78494bb61d8b8b63ea09af32c95bfd33a6628ae58d0cf00f210382326f0de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8c78494bb61d8b8b63ea09af32c95bfd33a6628ae58d0cf00f210382326f0de","first_computed_at":"2026-05-18T03:54:50.241590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:50.241590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2ireNRoBu7pBCcE3SStlT0ZWVQgF5sB1ZtZIhztzNB7CjoTKpP/Tubc89tBqR2THwNPHdNeGc3x8UQdIBX/5BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:50.242156Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.4505","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7f93bf9c35ec98e128a93b3d4722e1dea6829e7f0b9475a2265761c7ddf946a","sha256:ee6b4b76a15ef952f1430dc4ab06c134ec974da9ddb9d27e952b30a52fd229a5"],"state_sha256":"97d6667ea07f066e0fdfc28a4b1f15507fb890cedc381ce02b1bdb1c1f5c7ee4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yW25oPPNrVXDD+P9+hkPCj2K8nbsojeGf0AYi8jOpqkt3ZaqqSLt19QltnyiG1h03vNwzsxueJpBh4LrGnQrCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T07:43:26.635094Z","bundle_sha256":"74c4045eb17353a7240389086fd596db06ae27994f513012fff48c7fd0de1864"}}