{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:XJ6OOCLQRDUQWFHDOHSJRCPSGJ","short_pith_number":"pith:XJ6OOCLQ","canonical_record":{"source":{"id":"1009.3678","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-09-20T01:56:28Z","cross_cats_sorted":[],"title_canon_sha256":"617b9077fb137fb1a08f6fe585eb95a423fe56a7c02cc7322968dcb8e1193b7b","abstract_canon_sha256":"b80c024c4a495e5655df993eacf73252ee9ba9e9115bfd7ba7ccdb0664e452ae"},"schema_version":"1.0"},"canonical_sha256":"ba7ce7097088e90b14e371e49889f23274fa81fab83f2509022ca0af162b5958","source":{"kind":"arxiv","id":"1009.3678","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.3678","created_at":"2026-05-18T04:40:44Z"},{"alias_kind":"arxiv_version","alias_value":"1009.3678v1","created_at":"2026-05-18T04:40:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3678","created_at":"2026-05-18T04:40:44Z"},{"alias_kind":"pith_short_12","alias_value":"XJ6OOCLQRDUQ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XJ6OOCLQRDUQWFHD","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XJ6OOCLQ","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:XJ6OOCLQRDUQWFHDOHSJRCPSGJ","target":"record","payload":{"canonical_record":{"source":{"id":"1009.3678","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-09-20T01:56:28Z","cross_cats_sorted":[],"title_canon_sha256":"617b9077fb137fb1a08f6fe585eb95a423fe56a7c02cc7322968dcb8e1193b7b","abstract_canon_sha256":"b80c024c4a495e5655df993eacf73252ee9ba9e9115bfd7ba7ccdb0664e452ae"},"schema_version":"1.0"},"canonical_sha256":"ba7ce7097088e90b14e371e49889f23274fa81fab83f2509022ca0af162b5958","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:44.208641Z","signature_b64":"A/ayVifGJRJOc6sRscbZRaFOhQENwAKZaf5ufongi5duHGKHh1vvzXZqibxoaEOp5nnvaO6/gDrlteos4G3wCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba7ce7097088e90b14e371e49889f23274fa81fab83f2509022ca0af162b5958","last_reissued_at":"2026-05-18T04:40:44.207831Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:44.207831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.3678","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":"2026-05-18T04:40:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b8dAqGqqYx5XonLxASa+ltipIDZvLTLnkXmDnsYqAycjJHcLves5tCP0du3VyXfqfs6WvnywnzjiIvpaERhcDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T14:00:04.777439Z"},"content_sha256":"1f53266e53094d49e92c73a6367a852ac0dd944fc1787bca46434e34ca364b41","schema_version":"1.0","event_id":"sha256:1f53266e53094d49e92c73a6367a852ac0dd944fc1787bca46434e34ca364b41"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:XJ6OOCLQRDUQWFHDOHSJRCPSGJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boundary quotients of the Toeplitz algebra of the affine semigroup over the natural numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Astrid an Huef, Iain Raeburn, Marcelo Laca, Nathan Brownlowe","submitted_at":"2010-09-20T01:56:28Z","abstract_excerpt":"We study the Toeplitz algebra $\\TT(\\N\\rtimes\\N^\\times)$ and three quotients of this algebra: the $C^*$-algebra $\\qn$ recntly introduced by Cuntz, and two new ones, which we call the additive and multiplicative boundary quotients. These quotients are universal for Nica-covariant representations of $\\N\\rtimes\\N^\\times$ satisfying extra relations, and can be realised as partial crossed products. We use the structure theory for partial crossed products to prove a uniqueness theorem for the additive boundary quotient, and use the recent analysis of KMS states on $\\TT(\\nxnx)$ to describe the KMS sta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3678","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":"2026-05-18T04:40:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9C0GMdXzSF6onbxkjMNd6BBNhXifxuvl3kuZS2MhVGpTMM60xanf3b6ou/5XkuZdq6duSnaHrl/H0I8zPZznAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T14:00:04.777788Z"},"content_sha256":"a6ea54825a44a1f6c771694d2642301d445847028451c696e5acd35852d7d4b4","schema_version":"1.0","event_id":"sha256:a6ea54825a44a1f6c771694d2642301d445847028451c696e5acd35852d7d4b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XJ6OOCLQRDUQWFHDOHSJRCPSGJ/bundle.json","state_url":"https://pith.science/pith/XJ6OOCLQRDUQWFHDOHSJRCPSGJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XJ6OOCLQRDUQWFHDOHSJRCPSGJ/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":"2026-06-09T14:00:04Z","links":{"resolver":"https://pith.science/pith/XJ6OOCLQRDUQWFHDOHSJRCPSGJ","bundle":"https://pith.science/pith/XJ6OOCLQRDUQWFHDOHSJRCPSGJ/bundle.json","state":"https://pith.science/pith/XJ6OOCLQRDUQWFHDOHSJRCPSGJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XJ6OOCLQRDUQWFHDOHSJRCPSGJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XJ6OOCLQRDUQWFHDOHSJRCPSGJ","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":"b80c024c4a495e5655df993eacf73252ee9ba9e9115bfd7ba7ccdb0664e452ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-09-20T01:56:28Z","title_canon_sha256":"617b9077fb137fb1a08f6fe585eb95a423fe56a7c02cc7322968dcb8e1193b7b"},"schema_version":"1.0","source":{"id":"1009.3678","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.3678","created_at":"2026-05-18T04:40:44Z"},{"alias_kind":"arxiv_version","alias_value":"1009.3678v1","created_at":"2026-05-18T04:40:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3678","created_at":"2026-05-18T04:40:44Z"},{"alias_kind":"pith_short_12","alias_value":"XJ6OOCLQRDUQ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XJ6OOCLQRDUQWFHD","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XJ6OOCLQ","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:a6ea54825a44a1f6c771694d2642301d445847028451c696e5acd35852d7d4b4","target":"graph","created_at":"2026-05-18T04:40:44Z","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 the Toeplitz algebra $\\TT(\\N\\rtimes\\N^\\times)$ and three quotients of this algebra: the $C^*$-algebra $\\qn$ recntly introduced by Cuntz, and two new ones, which we call the additive and multiplicative boundary quotients. These quotients are universal for Nica-covariant representations of $\\N\\rtimes\\N^\\times$ satisfying extra relations, and can be realised as partial crossed products. We use the structure theory for partial crossed products to prove a uniqueness theorem for the additive boundary quotient, and use the recent analysis of KMS states on $\\TT(\\nxnx)$ to describe the KMS sta","authors_text":"Astrid an Huef, Iain Raeburn, Marcelo Laca, Nathan Brownlowe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-09-20T01:56:28Z","title":"Boundary quotients of the Toeplitz algebra of the affine semigroup over the natural numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3678","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":"sha256:1f53266e53094d49e92c73a6367a852ac0dd944fc1787bca46434e34ca364b41","target":"record","created_at":"2026-05-18T04:40:44Z","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":"b80c024c4a495e5655df993eacf73252ee9ba9e9115bfd7ba7ccdb0664e452ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-09-20T01:56:28Z","title_canon_sha256":"617b9077fb137fb1a08f6fe585eb95a423fe56a7c02cc7322968dcb8e1193b7b"},"schema_version":"1.0","source":{"id":"1009.3678","kind":"arxiv","version":1}},"canonical_sha256":"ba7ce7097088e90b14e371e49889f23274fa81fab83f2509022ca0af162b5958","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba7ce7097088e90b14e371e49889f23274fa81fab83f2509022ca0af162b5958","first_computed_at":"2026-05-18T04:40:44.207831Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:44.207831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A/ayVifGJRJOc6sRscbZRaFOhQENwAKZaf5ufongi5duHGKHh1vvzXZqibxoaEOp5nnvaO6/gDrlteos4G3wCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:44.208641Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.3678","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f53266e53094d49e92c73a6367a852ac0dd944fc1787bca46434e34ca364b41","sha256:a6ea54825a44a1f6c771694d2642301d445847028451c696e5acd35852d7d4b4"],"state_sha256":"63b5a6027519f1af090fa99f3e41698a3b98787c5db756410c760365c158aff7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nqAb2+UtxQkFipq96NazWv+T2ZtP570hmWMR1GlAlgWh8e3BhAZ0MWII2mcntw0vTX2jMqfID4bv9UHZQnaXDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T14:00:04.779731Z","bundle_sha256":"198319f9cf9026944ac3e6a1bc0ab9bd56f2c146879bd0e2b23eb5b63e46bf0e"}}