{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:AD3G3HIW5F35ZNK2YYES2CIS22","short_pith_number":"pith:AD3G3HIW","canonical_record":{"source":{"id":"1208.3221","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-08-15T20:52:35Z","cross_cats_sorted":[],"title_canon_sha256":"bbab50e613dfeec10f7b12c846e0d0b7c9a6db9339f7e1769c0f79e27459741d","abstract_canon_sha256":"15e8f394da87ecd052ad95a1bc7b29b9190c02b0210ad4928a4865b1ea9fedcc"},"schema_version":"1.0"},"canonical_sha256":"00f66d9d16e977dcb55ac6092d0912d68aaed15b160b1b895e50976f23e3c928","source":{"kind":"arxiv","id":"1208.3221","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3221","created_at":"2026-05-18T01:53:27Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3221v4","created_at":"2026-05-18T01:53:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3221","created_at":"2026-05-18T01:53:27Z"},{"alias_kind":"pith_short_12","alias_value":"AD3G3HIW5F35","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AD3G3HIW5F35ZNK2","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AD3G3HIW","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:AD3G3HIW5F35ZNK2YYES2CIS22","target":"record","payload":{"canonical_record":{"source":{"id":"1208.3221","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-08-15T20:52:35Z","cross_cats_sorted":[],"title_canon_sha256":"bbab50e613dfeec10f7b12c846e0d0b7c9a6db9339f7e1769c0f79e27459741d","abstract_canon_sha256":"15e8f394da87ecd052ad95a1bc7b29b9190c02b0210ad4928a4865b1ea9fedcc"},"schema_version":"1.0"},"canonical_sha256":"00f66d9d16e977dcb55ac6092d0912d68aaed15b160b1b895e50976f23e3c928","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:53:27.503222Z","signature_b64":"dSh90kjSB2Tsb+Q4AsyKPa5JtZEkDSmkrFLFSoYYSUH0Kw422U7oBIGYueYbMk+JTwE7RA0Cj7HGGyr9V/dtBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00f66d9d16e977dcb55ac6092d0912d68aaed15b160b1b895e50976f23e3c928","last_reissued_at":"2026-05-18T01:53:27.502652Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:53:27.502652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.3221","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:53:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5O2ndc6lNPYeEu4LJLP+1JD0XAelKpKgb6r4WoqhlMs4VjSsk9WI2tvH6kLiZQhcltv7hCQcGhWHQYF9Vm1WCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:59:54.855496Z"},"content_sha256":"5df5cf8615a1c30916804482e665ab88060112c30bf9fcd0a92d07967d8c7df0","schema_version":"1.0","event_id":"sha256:5df5cf8615a1c30916804482e665ab88060112c30bf9fcd0a92d07967d8c7df0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:AD3G3HIW5F35ZNK2YYES2CIS22","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On $p$-filtrations of Weyl modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Brian Parshall, Leonard Scott","submitted_at":"2012-08-15T20:52:35Z","abstract_excerpt":"This paper considers Weyl modules for a simple, simply connected algebraic group over an algebraically closed field $k$ of positive characteristic $p\\not=2$. The main result proves, if $p\\geq 2h-2$ (where $h$ is the Coxeter number) and if the Lusztig character formula holds for all (irreducible modules with) regular restricted highest weights, then any Weyl module $\\Delta(\\lambda)$ has a $\\Delta^p$-filtration, namely, a filtration with sections of the form $\\Delta^p(\\mu_0+p\\mu_1):=L(\\mu_0)\\otimes\\Delta(\\mu_1)^{[1]}$, where $\\mu_0$ is restricted and $\\mu_1$ is arbitrary dominant. In case the hi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3221","kind":"arxiv","version":4},"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":"2026-05-18T01:53:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VvLj9HRmc4rWpKNNr2Uuf4sDDydzrQtu0Ml1YD9JWucseDqgOs19sllniK307cyed8msyHyEC6jlJncnF/OBBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:59:54.855840Z"},"content_sha256":"2d264fd7c4a35fddda9e66dab8aacd23fb597c8709e39963dac396f488ae27da","schema_version":"1.0","event_id":"sha256:2d264fd7c4a35fddda9e66dab8aacd23fb597c8709e39963dac396f488ae27da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AD3G3HIW5F35ZNK2YYES2CIS22/bundle.json","state_url":"https://pith.science/pith/AD3G3HIW5F35ZNK2YYES2CIS22/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AD3G3HIW5F35ZNK2YYES2CIS22/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":"2026-05-30T19:59:54Z","links":{"resolver":"https://pith.science/pith/AD3G3HIW5F35ZNK2YYES2CIS22","bundle":"https://pith.science/pith/AD3G3HIW5F35ZNK2YYES2CIS22/bundle.json","state":"https://pith.science/pith/AD3G3HIW5F35ZNK2YYES2CIS22/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AD3G3HIW5F35ZNK2YYES2CIS22/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AD3G3HIW5F35ZNK2YYES2CIS22","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":"15e8f394da87ecd052ad95a1bc7b29b9190c02b0210ad4928a4865b1ea9fedcc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-08-15T20:52:35Z","title_canon_sha256":"bbab50e613dfeec10f7b12c846e0d0b7c9a6db9339f7e1769c0f79e27459741d"},"schema_version":"1.0","source":{"id":"1208.3221","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3221","created_at":"2026-05-18T01:53:27Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3221v4","created_at":"2026-05-18T01:53:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3221","created_at":"2026-05-18T01:53:27Z"},{"alias_kind":"pith_short_12","alias_value":"AD3G3HIW5F35","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AD3G3HIW5F35ZNK2","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AD3G3HIW","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:2d264fd7c4a35fddda9e66dab8aacd23fb597c8709e39963dac396f488ae27da","target":"graph","created_at":"2026-05-18T01:53:27Z","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":"This paper considers Weyl modules for a simple, simply connected algebraic group over an algebraically closed field $k$ of positive characteristic $p\\not=2$. The main result proves, if $p\\geq 2h-2$ (where $h$ is the Coxeter number) and if the Lusztig character formula holds for all (irreducible modules with) regular restricted highest weights, then any Weyl module $\\Delta(\\lambda)$ has a $\\Delta^p$-filtration, namely, a filtration with sections of the form $\\Delta^p(\\mu_0+p\\mu_1):=L(\\mu_0)\\otimes\\Delta(\\mu_1)^{[1]}$, where $\\mu_0$ is restricted and $\\mu_1$ is arbitrary dominant. In case the hi","authors_text":"Brian Parshall, Leonard Scott","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-08-15T20:52:35Z","title":"On $p$-filtrations of Weyl modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3221","kind":"arxiv","version":4},"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":"sha256:5df5cf8615a1c30916804482e665ab88060112c30bf9fcd0a92d07967d8c7df0","target":"record","created_at":"2026-05-18T01:53:27Z","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":"15e8f394da87ecd052ad95a1bc7b29b9190c02b0210ad4928a4865b1ea9fedcc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-08-15T20:52:35Z","title_canon_sha256":"bbab50e613dfeec10f7b12c846e0d0b7c9a6db9339f7e1769c0f79e27459741d"},"schema_version":"1.0","source":{"id":"1208.3221","kind":"arxiv","version":4}},"canonical_sha256":"00f66d9d16e977dcb55ac6092d0912d68aaed15b160b1b895e50976f23e3c928","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00f66d9d16e977dcb55ac6092d0912d68aaed15b160b1b895e50976f23e3c928","first_computed_at":"2026-05-18T01:53:27.502652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:53:27.502652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dSh90kjSB2Tsb+Q4AsyKPa5JtZEkDSmkrFLFSoYYSUH0Kw422U7oBIGYueYbMk+JTwE7RA0Cj7HGGyr9V/dtBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:53:27.503222Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.3221","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5df5cf8615a1c30916804482e665ab88060112c30bf9fcd0a92d07967d8c7df0","sha256:2d264fd7c4a35fddda9e66dab8aacd23fb597c8709e39963dac396f488ae27da"],"state_sha256":"64802c3e182d99597f5aebd1ffe328a1ce114849877dde93dd03de22d5edea37"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o1KHTg7Edr6OGp6F7yu/G/3aDS4oKo/JZ7dgAdUNSfgwxXtrrwui2/f1WEvOUfLAvWFX0k0XoAFpx7zE46rZDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T19:59:54.857870Z","bundle_sha256":"5707a3294c3e79def0636b64131b822a9725cdf3acf53c1edabdb526c3a11ca2"}}