{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:6ZU2VHSZW2S6CSV34S3PBJ3TVJ","short_pith_number":"pith:6ZU2VHSZ","canonical_record":{"source":{"id":"math-ph/0603083","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2006-03-30T13:30:28Z","cross_cats_sorted":["math.MP","math.OA"],"title_canon_sha256":"12976f9c86e5a3cd4077ad31be7ec4968047c4ab2afb131783c40befd57c3a05","abstract_canon_sha256":"16a2c86fa9fe0157695651c4bec9314cf3b5d8c073c8aae02eb6e204557fa466"},"schema_version":"1.0"},"canonical_sha256":"f669aa9e59b6a5e14abbe4b6f0a773aa7ec9d7a1b5c2f6b6a32fd098dc240f04","source":{"kind":"arxiv","id":"math-ph/0603083","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0603083","created_at":"2026-07-04T15:17:51Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0603083v2","created_at":"2026-07-04T15:17:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0603083","created_at":"2026-07-04T15:17:51Z"},{"alias_kind":"pith_short_12","alias_value":"6ZU2VHSZW2S6","created_at":"2026-07-04T15:17:51Z"},{"alias_kind":"pith_short_16","alias_value":"6ZU2VHSZW2S6CSV3","created_at":"2026-07-04T15:17:51Z"},{"alias_kind":"pith_short_8","alias_value":"6ZU2VHSZ","created_at":"2026-07-04T15:17:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:6ZU2VHSZW2S6CSV34S3PBJ3TVJ","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0603083","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2006-03-30T13:30:28Z","cross_cats_sorted":["math.MP","math.OA"],"title_canon_sha256":"12976f9c86e5a3cd4077ad31be7ec4968047c4ab2afb131783c40befd57c3a05","abstract_canon_sha256":"16a2c86fa9fe0157695651c4bec9314cf3b5d8c073c8aae02eb6e204557fa466"},"schema_version":"1.0"},"canonical_sha256":"f669aa9e59b6a5e14abbe4b6f0a773aa7ec9d7a1b5c2f6b6a32fd098dc240f04","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:17:51.530761Z","signature_b64":"RHdlxsleyfdgHzfhHoyYB1QL45+p6+WqPrjcP+8MEfYDgYVQM94rWP5hpyjTuqGglFlqbZNFRiDyDl45C3yRAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f669aa9e59b6a5e14abbe4b6f0a773aa7ec9d7a1b5c2f6b6a32fd098dc240f04","last_reissued_at":"2026-07-04T15:17:51.530165Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:17:51.530165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0603083","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":"2026-07-04T15:17:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"99ogd6f8rYMrC3JPPBM9yjQv+vnMwWn5embVlB/AGZAUz2OX7yE73Gd0hyE8Ew6qoq3+yN7YrIUZs8j0sQ1NAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T08:40:13.803757Z"},"content_sha256":"baea8119f6780b67959296cee6c6ddaba0ef37046087b1e9f1004c55ac3e8267","schema_version":"1.0","event_id":"sha256:baea8119f6780b67959296cee6c6ddaba0ef37046087b1e9f1004c55ac3e8267"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:6ZU2VHSZW2S6CSV34S3PBJ3TVJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nuclearity and Thermal States in Conformal Field Theory","license":"","headline":"","cross_cats":["math.MP","math.OA"],"primary_cat":"math-ph","authors_text":"Claudio D'Antoni, Detlev Buchholz, Roberto Longo","submitted_at":"2006-03-30T13:30:28Z","abstract_excerpt":"We introduce a new type of spectral density condition, that we call L^2-nuclearity. One formulation concerns lowest weight unitary representations of SL(2,R) and turns out to be equivalent to the existence of characters. A second formulation concerns inclusions of local observable von Neumann algebras in Quantum Field Theory. We show the two formulations to agree in chiral Conformal QFT and, starting from the trace class condition for the semigroup generated by the conformal Hamiltonian L_0, we infer and naturally estimate the Buchholz-Wichmann nuclearity condition and the (distal) split prope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0603083","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/0603083/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:17:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H6otQ0ks1smb1Ee+AaIWpR0liNUL/VdwGoW1FYtLrxkTxvQ7vYEV4iAo001pkW1smXBESGv9FQxD4Lh/C+t2BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T08:40:13.804123Z"},"content_sha256":"58a2159d615f8ebb6c6732eaafc957ea1dea1281e250de7cef2f48b2c173948a","schema_version":"1.0","event_id":"sha256:58a2159d615f8ebb6c6732eaafc957ea1dea1281e250de7cef2f48b2c173948a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6ZU2VHSZW2S6CSV34S3PBJ3TVJ/bundle.json","state_url":"https://pith.science/pith/6ZU2VHSZW2S6CSV34S3PBJ3TVJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6ZU2VHSZW2S6CSV34S3PBJ3TVJ/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":"2026-07-05T08:40:13Z","links":{"resolver":"https://pith.science/pith/6ZU2VHSZW2S6CSV34S3PBJ3TVJ","bundle":"https://pith.science/pith/6ZU2VHSZW2S6CSV34S3PBJ3TVJ/bundle.json","state":"https://pith.science/pith/6ZU2VHSZW2S6CSV34S3PBJ3TVJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6ZU2VHSZW2S6CSV34S3PBJ3TVJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:6ZU2VHSZW2S6CSV34S3PBJ3TVJ","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":"16a2c86fa9fe0157695651c4bec9314cf3b5d8c073c8aae02eb6e204557fa466","cross_cats_sorted":["math.MP","math.OA"],"license":"","primary_cat":"math-ph","submitted_at":"2006-03-30T13:30:28Z","title_canon_sha256":"12976f9c86e5a3cd4077ad31be7ec4968047c4ab2afb131783c40befd57c3a05"},"schema_version":"1.0","source":{"id":"math-ph/0603083","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0603083","created_at":"2026-07-04T15:17:51Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0603083v2","created_at":"2026-07-04T15:17:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0603083","created_at":"2026-07-04T15:17:51Z"},{"alias_kind":"pith_short_12","alias_value":"6ZU2VHSZW2S6","created_at":"2026-07-04T15:17:51Z"},{"alias_kind":"pith_short_16","alias_value":"6ZU2VHSZW2S6CSV3","created_at":"2026-07-04T15:17:51Z"},{"alias_kind":"pith_short_8","alias_value":"6ZU2VHSZ","created_at":"2026-07-04T15:17:51Z"}],"graph_snapshots":[{"event_id":"sha256:58a2159d615f8ebb6c6732eaafc957ea1dea1281e250de7cef2f48b2c173948a","target":"graph","created_at":"2026-07-04T15:17:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math-ph/0603083/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a new type of spectral density condition, that we call L^2-nuclearity. One formulation concerns lowest weight unitary representations of SL(2,R) and turns out to be equivalent to the existence of characters. A second formulation concerns inclusions of local observable von Neumann algebras in Quantum Field Theory. We show the two formulations to agree in chiral Conformal QFT and, starting from the trace class condition for the semigroup generated by the conformal Hamiltonian L_0, we infer and naturally estimate the Buchholz-Wichmann nuclearity condition and the (distal) split prope","authors_text":"Claudio D'Antoni, Detlev Buchholz, Roberto Longo","cross_cats":["math.MP","math.OA"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2006-03-30T13:30:28Z","title":"Nuclearity and Thermal States in Conformal Field Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0603083","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:baea8119f6780b67959296cee6c6ddaba0ef37046087b1e9f1004c55ac3e8267","target":"record","created_at":"2026-07-04T15:17:51Z","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":"16a2c86fa9fe0157695651c4bec9314cf3b5d8c073c8aae02eb6e204557fa466","cross_cats_sorted":["math.MP","math.OA"],"license":"","primary_cat":"math-ph","submitted_at":"2006-03-30T13:30:28Z","title_canon_sha256":"12976f9c86e5a3cd4077ad31be7ec4968047c4ab2afb131783c40befd57c3a05"},"schema_version":"1.0","source":{"id":"math-ph/0603083","kind":"arxiv","version":2}},"canonical_sha256":"f669aa9e59b6a5e14abbe4b6f0a773aa7ec9d7a1b5c2f6b6a32fd098dc240f04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f669aa9e59b6a5e14abbe4b6f0a773aa7ec9d7a1b5c2f6b6a32fd098dc240f04","first_computed_at":"2026-07-04T15:17:51.530165Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:17:51.530165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RHdlxsleyfdgHzfhHoyYB1QL45+p6+WqPrjcP+8MEfYDgYVQM94rWP5hpyjTuqGglFlqbZNFRiDyDl45C3yRAg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:17:51.530761Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0603083","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:baea8119f6780b67959296cee6c6ddaba0ef37046087b1e9f1004c55ac3e8267","sha256:58a2159d615f8ebb6c6732eaafc957ea1dea1281e250de7cef2f48b2c173948a"],"state_sha256":"6b79d9798c05fb194bc4776f71e661686a5a0e239ec3debca442f585d3df15d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GEGNjhne0h9BLAdb9x/WDv1wg2ACTA48nkp67IvTx4fdo4qOrFnAsqVdLxsClWf0aoS00ojPuEi92ODoq5+0BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T08:40:13.806211Z","bundle_sha256":"2a2fd14cf917002f992168b837c3d43fe31cce4fca316458079fd716f3af94f7"}}