{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:WFVTHTLUYIWIG2QPWBTNRZQ3C6","short_pith_number":"pith:WFVTHTLU","canonical_record":{"source":{"id":"1711.01698","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-11-06T02:14:52Z","cross_cats_sorted":[],"title_canon_sha256":"66cf252ae13d05bd73fce92e74792dc638bd7b4d1b27c2a7fbd6fcb3c9a95cf1","abstract_canon_sha256":"6569e2c52b5d4c0893ab3881e7395a4fa97d5fc56e11053574806f2c12bcd74a"},"schema_version":"1.0"},"canonical_sha256":"b16b33cd74c22c836a0fb066d8e61b17b81035c7dd2d75d845d8e2f813633ef6","source":{"kind":"arxiv","id":"1711.01698","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.01698","created_at":"2026-05-18T00:06:48Z"},{"alias_kind":"arxiv_version","alias_value":"1711.01698v2","created_at":"2026-05-18T00:06:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.01698","created_at":"2026-05-18T00:06:48Z"},{"alias_kind":"pith_short_12","alias_value":"WFVTHTLUYIWI","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WFVTHTLUYIWIG2QP","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WFVTHTLU","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:WFVTHTLUYIWIG2QPWBTNRZQ3C6","target":"record","payload":{"canonical_record":{"source":{"id":"1711.01698","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-11-06T02:14:52Z","cross_cats_sorted":[],"title_canon_sha256":"66cf252ae13d05bd73fce92e74792dc638bd7b4d1b27c2a7fbd6fcb3c9a95cf1","abstract_canon_sha256":"6569e2c52b5d4c0893ab3881e7395a4fa97d5fc56e11053574806f2c12bcd74a"},"schema_version":"1.0"},"canonical_sha256":"b16b33cd74c22c836a0fb066d8e61b17b81035c7dd2d75d845d8e2f813633ef6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:48.356855Z","signature_b64":"5yRJ7LZiF5HvbYPgt+8lYPpu3kSO2Kdz9kEPFGo3YdIVEoOVsTSTYj9gJmQ4+i2VkncB/eEa2uZS33RZJsRGCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b16b33cd74c22c836a0fb066d8e61b17b81035c7dd2d75d845d8e2f813633ef6","last_reissued_at":"2026-05-18T00:06:48.356369Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:48.356369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.01698","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":"2026-05-18T00:06:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ml+Uc3GhOT/P2u7QUBl1jP319lgl9xIshodan+rGtc8w6NhUGhQ5AF1Og4epeiG0wToSTjM9HEZAmCf5D174DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:14:24.584593Z"},"content_sha256":"9b75b003cbeacb836e1a082670282eb9a3d78d8d4f00cca01efe9bbaccbde3eb","schema_version":"1.0","event_id":"sha256:9b75b003cbeacb836e1a082670282eb9a3d78d8d4f00cca01efe9bbaccbde3eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:WFVTHTLUYIWIG2QPWBTNRZQ3C6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher-rank graph algebras are iterated Cuntz-Pimsner algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"James Fletcher","submitted_at":"2017-11-06T02:14:52Z","abstract_excerpt":"Given a finitely aligned $k$-graph $\\Lambda$, we let $\\Lambda^i$ denote the $(k-1)$-graph formed by removing all edges of degree $e_i$ from $\\Lambda$. We show that the Toeplitz-Cuntz-Krieger algebra of $\\Lambda$, denoted by $\\mathcal{T}C^*(\\Lambda)$, may be realised as the Toeplitz algebra of a Hilbert $\\mathcal{T}C^*(\\Lambda^i)$-bimodule. When $\\Lambda$ is locally-convex, we show that the Cuntz-Krieger algebra of $\\Lambda$, which we denote by $C^*(\\Lambda)$, may be realised as the Cuntz-Pimsner algebra of a Hilbert $C^*(\\Lambda^i)$-bimodule. Consequently, $\\mathcal{T}C^*(\\Lambda)$ and $C^*(\\L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01698","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":"2026-05-18T00:06:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mxL7EByqtAGLmIL6St7C1cKO4p8sxEmpqoT8S4XMoHXvhcXAYfERCs64Er2GDinTXIZYRaNKINM7NhWelWqcCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:14:24.584943Z"},"content_sha256":"28eee83b599400979f0a198412e87f3b2b558a67832ede6d918e421871911601","schema_version":"1.0","event_id":"sha256:28eee83b599400979f0a198412e87f3b2b558a67832ede6d918e421871911601"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WFVTHTLUYIWIG2QPWBTNRZQ3C6/bundle.json","state_url":"https://pith.science/pith/WFVTHTLUYIWIG2QPWBTNRZQ3C6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WFVTHTLUYIWIG2QPWBTNRZQ3C6/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":"2026-06-25T09:14:24Z","links":{"resolver":"https://pith.science/pith/WFVTHTLUYIWIG2QPWBTNRZQ3C6","bundle":"https://pith.science/pith/WFVTHTLUYIWIG2QPWBTNRZQ3C6/bundle.json","state":"https://pith.science/pith/WFVTHTLUYIWIG2QPWBTNRZQ3C6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WFVTHTLUYIWIG2QPWBTNRZQ3C6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WFVTHTLUYIWIG2QPWBTNRZQ3C6","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":"6569e2c52b5d4c0893ab3881e7395a4fa97d5fc56e11053574806f2c12bcd74a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-11-06T02:14:52Z","title_canon_sha256":"66cf252ae13d05bd73fce92e74792dc638bd7b4d1b27c2a7fbd6fcb3c9a95cf1"},"schema_version":"1.0","source":{"id":"1711.01698","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.01698","created_at":"2026-05-18T00:06:48Z"},{"alias_kind":"arxiv_version","alias_value":"1711.01698v2","created_at":"2026-05-18T00:06:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.01698","created_at":"2026-05-18T00:06:48Z"},{"alias_kind":"pith_short_12","alias_value":"WFVTHTLUYIWI","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WFVTHTLUYIWIG2QP","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WFVTHTLU","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:28eee83b599400979f0a198412e87f3b2b558a67832ede6d918e421871911601","target":"graph","created_at":"2026-05-18T00:06:48Z","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":"Given a finitely aligned $k$-graph $\\Lambda$, we let $\\Lambda^i$ denote the $(k-1)$-graph formed by removing all edges of degree $e_i$ from $\\Lambda$. We show that the Toeplitz-Cuntz-Krieger algebra of $\\Lambda$, denoted by $\\mathcal{T}C^*(\\Lambda)$, may be realised as the Toeplitz algebra of a Hilbert $\\mathcal{T}C^*(\\Lambda^i)$-bimodule. When $\\Lambda$ is locally-convex, we show that the Cuntz-Krieger algebra of $\\Lambda$, which we denote by $C^*(\\Lambda)$, may be realised as the Cuntz-Pimsner algebra of a Hilbert $C^*(\\Lambda^i)$-bimodule. Consequently, $\\mathcal{T}C^*(\\Lambda)$ and $C^*(\\L","authors_text":"James Fletcher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-11-06T02:14:52Z","title":"Higher-rank graph algebras are iterated Cuntz-Pimsner algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01698","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":"sha256:9b75b003cbeacb836e1a082670282eb9a3d78d8d4f00cca01efe9bbaccbde3eb","target":"record","created_at":"2026-05-18T00:06:48Z","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":"6569e2c52b5d4c0893ab3881e7395a4fa97d5fc56e11053574806f2c12bcd74a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-11-06T02:14:52Z","title_canon_sha256":"66cf252ae13d05bd73fce92e74792dc638bd7b4d1b27c2a7fbd6fcb3c9a95cf1"},"schema_version":"1.0","source":{"id":"1711.01698","kind":"arxiv","version":2}},"canonical_sha256":"b16b33cd74c22c836a0fb066d8e61b17b81035c7dd2d75d845d8e2f813633ef6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b16b33cd74c22c836a0fb066d8e61b17b81035c7dd2d75d845d8e2f813633ef6","first_computed_at":"2026-05-18T00:06:48.356369Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:48.356369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5yRJ7LZiF5HvbYPgt+8lYPpu3kSO2Kdz9kEPFGo3YdIVEoOVsTSTYj9gJmQ4+i2VkncB/eEa2uZS33RZJsRGCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:48.356855Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.01698","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b75b003cbeacb836e1a082670282eb9a3d78d8d4f00cca01efe9bbaccbde3eb","sha256:28eee83b599400979f0a198412e87f3b2b558a67832ede6d918e421871911601"],"state_sha256":"73fa86ffa76c10a90938e08a31f585f2f6c09872805fe183d2642569c6ada0da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y452bpQoXq3aNM3bh1nQp1qqkcKmba3x613TNGM33NrSDWKdyVfkaNT3KtCAxkPGXpqzdsywmrSTc2zeDqLzCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T09:14:24.587572Z","bundle_sha256":"cf3efb14a91c334985f47d5438636870f94a8fd731950220e3f63d0e60b34379"}}