{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:MZ2GG653TU2DVCYEPQKUAID7EJ","short_pith_number":"pith:MZ2GG653","canonical_record":{"source":{"id":"2601.03253","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-01-06T18:57:29Z","cross_cats_sorted":[],"title_canon_sha256":"ae3b12f9fc3a6a9f0a18d8bfb070be1451c4b58a767b7d0ceb87d4f8405ea2e0","abstract_canon_sha256":"211270fb5b6fb5566e224915a3936fdc2a602e667b167b300bb231b7233e3450"},"schema_version":"1.0"},"canonical_sha256":"6674637bbb9d343a8b047c1540207f226ec319e7fae4294f8a1b540eb1a028d8","source":{"kind":"arxiv","id":"2601.03253","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.03253","created_at":"2026-05-22T01:03:53Z"},{"alias_kind":"arxiv_version","alias_value":"2601.03253v3","created_at":"2026-05-22T01:03:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.03253","created_at":"2026-05-22T01:03:53Z"},{"alias_kind":"pith_short_12","alias_value":"MZ2GG653TU2D","created_at":"2026-05-22T01:03:53Z"},{"alias_kind":"pith_short_16","alias_value":"MZ2GG653TU2DVCYE","created_at":"2026-05-22T01:03:53Z"},{"alias_kind":"pith_short_8","alias_value":"MZ2GG653","created_at":"2026-05-22T01:03:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:MZ2GG653TU2DVCYEPQKUAID7EJ","target":"record","payload":{"canonical_record":{"source":{"id":"2601.03253","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-01-06T18:57:29Z","cross_cats_sorted":[],"title_canon_sha256":"ae3b12f9fc3a6a9f0a18d8bfb070be1451c4b58a767b7d0ceb87d4f8405ea2e0","abstract_canon_sha256":"211270fb5b6fb5566e224915a3936fdc2a602e667b167b300bb231b7233e3450"},"schema_version":"1.0"},"canonical_sha256":"6674637bbb9d343a8b047c1540207f226ec319e7fae4294f8a1b540eb1a028d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:03:53.106720Z","signature_b64":"8lyILjbbJsELL5SmiiYmRtQJ/S4NU4jXp4Taqb1DHAs8nApL9tIyebIkLIqzhC6eQDDC26/8udiykuWCnoUjCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6674637bbb9d343a8b047c1540207f226ec319e7fae4294f8a1b540eb1a028d8","last_reissued_at":"2026-05-22T01:03:53.105706Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:03:53.105706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2601.03253","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-22T01:03:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UIblWVq48Sa2rt5LiV5m2gKueynFwOqnz68eG7sEwNAiR6c/Xg8MsLJQTe9oCz/kzZmxXCsqGhhfAREl3aDWDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T20:44:28.006299Z"},"content_sha256":"d74282d859664113c3a76c308b4061d669a953d137054b594a53f05b6c9d0093","schema_version":"1.0","event_id":"sha256:d74282d859664113c3a76c308b4061d669a953d137054b594a53f05b6c9d0093"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:MZ2GG653TU2DVCYEPQKUAID7EJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Grand-Canonical Typicality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Cedric Igelspacher, Cornelia Vogel, Roderich Tumulka","submitted_at":"2026-01-06T18:57:29Z","abstract_excerpt":"We study how the grand-canonical density matrix arises in macroscopic quantum systems. ``Canonical typicality'' is the known statement that for a typical wave function $\\Psi$ from a micro-canonical energy shell of a quantum system $S$ weakly coupled to a large but finite quantum system $B$, the reduced density matrix $\\hat{\\rho}^S_\\Psi=\\mathrm{tr}^B |\\Psi\\rangle\\langle \\Psi|$ is approximately equal to the canonical density matrix $\\hat{\\rho}_\\mathrm{can}=Z^{-1}_\\mathrm{can} \\exp(-\\beta \\hat{H}^S)$. Here, we discuss the analogous statement and related questions for the \\emph{grand-canonical} de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.03253","kind":"arxiv","version":3},"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/2601.03253/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":"2026-05-22T01:03:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HLtiGgh+nIpFXND6dlmupGFkMQgHkBBuPBPgl76+oT/aj4XaVXOESlpad/MLi0FdUqEf182j1gn8XMoy7nyUBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T20:44:28.007020Z"},"content_sha256":"ee0c063dee8b6ef56d1c8429d3009c97055994b487fcdb7f4244e92b24b63907","schema_version":"1.0","event_id":"sha256:ee0c063dee8b6ef56d1c8429d3009c97055994b487fcdb7f4244e92b24b63907"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MZ2GG653TU2DVCYEPQKUAID7EJ/bundle.json","state_url":"https://pith.science/pith/MZ2GG653TU2DVCYEPQKUAID7EJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MZ2GG653TU2DVCYEPQKUAID7EJ/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":"2026-05-24T20:44:28Z","links":{"resolver":"https://pith.science/pith/MZ2GG653TU2DVCYEPQKUAID7EJ","bundle":"https://pith.science/pith/MZ2GG653TU2DVCYEPQKUAID7EJ/bundle.json","state":"https://pith.science/pith/MZ2GG653TU2DVCYEPQKUAID7EJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MZ2GG653TU2DVCYEPQKUAID7EJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MZ2GG653TU2DVCYEPQKUAID7EJ","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":"211270fb5b6fb5566e224915a3936fdc2a602e667b167b300bb231b7233e3450","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-01-06T18:57:29Z","title_canon_sha256":"ae3b12f9fc3a6a9f0a18d8bfb070be1451c4b58a767b7d0ceb87d4f8405ea2e0"},"schema_version":"1.0","source":{"id":"2601.03253","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.03253","created_at":"2026-05-22T01:03:53Z"},{"alias_kind":"arxiv_version","alias_value":"2601.03253v3","created_at":"2026-05-22T01:03:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.03253","created_at":"2026-05-22T01:03:53Z"},{"alias_kind":"pith_short_12","alias_value":"MZ2GG653TU2D","created_at":"2026-05-22T01:03:53Z"},{"alias_kind":"pith_short_16","alias_value":"MZ2GG653TU2DVCYE","created_at":"2026-05-22T01:03:53Z"},{"alias_kind":"pith_short_8","alias_value":"MZ2GG653","created_at":"2026-05-22T01:03:53Z"}],"graph_snapshots":[{"event_id":"sha256:ee0c063dee8b6ef56d1c8429d3009c97055994b487fcdb7f4244e92b24b63907","target":"graph","created_at":"2026-05-22T01:03:53Z","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/2601.03253/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study how the grand-canonical density matrix arises in macroscopic quantum systems. ``Canonical typicality'' is the known statement that for a typical wave function $\\Psi$ from a micro-canonical energy shell of a quantum system $S$ weakly coupled to a large but finite quantum system $B$, the reduced density matrix $\\hat{\\rho}^S_\\Psi=\\mathrm{tr}^B |\\Psi\\rangle\\langle \\Psi|$ is approximately equal to the canonical density matrix $\\hat{\\rho}_\\mathrm{can}=Z^{-1}_\\mathrm{can} \\exp(-\\beta \\hat{H}^S)$. Here, we discuss the analogous statement and related questions for the \\emph{grand-canonical} de","authors_text":"Cedric Igelspacher, Cornelia Vogel, Roderich Tumulka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-01-06T18:57:29Z","title":"Grand-Canonical Typicality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.03253","kind":"arxiv","version":3},"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:d74282d859664113c3a76c308b4061d669a953d137054b594a53f05b6c9d0093","target":"record","created_at":"2026-05-22T01:03:53Z","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":"211270fb5b6fb5566e224915a3936fdc2a602e667b167b300bb231b7233e3450","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-01-06T18:57:29Z","title_canon_sha256":"ae3b12f9fc3a6a9f0a18d8bfb070be1451c4b58a767b7d0ceb87d4f8405ea2e0"},"schema_version":"1.0","source":{"id":"2601.03253","kind":"arxiv","version":3}},"canonical_sha256":"6674637bbb9d343a8b047c1540207f226ec319e7fae4294f8a1b540eb1a028d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6674637bbb9d343a8b047c1540207f226ec319e7fae4294f8a1b540eb1a028d8","first_computed_at":"2026-05-22T01:03:53.105706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:03:53.105706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8lyILjbbJsELL5SmiiYmRtQJ/S4NU4jXp4Taqb1DHAs8nApL9tIyebIkLIqzhC6eQDDC26/8udiykuWCnoUjCw==","signature_status":"signed_v1","signed_at":"2026-05-22T01:03:53.106720Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.03253","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d74282d859664113c3a76c308b4061d669a953d137054b594a53f05b6c9d0093","sha256:ee0c063dee8b6ef56d1c8429d3009c97055994b487fcdb7f4244e92b24b63907"],"state_sha256":"71d5c5b0fd5d4be900e9ceb47a7aebb81360fbfb169c0e8922a9992e78076277"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QniZd6sh+07DaXIsSgVc4HL9FdQUaPYtGUGrCZGEWSkj2dw2SufJ3bwZ8kHtjfG/9r59r4VfGJVCpqmj87+vBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T20:44:28.009576Z","bundle_sha256":"e35dbcd03071a858e513e7a1291be0dceefbaf02a3ecf0cd20b4be1d1dc2222d"}}