{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:QJPFPBFHC2U3JC3ZPQMBLPO7ZO","short_pith_number":"pith:QJPFPBFH","canonical_record":{"source":{"id":"1806.03570","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-06-10T01:58:42Z","cross_cats_sorted":[],"title_canon_sha256":"7dc80eeaa386444b301102eea5af9bbaa39aa57667c0ccd2ffed1e3521184e03","abstract_canon_sha256":"08efc2ce958a0abdb9b6e166849c1f36d918535cac4cdcac8ad28374d2c11229"},"schema_version":"1.0"},"canonical_sha256":"825e5784a716a9b48b797c1815bddfcbbe3504875bbe255c79550cdf4a06d4ae","source":{"kind":"arxiv","id":"1806.03570","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03570","created_at":"2026-05-18T00:13:21Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03570v2","created_at":"2026-05-18T00:13:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03570","created_at":"2026-05-18T00:13:21Z"},{"alias_kind":"pith_short_12","alias_value":"QJPFPBFHC2U3","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QJPFPBFHC2U3JC3Z","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QJPFPBFH","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:QJPFPBFHC2U3JC3ZPQMBLPO7ZO","target":"record","payload":{"canonical_record":{"source":{"id":"1806.03570","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-06-10T01:58:42Z","cross_cats_sorted":[],"title_canon_sha256":"7dc80eeaa386444b301102eea5af9bbaa39aa57667c0ccd2ffed1e3521184e03","abstract_canon_sha256":"08efc2ce958a0abdb9b6e166849c1f36d918535cac4cdcac8ad28374d2c11229"},"schema_version":"1.0"},"canonical_sha256":"825e5784a716a9b48b797c1815bddfcbbe3504875bbe255c79550cdf4a06d4ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:21.200807Z","signature_b64":"hYf0QTLasjngLaJ1wjbxJzZsrFPGxUcvWytVWNV41+iWumEssPWmNowyWFWB2POebWzt4E0fthuk4jLyWTQMCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"825e5784a716a9b48b797c1815bddfcbbe3504875bbe255c79550cdf4a06d4ae","last_reissued_at":"2026-05-18T00:13:21.200214Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:21.200214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.03570","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":"2026-05-18T00:13:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T7B5r4Gy7tk7uMdgNExlHVAVneDYyCHHSbbqLQCnpp0guRnCDj1/1jnzNRzdAWYCKNM/492juZn7+Yq/lsmWDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T01:58:18.614539Z"},"content_sha256":"0f69190cf4810209285e239ff7066e5d9e936278c6bdb9260fe2681509d4ba30","schema_version":"1.0","event_id":"sha256:0f69190cf4810209285e239ff7066e5d9e936278c6bdb9260fe2681509d4ba30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:QJPFPBFHC2U3JC3ZPQMBLPO7ZO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Purely atomic representations of higher-rank graph C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Carla Farsi, Elizabeth Gillaspy, Judith Packer, Palle Jorgensen, Sooran Kang","submitted_at":"2018-06-10T01:58:42Z","abstract_excerpt":"We study purely atomic representations of C*-algebras associated to row-finite and source-free higher-rank graphs. We describe when purely atomic representations are unitarily equivalent and we give necessary and sufficient conditions for a purely atomic representation to be irreducible in terms of the associated projection valued measure. We also investigate the relationship between purely atomic representations, monic representations and permutative representations, and we describe when a purely atomic representation admits a decomposition consisting of permutative representations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03570","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":"2026-05-18T00:13:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fjoDZRY9+fpQWJK1r5zxvkKRo0B93eKVAIzAQCYS08osQSWCm/I8ylW7sITlGgmkzfainy1NneHaQciHyEwqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T01:58:18.614887Z"},"content_sha256":"1d6b360dab529d0ab69d92175fca4ba2dbfe5d47f3315b8372cc6891c12122e8","schema_version":"1.0","event_id":"sha256:1d6b360dab529d0ab69d92175fca4ba2dbfe5d47f3315b8372cc6891c12122e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QJPFPBFHC2U3JC3ZPQMBLPO7ZO/bundle.json","state_url":"https://pith.science/pith/QJPFPBFHC2U3JC3ZPQMBLPO7ZO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QJPFPBFHC2U3JC3ZPQMBLPO7ZO/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":"2026-06-22T01:58:18Z","links":{"resolver":"https://pith.science/pith/QJPFPBFHC2U3JC3ZPQMBLPO7ZO","bundle":"https://pith.science/pith/QJPFPBFHC2U3JC3ZPQMBLPO7ZO/bundle.json","state":"https://pith.science/pith/QJPFPBFHC2U3JC3ZPQMBLPO7ZO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QJPFPBFHC2U3JC3ZPQMBLPO7ZO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QJPFPBFHC2U3JC3ZPQMBLPO7ZO","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":"08efc2ce958a0abdb9b6e166849c1f36d918535cac4cdcac8ad28374d2c11229","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-06-10T01:58:42Z","title_canon_sha256":"7dc80eeaa386444b301102eea5af9bbaa39aa57667c0ccd2ffed1e3521184e03"},"schema_version":"1.0","source":{"id":"1806.03570","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03570","created_at":"2026-05-18T00:13:21Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03570v2","created_at":"2026-05-18T00:13:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03570","created_at":"2026-05-18T00:13:21Z"},{"alias_kind":"pith_short_12","alias_value":"QJPFPBFHC2U3","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QJPFPBFHC2U3JC3Z","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QJPFPBFH","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:1d6b360dab529d0ab69d92175fca4ba2dbfe5d47f3315b8372cc6891c12122e8","target":"graph","created_at":"2026-05-18T00:13:21Z","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 study purely atomic representations of C*-algebras associated to row-finite and source-free higher-rank graphs. We describe when purely atomic representations are unitarily equivalent and we give necessary and sufficient conditions for a purely atomic representation to be irreducible in terms of the associated projection valued measure. We also investigate the relationship between purely atomic representations, monic representations and permutative representations, and we describe when a purely atomic representation admits a decomposition consisting of permutative representations.","authors_text":"Carla Farsi, Elizabeth Gillaspy, Judith Packer, Palle Jorgensen, Sooran Kang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-06-10T01:58:42Z","title":"Purely atomic representations of higher-rank graph C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03570","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":"sha256:0f69190cf4810209285e239ff7066e5d9e936278c6bdb9260fe2681509d4ba30","target":"record","created_at":"2026-05-18T00:13:21Z","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":"08efc2ce958a0abdb9b6e166849c1f36d918535cac4cdcac8ad28374d2c11229","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-06-10T01:58:42Z","title_canon_sha256":"7dc80eeaa386444b301102eea5af9bbaa39aa57667c0ccd2ffed1e3521184e03"},"schema_version":"1.0","source":{"id":"1806.03570","kind":"arxiv","version":2}},"canonical_sha256":"825e5784a716a9b48b797c1815bddfcbbe3504875bbe255c79550cdf4a06d4ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"825e5784a716a9b48b797c1815bddfcbbe3504875bbe255c79550cdf4a06d4ae","first_computed_at":"2026-05-18T00:13:21.200214Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:21.200214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hYf0QTLasjngLaJ1wjbxJzZsrFPGxUcvWytVWNV41+iWumEssPWmNowyWFWB2POebWzt4E0fthuk4jLyWTQMCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:21.200807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.03570","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f69190cf4810209285e239ff7066e5d9e936278c6bdb9260fe2681509d4ba30","sha256:1d6b360dab529d0ab69d92175fca4ba2dbfe5d47f3315b8372cc6891c12122e8"],"state_sha256":"77965a1a8c4e3852cb50c077ac2f9a47715fe0946350d3d229e1f92d94ef0b91"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wPiLRlYMk41iwd8F8YnJYNP8ScMlqGG0KbxMwlDWZrdHLA2DvHF+rcV2XLsNfW7h1XMCgrv/m8+f4gAx0m9bBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T01:58:18.616864Z","bundle_sha256":"33415adcee81d568172dabc6824f308f9b85c0c074bfb261f45fd4f7151a20bf"}}