{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:WR2EPYCAVLX7443MNJRNQI7YXL","short_pith_number":"pith:WR2EPYCA","canonical_record":{"source":{"id":"1111.3510","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-15T11:53:08Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"5930ef8deb8f467b28aa75aea4ba915450ce71c391357b6fafacefeac33ba7d8","abstract_canon_sha256":"0850ecafa3c740292de2e87813cece5af1de511d6825f6c07f84b360956919d3"},"schema_version":"1.0"},"canonical_sha256":"b47447e040aaeffe736c6a62d823f8bad2b27403d5b2d29e2648d05c3ae53601","source":{"kind":"arxiv","id":"1111.3510","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.3510","created_at":"2026-05-18T01:36:39Z"},{"alias_kind":"arxiv_version","alias_value":"1111.3510v2","created_at":"2026-05-18T01:36:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.3510","created_at":"2026-05-18T01:36:39Z"},{"alias_kind":"pith_short_12","alias_value":"WR2EPYCAVLX7","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WR2EPYCAVLX7443M","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WR2EPYCA","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:WR2EPYCAVLX7443MNJRNQI7YXL","target":"record","payload":{"canonical_record":{"source":{"id":"1111.3510","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-15T11:53:08Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"5930ef8deb8f467b28aa75aea4ba915450ce71c391357b6fafacefeac33ba7d8","abstract_canon_sha256":"0850ecafa3c740292de2e87813cece5af1de511d6825f6c07f84b360956919d3"},"schema_version":"1.0"},"canonical_sha256":"b47447e040aaeffe736c6a62d823f8bad2b27403d5b2d29e2648d05c3ae53601","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:39.258385Z","signature_b64":"tcB0nJJ81VS0JFU3gnQ6E7bECh6BHDGo7gQPU4MoIb1CJ53dpRNW9MvZ6lC5TmhL252CP6fAFhVCmBhEolaKAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b47447e040aaeffe736c6a62d823f8bad2b27403d5b2d29e2648d05c3ae53601","last_reissued_at":"2026-05-18T01:36:39.257594Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:39.257594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.3510","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rn1o4CfQETGQISlqlt8Lm1ij2OjzlnGuBVNXZfmlJJcqxUHfGkPxnSh79srq4GG28pSEQxPcRl+poGY2xKHEAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:55:28.121276Z"},"content_sha256":"6d0ae9bc487e55d9fdebc98150658668666e86fd554a8ece4602c02b0a0b05e7","schema_version":"1.0","event_id":"sha256:6d0ae9bc487e55d9fdebc98150658668666e86fd554a8ece4602c02b0a0b05e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:WR2EPYCAVLX7443MNJRNQI7YXL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simple-root bases for Shi arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Hiroaki Terao, Takuro Abe","submitted_at":"2011-11-15T11:53:08Z","abstract_excerpt":"In his affirmative answer to the Edelman-Reiner conjecture, Yoshinaga proved that the logarithmic derivation modules of the cones of the extended Shi arrangements are free modules. However, all we know about the bases is their existence and degrees. In this article, we introduce two distinguished bases for the modules. More specifically, we will define and study the simple-root basis plus (SRB+) and the simple-root basis minus (SRB-) when a primitive derivation is fixed. They have remarkable properties relevant to the simple roots and those properties characterize the bases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3510","kind":"arxiv","version":2},"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":"2026-05-18T01:36:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"znBgei+wRe9WBwO9zYu/eOdWR9qvtUqOGb7KdlmiBdBNy1RTrauXD8VlZSwjVxm17MVoAo72EqJJ+PyWjggzCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:55:28.121684Z"},"content_sha256":"37bbb6dedb4693cb5e64a7f1fe41c7620abe66054ec163cc295a134fb6086f50","schema_version":"1.0","event_id":"sha256:37bbb6dedb4693cb5e64a7f1fe41c7620abe66054ec163cc295a134fb6086f50"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WR2EPYCAVLX7443MNJRNQI7YXL/bundle.json","state_url":"https://pith.science/pith/WR2EPYCAVLX7443MNJRNQI7YXL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WR2EPYCAVLX7443MNJRNQI7YXL/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":"2026-06-25T18:55:28Z","links":{"resolver":"https://pith.science/pith/WR2EPYCAVLX7443MNJRNQI7YXL","bundle":"https://pith.science/pith/WR2EPYCAVLX7443MNJRNQI7YXL/bundle.json","state":"https://pith.science/pith/WR2EPYCAVLX7443MNJRNQI7YXL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WR2EPYCAVLX7443MNJRNQI7YXL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WR2EPYCAVLX7443MNJRNQI7YXL","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":"0850ecafa3c740292de2e87813cece5af1de511d6825f6c07f84b360956919d3","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-15T11:53:08Z","title_canon_sha256":"5930ef8deb8f467b28aa75aea4ba915450ce71c391357b6fafacefeac33ba7d8"},"schema_version":"1.0","source":{"id":"1111.3510","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.3510","created_at":"2026-05-18T01:36:39Z"},{"alias_kind":"arxiv_version","alias_value":"1111.3510v2","created_at":"2026-05-18T01:36:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.3510","created_at":"2026-05-18T01:36:39Z"},{"alias_kind":"pith_short_12","alias_value":"WR2EPYCAVLX7","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WR2EPYCAVLX7443M","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WR2EPYCA","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:37bbb6dedb4693cb5e64a7f1fe41c7620abe66054ec163cc295a134fb6086f50","target":"graph","created_at":"2026-05-18T01:36:39Z","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":"In his affirmative answer to the Edelman-Reiner conjecture, Yoshinaga proved that the logarithmic derivation modules of the cones of the extended Shi arrangements are free modules. However, all we know about the bases is their existence and degrees. In this article, we introduce two distinguished bases for the modules. More specifically, we will define and study the simple-root basis plus (SRB+) and the simple-root basis minus (SRB-) when a primitive derivation is fixed. They have remarkable properties relevant to the simple roots and those properties characterize the bases.","authors_text":"Hiroaki Terao, Takuro Abe","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-15T11:53:08Z","title":"Simple-root bases for Shi arrangements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3510","kind":"arxiv","version":2},"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":"sha256:6d0ae9bc487e55d9fdebc98150658668666e86fd554a8ece4602c02b0a0b05e7","target":"record","created_at":"2026-05-18T01:36:39Z","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":"0850ecafa3c740292de2e87813cece5af1de511d6825f6c07f84b360956919d3","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-15T11:53:08Z","title_canon_sha256":"5930ef8deb8f467b28aa75aea4ba915450ce71c391357b6fafacefeac33ba7d8"},"schema_version":"1.0","source":{"id":"1111.3510","kind":"arxiv","version":2}},"canonical_sha256":"b47447e040aaeffe736c6a62d823f8bad2b27403d5b2d29e2648d05c3ae53601","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b47447e040aaeffe736c6a62d823f8bad2b27403d5b2d29e2648d05c3ae53601","first_computed_at":"2026-05-18T01:36:39.257594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:39.257594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tcB0nJJ81VS0JFU3gnQ6E7bECh6BHDGo7gQPU4MoIb1CJ53dpRNW9MvZ6lC5TmhL252CP6fAFhVCmBhEolaKAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:39.258385Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.3510","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d0ae9bc487e55d9fdebc98150658668666e86fd554a8ece4602c02b0a0b05e7","sha256:37bbb6dedb4693cb5e64a7f1fe41c7620abe66054ec163cc295a134fb6086f50"],"state_sha256":"66442ef7eb8b8502fb478ffad16dcd7dfecc2166e422206e83e42343859b7f4b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pq/mJrCNFc2edPRzMNJnpzzK5dsYhdpI/yHYREVtglDnjj+Jc1JvVdUUmsfgQIalquNgdsZ81mzes/WoufqDDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T18:55:28.124063Z","bundle_sha256":"ea21fcbec61dbf4bed289efb179aeb3f12d617fbc40de93762755db35402c3f5"}}