{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:D6G5RYM2R355RQI6KLCL3NITS6","short_pith_number":"pith:D6G5RYM2","canonical_record":{"source":{"id":"1010.5266","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-25T21:11:31Z","cross_cats_sorted":[],"title_canon_sha256":"e66ac348785816d33edfec1765be190cc67892eebde5326fd711f8747fefdd6f","abstract_canon_sha256":"473c90e8113a3fb749e824723dec3d4f7db6bc5dc46b4f924129c7a7dfa4cd1a"},"schema_version":"1.0"},"canonical_sha256":"1f8dd8e19a8efbd8c11e52c4bdb51397ab4ce593af00b56411139d2cad9a1163","source":{"kind":"arxiv","id":"1010.5266","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5266","created_at":"2026-05-18T01:36:39Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5266v1","created_at":"2026-05-18T01:36:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5266","created_at":"2026-05-18T01:36:39Z"},{"alias_kind":"pith_short_12","alias_value":"D6G5RYM2R355","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"D6G5RYM2R355RQI6","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"D6G5RYM2","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:D6G5RYM2R355RQI6KLCL3NITS6","target":"record","payload":{"canonical_record":{"source":{"id":"1010.5266","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-25T21:11:31Z","cross_cats_sorted":[],"title_canon_sha256":"e66ac348785816d33edfec1765be190cc67892eebde5326fd711f8747fefdd6f","abstract_canon_sha256":"473c90e8113a3fb749e824723dec3d4f7db6bc5dc46b4f924129c7a7dfa4cd1a"},"schema_version":"1.0"},"canonical_sha256":"1f8dd8e19a8efbd8c11e52c4bdb51397ab4ce593af00b56411139d2cad9a1163","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:39.298246Z","signature_b64":"scNq7Po7BTTXeg2I+xuV1ObhvAYT4djimRw65lFxPx6cU7BOpYJjIIpClljrY9aLTcpprtsIF3TEbp2QSxdDDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f8dd8e19a8efbd8c11e52c4bdb51397ab4ce593af00b56411139d2cad9a1163","last_reissued_at":"2026-05-18T01:36:39.297675Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:39.297675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.5266","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":"2026-05-18T01:36:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"56xUXoAmgMnhoESUYQoIOuwRrZ2hoeRMMBIz5FoeiQ9gImkPkGljIf787X6+Rr+J1xzRB3vBaQ26iM27JVLIBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:43:39.938020Z"},"content_sha256":"d9b6ed2b1718b58879bf925e73cd65872a03cc64de186a4f943fc5e6b340c0b2","schema_version":"1.0","event_id":"sha256:d9b6ed2b1718b58879bf925e73cd65872a03cc64de186a4f943fc5e6b340c0b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:D6G5RYM2R355RQI6KLCL3NITS6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bases for the derivation modules of two-dimensional multi-Coxeter arrangements and universal derivations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Atsushi Wakamiko","submitted_at":"2010-10-25T21:11:31Z","abstract_excerpt":"Let $\\A$ be an irreducible Coxeter arrangement and $\\bfk$ be a multiplicity of $\\A$. We study the derivation module $D(\\A, \\bfk)$. Any two-dimensional irreducible Coxeter arrangement with even number of lines is decomposed into two orbits under the action of the Coxeter group. In this paper, we will {explicitly} construct a basis for $D(\\A, \\bfk)$ assuming $\\bfk$ is constant on each orbit. Consequently we will determine the exponents of $(\\A, \\bfk)$ under this assumption. For this purpose we develop a theory of universal derivations and introduce a map to deal with our exceptional cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5266","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":""},"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":"7m19/xJuFzGtKRVruDAgHbnO5Lqmvr/5pfowpagFeWG4l7ZReaHNm+4SY4vAynbz5QzpKM1AuVDLV1F7xDXjCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:43:39.938387Z"},"content_sha256":"98aa0270344cd88aa5c4533a9668a320366f8d3ad287055546fe22439b3fed8b","schema_version":"1.0","event_id":"sha256:98aa0270344cd88aa5c4533a9668a320366f8d3ad287055546fe22439b3fed8b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D6G5RYM2R355RQI6KLCL3NITS6/bundle.json","state_url":"https://pith.science/pith/D6G5RYM2R355RQI6KLCL3NITS6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D6G5RYM2R355RQI6KLCL3NITS6/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":"2026-06-25T23:43:39Z","links":{"resolver":"https://pith.science/pith/D6G5RYM2R355RQI6KLCL3NITS6","bundle":"https://pith.science/pith/D6G5RYM2R355RQI6KLCL3NITS6/bundle.json","state":"https://pith.science/pith/D6G5RYM2R355RQI6KLCL3NITS6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D6G5RYM2R355RQI6KLCL3NITS6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:D6G5RYM2R355RQI6KLCL3NITS6","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":"473c90e8113a3fb749e824723dec3d4f7db6bc5dc46b4f924129c7a7dfa4cd1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-25T21:11:31Z","title_canon_sha256":"e66ac348785816d33edfec1765be190cc67892eebde5326fd711f8747fefdd6f"},"schema_version":"1.0","source":{"id":"1010.5266","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5266","created_at":"2026-05-18T01:36:39Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5266v1","created_at":"2026-05-18T01:36:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5266","created_at":"2026-05-18T01:36:39Z"},{"alias_kind":"pith_short_12","alias_value":"D6G5RYM2R355","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"D6G5RYM2R355RQI6","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"D6G5RYM2","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:98aa0270344cd88aa5c4533a9668a320366f8d3ad287055546fe22439b3fed8b","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":"Let $\\A$ be an irreducible Coxeter arrangement and $\\bfk$ be a multiplicity of $\\A$. We study the derivation module $D(\\A, \\bfk)$. Any two-dimensional irreducible Coxeter arrangement with even number of lines is decomposed into two orbits under the action of the Coxeter group. In this paper, we will {explicitly} construct a basis for $D(\\A, \\bfk)$ assuming $\\bfk$ is constant on each orbit. Consequently we will determine the exponents of $(\\A, \\bfk)$ under this assumption. For this purpose we develop a theory of universal derivations and introduce a map to deal with our exceptional cases.","authors_text":"Atsushi Wakamiko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-25T21:11:31Z","title":"Bases for the derivation modules of two-dimensional multi-Coxeter arrangements and universal derivations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5266","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:d9b6ed2b1718b58879bf925e73cd65872a03cc64de186a4f943fc5e6b340c0b2","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":"473c90e8113a3fb749e824723dec3d4f7db6bc5dc46b4f924129c7a7dfa4cd1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-25T21:11:31Z","title_canon_sha256":"e66ac348785816d33edfec1765be190cc67892eebde5326fd711f8747fefdd6f"},"schema_version":"1.0","source":{"id":"1010.5266","kind":"arxiv","version":1}},"canonical_sha256":"1f8dd8e19a8efbd8c11e52c4bdb51397ab4ce593af00b56411139d2cad9a1163","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f8dd8e19a8efbd8c11e52c4bdb51397ab4ce593af00b56411139d2cad9a1163","first_computed_at":"2026-05-18T01:36:39.297675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:39.297675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"scNq7Po7BTTXeg2I+xuV1ObhvAYT4djimRw65lFxPx6cU7BOpYJjIIpClljrY9aLTcpprtsIF3TEbp2QSxdDDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:39.298246Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.5266","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9b6ed2b1718b58879bf925e73cd65872a03cc64de186a4f943fc5e6b340c0b2","sha256:98aa0270344cd88aa5c4533a9668a320366f8d3ad287055546fe22439b3fed8b"],"state_sha256":"fa7593fcb1e509eec94d6b32a60e8581520c5b431bc11211c7f40e149e2d332d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZqdRq9+3RNRasFTm218sdYUJ/dkV6CQQd17HoCoPVOGswshcg1UpIgI565OJVXD0fiB+F3T8dAvzXRk8NpViDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T23:43:39.940435Z","bundle_sha256":"a8aacb1a04492038430e43687d6bad86b0c6850e660e354a80abd087eac498e4"}}