{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:7LMZ24GSFXBLR7LEM7FIHA6TLV","short_pith_number":"pith:7LMZ24GS","canonical_record":{"source":{"id":"1010.0599","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-10-04T14:18:12Z","cross_cats_sorted":[],"title_canon_sha256":"85f606ea8862fe6816ff732469b7db27b3a38c03d63da285073ab4ad7040bddb","abstract_canon_sha256":"d065952166da84737828d53c201b12fad0a015a7c0041a1f09f545767edc4e68"},"schema_version":"1.0"},"canonical_sha256":"fad99d70d22dc2b8fd6467ca8383d35d74f91ffe501f47979f715934fae95143","source":{"kind":"arxiv","id":"1010.0599","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0599","created_at":"2026-05-18T04:39:51Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0599v1","created_at":"2026-05-18T04:39:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0599","created_at":"2026-05-18T04:39:51Z"},{"alias_kind":"pith_short_12","alias_value":"7LMZ24GSFXBL","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7LMZ24GSFXBLR7LE","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7LMZ24GS","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:7LMZ24GSFXBLR7LEM7FIHA6TLV","target":"record","payload":{"canonical_record":{"source":{"id":"1010.0599","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-10-04T14:18:12Z","cross_cats_sorted":[],"title_canon_sha256":"85f606ea8862fe6816ff732469b7db27b3a38c03d63da285073ab4ad7040bddb","abstract_canon_sha256":"d065952166da84737828d53c201b12fad0a015a7c0041a1f09f545767edc4e68"},"schema_version":"1.0"},"canonical_sha256":"fad99d70d22dc2b8fd6467ca8383d35d74f91ffe501f47979f715934fae95143","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:51.734264Z","signature_b64":"4lcZFOXKZilsbaN2KOuMgwETt4Cp+eBFWCvgw2V6dIWQYqyGXtwrBArfEt8OO0rJZx4jrZTVf4d4D8DA1tadCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fad99d70d22dc2b8fd6467ca8383d35d74f91ffe501f47979f715934fae95143","last_reissued_at":"2026-05-18T04:39:51.733594Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:51.733594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.0599","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":"2026-05-18T04:39:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kActHaLfMkjgZjGSN3NKsJ5ETPTrBuYVG/3XVktBCQVz8tGctL+1YEUE6RT2YyCN0jlMet0XtNXEjKn9/e8EDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T07:48:10.396423Z"},"content_sha256":"899c686e3168c176cc3c51dbf04f88cd36566065207b41c4efb9276ccf9520b2","schema_version":"1.0","event_id":"sha256:899c686e3168c176cc3c51dbf04f88cd36566065207b41c4efb9276ccf9520b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:7LMZ24GSFXBLR7LEM7FIHA6TLV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Type III_1 equilibrium states 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":"Marcelo Laca, Sergey Neshveyev","submitted_at":"2010-10-04T14:18:12Z","abstract_excerpt":"We complete the analysis of KMS-states of the Toeplitz algebra of the affine semigroup over the natural numbers, recently studied by Raeburn and the first author, by showing that for every inverse temperature beta in the critical interval [1,2], the unique KMS_beta-state is of type III_1. We prove this by reducing the type classification from the Toeplitz algebra to that of the symmetric part of the Bost-Connes system, with a shift in inverse temperature. To carry out this reduction we first obtain a parametrization of the Nica spectrum of the Toeplitz algebra in terms of an adelic space. Comb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0599","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":"2026-05-18T04:39:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xqgnVS4QgOYV3GiLFoxc8iLZUr2r3zJO4Ehw9n35kxOfDuQfz68yjz5G3M99h3SOO/rVhWtZDfZ28SwEJmjJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T07:48:10.396951Z"},"content_sha256":"d3f1dbded9df157ff3fcd0f8bb4fc6fb07bc7d55d6413d5390f09ad3fd93b708","schema_version":"1.0","event_id":"sha256:d3f1dbded9df157ff3fcd0f8bb4fc6fb07bc7d55d6413d5390f09ad3fd93b708"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7LMZ24GSFXBLR7LEM7FIHA6TLV/bundle.json","state_url":"https://pith.science/pith/7LMZ24GSFXBLR7LEM7FIHA6TLV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7LMZ24GSFXBLR7LEM7FIHA6TLV/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":"2026-06-07T07:48:10Z","links":{"resolver":"https://pith.science/pith/7LMZ24GSFXBLR7LEM7FIHA6TLV","bundle":"https://pith.science/pith/7LMZ24GSFXBLR7LEM7FIHA6TLV/bundle.json","state":"https://pith.science/pith/7LMZ24GSFXBLR7LEM7FIHA6TLV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7LMZ24GSFXBLR7LEM7FIHA6TLV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7LMZ24GSFXBLR7LEM7FIHA6TLV","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":"d065952166da84737828d53c201b12fad0a015a7c0041a1f09f545767edc4e68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-10-04T14:18:12Z","title_canon_sha256":"85f606ea8862fe6816ff732469b7db27b3a38c03d63da285073ab4ad7040bddb"},"schema_version":"1.0","source":{"id":"1010.0599","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0599","created_at":"2026-05-18T04:39:51Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0599v1","created_at":"2026-05-18T04:39:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0599","created_at":"2026-05-18T04:39:51Z"},{"alias_kind":"pith_short_12","alias_value":"7LMZ24GSFXBL","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7LMZ24GSFXBLR7LE","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7LMZ24GS","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:d3f1dbded9df157ff3fcd0f8bb4fc6fb07bc7d55d6413d5390f09ad3fd93b708","target":"graph","created_at":"2026-05-18T04:39:51Z","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 complete the analysis of KMS-states of the Toeplitz algebra of the affine semigroup over the natural numbers, recently studied by Raeburn and the first author, by showing that for every inverse temperature beta in the critical interval [1,2], the unique KMS_beta-state is of type III_1. We prove this by reducing the type classification from the Toeplitz algebra to that of the symmetric part of the Bost-Connes system, with a shift in inverse temperature. To carry out this reduction we first obtain a parametrization of the Nica spectrum of the Toeplitz algebra in terms of an adelic space. Comb","authors_text":"Marcelo Laca, Sergey Neshveyev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-10-04T14:18:12Z","title":"Type III_1 equilibrium states 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":"1010.0599","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":"sha256:899c686e3168c176cc3c51dbf04f88cd36566065207b41c4efb9276ccf9520b2","target":"record","created_at":"2026-05-18T04:39:51Z","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":"d065952166da84737828d53c201b12fad0a015a7c0041a1f09f545767edc4e68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-10-04T14:18:12Z","title_canon_sha256":"85f606ea8862fe6816ff732469b7db27b3a38c03d63da285073ab4ad7040bddb"},"schema_version":"1.0","source":{"id":"1010.0599","kind":"arxiv","version":1}},"canonical_sha256":"fad99d70d22dc2b8fd6467ca8383d35d74f91ffe501f47979f715934fae95143","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fad99d70d22dc2b8fd6467ca8383d35d74f91ffe501f47979f715934fae95143","first_computed_at":"2026-05-18T04:39:51.733594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:51.733594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4lcZFOXKZilsbaN2KOuMgwETt4Cp+eBFWCvgw2V6dIWQYqyGXtwrBArfEt8OO0rJZx4jrZTVf4d4D8DA1tadCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:51.734264Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.0599","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:899c686e3168c176cc3c51dbf04f88cd36566065207b41c4efb9276ccf9520b2","sha256:d3f1dbded9df157ff3fcd0f8bb4fc6fb07bc7d55d6413d5390f09ad3fd93b708"],"state_sha256":"41d1cfaec24eadc7c4eb265bb8ae5a089a206bd5d4ce4e6188772e5dc174ec8e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BSIajlk+NjeoYoYt9AxrtRirf78XKa98PkBgKm7zubkyJREBC36klKqeTkqFl1Q5Oaey4SGjwo/gBcWB8+UPBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T07:48:10.400040Z","bundle_sha256":"3ecbd32fbb4692a0ec217dccd6b0c4240a913012f951826d2237324757d0eeab"}}