{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:G6Y3WH3L7OPN62X7YVNQLD7OO6","short_pith_number":"pith:G6Y3WH3L","canonical_record":{"source":{"id":"1311.0377","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-02T13:53:35Z","cross_cats_sorted":[],"title_canon_sha256":"50eeef34503903db8c0b8b5d12997f5c5d8d33eb48b7bd92924abb6a2850c646","abstract_canon_sha256":"8be58d3205d03e9944cd95be2ef19fa7329a5734d85a45bd216c7b1a9e42056a"},"schema_version":"1.0"},"canonical_sha256":"37b1bb1f6bfb9edf6affc55b058fee778598793b976a3113e01d8b43047f1397","source":{"kind":"arxiv","id":"1311.0377","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.0377","created_at":"2026-05-18T03:08:06Z"},{"alias_kind":"arxiv_version","alias_value":"1311.0377v1","created_at":"2026-05-18T03:08:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0377","created_at":"2026-05-18T03:08:06Z"},{"alias_kind":"pith_short_12","alias_value":"G6Y3WH3L7OPN","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"G6Y3WH3L7OPN62X7","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"G6Y3WH3L","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:G6Y3WH3L7OPN62X7YVNQLD7OO6","target":"record","payload":{"canonical_record":{"source":{"id":"1311.0377","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-02T13:53:35Z","cross_cats_sorted":[],"title_canon_sha256":"50eeef34503903db8c0b8b5d12997f5c5d8d33eb48b7bd92924abb6a2850c646","abstract_canon_sha256":"8be58d3205d03e9944cd95be2ef19fa7329a5734d85a45bd216c7b1a9e42056a"},"schema_version":"1.0"},"canonical_sha256":"37b1bb1f6bfb9edf6affc55b058fee778598793b976a3113e01d8b43047f1397","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:06.148899Z","signature_b64":"eZrrNEHaoUpEFHTzKP5ixbadkJ8mQHIph/WjzdaHiHeMw3N1RDBxDXdTuObUEnz0LjIjIfajMQLHf3jSASj6Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37b1bb1f6bfb9edf6affc55b058fee778598793b976a3113e01d8b43047f1397","last_reissued_at":"2026-05-18T03:08:06.148191Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:06.148191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.0377","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":"2026-05-18T03:08:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KqenbjM91jrbhvi9AmS7G+m3A0bfMPQ4Yjt7S0yLAhF8mFl6MIrOsk6S6EnUsUru0Nf+aX2FCf5AMAOAmXqXAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T07:16:52.561736Z"},"content_sha256":"d7c823a7b7b69bfbca1a6855311a62be2e107619c1855726311cf9fe5dd2b06d","schema_version":"1.0","event_id":"sha256:d7c823a7b7b69bfbca1a6855311a62be2e107619c1855726311cf9fe5dd2b06d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:G6Y3WH3L7OPN62X7YVNQLD7OO6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coxeter Transformations, the McKay correspondence, and the Slodowy correspondence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Rafael Stekolshchik","submitted_at":"2013-11-02T13:53:35Z","abstract_excerpt":"This talk was presented at Workshop \"Spectral Methods in Representation Theory of Algebras and Applications to the Study of Rings of Singularities\", 2008 (Banff, Canada). W. Ebeling established a connection between certain Poincare series, the Coxeter transformation C, and the corresponding affine Coxeter transformation C_a (in the context of the McKay correspondence). We consider the generalized Poincare series [\\tilde{P}_G(t)]_0 for the case of multiply-laced diagrams(in the context of the McKay-Slodowy correspondence) and extend the Ebeling theorem for this case: [\\tilde{P}_G(t)]_0 = X(t^2)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0377","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":"2026-05-18T03:08:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6qLMHwDdEW7pva3fGBVQN+B+9XIe1eu/viPkCZdk/bytpAUfdIM2YGOQEFSVIw8IIuaL0EgoD7QlWebHwuNOAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T07:16:52.562310Z"},"content_sha256":"557334372f605e2c16a22e17771c0b7156b2c9cc098e5a510a682fd533d9f3bd","schema_version":"1.0","event_id":"sha256:557334372f605e2c16a22e17771c0b7156b2c9cc098e5a510a682fd533d9f3bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G6Y3WH3L7OPN62X7YVNQLD7OO6/bundle.json","state_url":"https://pith.science/pith/G6Y3WH3L7OPN62X7YVNQLD7OO6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G6Y3WH3L7OPN62X7YVNQLD7OO6/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":"2026-07-01T07:16:52Z","links":{"resolver":"https://pith.science/pith/G6Y3WH3L7OPN62X7YVNQLD7OO6","bundle":"https://pith.science/pith/G6Y3WH3L7OPN62X7YVNQLD7OO6/bundle.json","state":"https://pith.science/pith/G6Y3WH3L7OPN62X7YVNQLD7OO6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G6Y3WH3L7OPN62X7YVNQLD7OO6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:G6Y3WH3L7OPN62X7YVNQLD7OO6","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":"8be58d3205d03e9944cd95be2ef19fa7329a5734d85a45bd216c7b1a9e42056a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-02T13:53:35Z","title_canon_sha256":"50eeef34503903db8c0b8b5d12997f5c5d8d33eb48b7bd92924abb6a2850c646"},"schema_version":"1.0","source":{"id":"1311.0377","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.0377","created_at":"2026-05-18T03:08:06Z"},{"alias_kind":"arxiv_version","alias_value":"1311.0377v1","created_at":"2026-05-18T03:08:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0377","created_at":"2026-05-18T03:08:06Z"},{"alias_kind":"pith_short_12","alias_value":"G6Y3WH3L7OPN","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"G6Y3WH3L7OPN62X7","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"G6Y3WH3L","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:557334372f605e2c16a22e17771c0b7156b2c9cc098e5a510a682fd533d9f3bd","target":"graph","created_at":"2026-05-18T03:08:06Z","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 talk was presented at Workshop \"Spectral Methods in Representation Theory of Algebras and Applications to the Study of Rings of Singularities\", 2008 (Banff, Canada). W. Ebeling established a connection between certain Poincare series, the Coxeter transformation C, and the corresponding affine Coxeter transformation C_a (in the context of the McKay correspondence). We consider the generalized Poincare series [\\tilde{P}_G(t)]_0 for the case of multiply-laced diagrams(in the context of the McKay-Slodowy correspondence) and extend the Ebeling theorem for this case: [\\tilde{P}_G(t)]_0 = X(t^2)","authors_text":"Rafael Stekolshchik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-02T13:53:35Z","title":"Coxeter Transformations, the McKay correspondence, and the Slodowy correspondence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0377","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:d7c823a7b7b69bfbca1a6855311a62be2e107619c1855726311cf9fe5dd2b06d","target":"record","created_at":"2026-05-18T03:08:06Z","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":"8be58d3205d03e9944cd95be2ef19fa7329a5734d85a45bd216c7b1a9e42056a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-02T13:53:35Z","title_canon_sha256":"50eeef34503903db8c0b8b5d12997f5c5d8d33eb48b7bd92924abb6a2850c646"},"schema_version":"1.0","source":{"id":"1311.0377","kind":"arxiv","version":1}},"canonical_sha256":"37b1bb1f6bfb9edf6affc55b058fee778598793b976a3113e01d8b43047f1397","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37b1bb1f6bfb9edf6affc55b058fee778598793b976a3113e01d8b43047f1397","first_computed_at":"2026-05-18T03:08:06.148191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:06.148191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eZrrNEHaoUpEFHTzKP5ixbadkJ8mQHIph/WjzdaHiHeMw3N1RDBxDXdTuObUEnz0LjIjIfajMQLHf3jSASj6Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:06.148899Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.0377","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7c823a7b7b69bfbca1a6855311a62be2e107619c1855726311cf9fe5dd2b06d","sha256:557334372f605e2c16a22e17771c0b7156b2c9cc098e5a510a682fd533d9f3bd"],"state_sha256":"eec8fa66d0a57a3d431ed1866a2b4843c76c91290b7c6a64015d1e346723f403"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uoPJLbX/jtkUmQKzpdvkOdVScPG0kGO86Jv/Pmj5j78DehHPmiLACk7K73k+WzbnQGtWsdfxLtiQs1RR+KqsAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T07:16:52.565852Z","bundle_sha256":"4f54df79834881def5f9b6585c9fa97da07556ca359960a8e24338284bfcba84"}}