{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:VD2TPUA3K244NVCEW7E5RLDV2R","short_pith_number":"pith:VD2TPUA3","canonical_record":{"source":{"id":"1205.0676","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2012-05-03T11:21:19Z","cross_cats_sorted":[],"title_canon_sha256":"0ad88fd0f91265927596b9b31a4693b03a92d22d24d1eaa539016a53c22801f5","abstract_canon_sha256":"e202ea5556e8ea88de8aab76bef6e3c7b64440c2ecd28444e6b3be79ea12f109"},"schema_version":"1.0"},"canonical_sha256":"a8f537d01b56b9c6d444b7c9d8ac75d47a3ea1c0511e147cb8d4f2f257e71981","source":{"kind":"arxiv","id":"1205.0676","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0676","created_at":"2026-05-18T00:50:43Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0676v4","created_at":"2026-05-18T00:50:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0676","created_at":"2026-05-18T00:50:43Z"},{"alias_kind":"pith_short_12","alias_value":"VD2TPUA3K244","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VD2TPUA3K244NVCE","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VD2TPUA3","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:VD2TPUA3K244NVCEW7E5RLDV2R","target":"record","payload":{"canonical_record":{"source":{"id":"1205.0676","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2012-05-03T11:21:19Z","cross_cats_sorted":[],"title_canon_sha256":"0ad88fd0f91265927596b9b31a4693b03a92d22d24d1eaa539016a53c22801f5","abstract_canon_sha256":"e202ea5556e8ea88de8aab76bef6e3c7b64440c2ecd28444e6b3be79ea12f109"},"schema_version":"1.0"},"canonical_sha256":"a8f537d01b56b9c6d444b7c9d8ac75d47a3ea1c0511e147cb8d4f2f257e71981","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:43.357559Z","signature_b64":"xodtnn78yVDJXFCvjE9fPlOyr9LvNRrRmRpHK91obyRTIs9NWYN+5o9SGDtRRF2LTXuhWe1SdFho/ldHcdgYBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8f537d01b56b9c6d444b7c9d8ac75d47a3ea1c0511e147cb8d4f2f257e71981","last_reissued_at":"2026-05-18T00:50:43.356834Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:43.356834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.0676","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":"2026-05-18T00:50:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LUlW39FoRWKsFLTMnClUHUzJLyL06S/eisGpDvOjIeEf9Bv8T6vZZY2PksaH6gpqhuH45uE7O3ZofSvLfKe6AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T16:00:56.366668Z"},"content_sha256":"6d868c74b9324149bffa91e3df3b028ab2df8a7d8d481203d398a3b5b4a7d342","schema_version":"1.0","event_id":"sha256:6d868c74b9324149bffa91e3df3b028ab2df8a7d8d481203d398a3b5b4a7d342"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:VD2TPUA3K244NVCEW7E5RLDV2R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Effective representations of Hecke-Kiselman monoids of type A","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Love Forsberg","submitted_at":"2012-05-03T11:21:19Z","abstract_excerpt":"We prove effectiveness of certain representations of Hecke-Kiselman monoids of type A constructed by Ganyushkin and Mazorchuk and also construct further classes of effective representations for these monoids. As a consequence the effective dimension of monoids of type A is determined. We also show that odd Fibonacci numbers appear as the cardinality of certain bipartite HK-monoids and count the number of multiplicity free elements in any HK-monoid of type A."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0676","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":"2026-05-18T00:50:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8QAJ9svKfoCSIM6Qe5EMvywafXiVMJUCEDhNIgPR+XrTIH1QtjyPcFLcNUQ8cDtpLG0WO/tOizG2qWSUCDzUAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T16:00:56.367389Z"},"content_sha256":"eba7994b94ad5ac3f3072bd12456e4a17cc87bb189a9016ac294f5871da65d5d","schema_version":"1.0","event_id":"sha256:eba7994b94ad5ac3f3072bd12456e4a17cc87bb189a9016ac294f5871da65d5d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VD2TPUA3K244NVCEW7E5RLDV2R/bundle.json","state_url":"https://pith.science/pith/VD2TPUA3K244NVCEW7E5RLDV2R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VD2TPUA3K244NVCEW7E5RLDV2R/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":"2026-06-10T16:00:56Z","links":{"resolver":"https://pith.science/pith/VD2TPUA3K244NVCEW7E5RLDV2R","bundle":"https://pith.science/pith/VD2TPUA3K244NVCEW7E5RLDV2R/bundle.json","state":"https://pith.science/pith/VD2TPUA3K244NVCEW7E5RLDV2R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VD2TPUA3K244NVCEW7E5RLDV2R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VD2TPUA3K244NVCEW7E5RLDV2R","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":"e202ea5556e8ea88de8aab76bef6e3c7b64440c2ecd28444e6b3be79ea12f109","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2012-05-03T11:21:19Z","title_canon_sha256":"0ad88fd0f91265927596b9b31a4693b03a92d22d24d1eaa539016a53c22801f5"},"schema_version":"1.0","source":{"id":"1205.0676","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0676","created_at":"2026-05-18T00:50:43Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0676v4","created_at":"2026-05-18T00:50:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0676","created_at":"2026-05-18T00:50:43Z"},{"alias_kind":"pith_short_12","alias_value":"VD2TPUA3K244","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VD2TPUA3K244NVCE","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VD2TPUA3","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:eba7994b94ad5ac3f3072bd12456e4a17cc87bb189a9016ac294f5871da65d5d","target":"graph","created_at":"2026-05-18T00:50:43Z","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 prove effectiveness of certain representations of Hecke-Kiselman monoids of type A constructed by Ganyushkin and Mazorchuk and also construct further classes of effective representations for these monoids. As a consequence the effective dimension of monoids of type A is determined. We also show that odd Fibonacci numbers appear as the cardinality of certain bipartite HK-monoids and count the number of multiplicity free elements in any HK-monoid of type A.","authors_text":"Love Forsberg","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2012-05-03T11:21:19Z","title":"Effective representations of Hecke-Kiselman monoids of type A"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0676","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":"sha256:6d868c74b9324149bffa91e3df3b028ab2df8a7d8d481203d398a3b5b4a7d342","target":"record","created_at":"2026-05-18T00:50:43Z","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":"e202ea5556e8ea88de8aab76bef6e3c7b64440c2ecd28444e6b3be79ea12f109","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2012-05-03T11:21:19Z","title_canon_sha256":"0ad88fd0f91265927596b9b31a4693b03a92d22d24d1eaa539016a53c22801f5"},"schema_version":"1.0","source":{"id":"1205.0676","kind":"arxiv","version":4}},"canonical_sha256":"a8f537d01b56b9c6d444b7c9d8ac75d47a3ea1c0511e147cb8d4f2f257e71981","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8f537d01b56b9c6d444b7c9d8ac75d47a3ea1c0511e147cb8d4f2f257e71981","first_computed_at":"2026-05-18T00:50:43.356834Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:43.356834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xodtnn78yVDJXFCvjE9fPlOyr9LvNRrRmRpHK91obyRTIs9NWYN+5o9SGDtRRF2LTXuhWe1SdFho/ldHcdgYBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:43.357559Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.0676","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d868c74b9324149bffa91e3df3b028ab2df8a7d8d481203d398a3b5b4a7d342","sha256:eba7994b94ad5ac3f3072bd12456e4a17cc87bb189a9016ac294f5871da65d5d"],"state_sha256":"2881105fa4cf708d56fdb59da4d390929f9eda6825abbf693072aaa198a646d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"64cYiUcy8WhvkCJgyV4l2uqfmvY5ONSpiwngGmgSUGCNMtEUtXvPczo7SJxWKI4dk2JSHkQxb+1g9icnjIS1Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T16:00:56.373215Z","bundle_sha256":"0f704d043c3243071e0b527eb330999f4b328de182430be299cd070d1583daf8"}}