{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:3GOKXDTQDJNH5WCELFW6AT247Z","short_pith_number":"pith:3GOKXDTQ","canonical_record":{"source":{"id":"2605.29725","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-05-28T10:19:40Z","cross_cats_sorted":["hep-th","math-ph","math.MP","stat.AP"],"title_canon_sha256":"0a65b43492bc784558ed37e462e1a52891036ba19ebb29df739ea7b791586253","abstract_canon_sha256":"69d34e1b99a3869c625256a7d31435e95412afe469772546d57563f2e676d303"},"schema_version":"1.0"},"canonical_sha256":"d99cab8e701a5a7ed844596de04f5cfe45e46a1248dbd21065e7d6d32f4325b4","source":{"kind":"arxiv","id":"2605.29725","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.29725","created_at":"2026-05-29T01:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"2605.29725v1","created_at":"2026-05-29T01:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.29725","created_at":"2026-05-29T01:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"3GOKXDTQDJNH","created_at":"2026-05-29T01:05:57Z"},{"alias_kind":"pith_short_16","alias_value":"3GOKXDTQDJNH5WCE","created_at":"2026-05-29T01:05:57Z"},{"alias_kind":"pith_short_8","alias_value":"3GOKXDTQ","created_at":"2026-05-29T01:05:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:3GOKXDTQDJNH5WCELFW6AT247Z","target":"record","payload":{"canonical_record":{"source":{"id":"2605.29725","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-05-28T10:19:40Z","cross_cats_sorted":["hep-th","math-ph","math.MP","stat.AP"],"title_canon_sha256":"0a65b43492bc784558ed37e462e1a52891036ba19ebb29df739ea7b791586253","abstract_canon_sha256":"69d34e1b99a3869c625256a7d31435e95412afe469772546d57563f2e676d303"},"schema_version":"1.0"},"canonical_sha256":"d99cab8e701a5a7ed844596de04f5cfe45e46a1248dbd21065e7d6d32f4325b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T01:05:57.023325Z","signature_b64":"C8+HmlTRLDo7IZjgS2u6GRxZFR7AYBr1qq3nQq7rIw7B2quI/KLZUNakOaVPjDsKYK84zZdeqkfcxfkv5a/0Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d99cab8e701a5a7ed844596de04f5cfe45e46a1248dbd21065e7d6d32f4325b4","last_reissued_at":"2026-05-29T01:05:57.022869Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T01:05:57.022869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.29725","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":"2026-05-29T01:05:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Qqd73/WPBU1o2yO+lBKyZnmay7nt4q7XCbArfHwHQzX/9akn9Pw4Ed+G4HATBWEy37z/0zqNgQK9Wl7jqRWBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T16:46:29.036201Z"},"content_sha256":"89590f2aaaee85a1b5fdd9592c56ef2660e62b2371f46b64b5f900b505659d1c","schema_version":"1.0","event_id":"sha256:89590f2aaaee85a1b5fdd9592c56ef2660e62b2371f46b64b5f900b505659d1c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:3GOKXDTQDJNH5WCELFW6AT247Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-Perturbative Closed Form for the Typical Bipartite Mutual Information of Haar-Random States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","stat.AP"],"primary_cat":"quant-ph","authors_text":"Pei-Wen Li, Samuel L. Braunstein, Zhi-Wei Wang","submitted_at":"2026-05-28T10:19:40Z","abstract_excerpt":"The average bipartite quantum mutual information $\\langle I(A{:}B)\\rangle$ of Haar-random pure states can be expressed exactly through Page's formula in terms of digamma functions. We show that this quantity admits a single non-perturbative closed form: $\\langle I(A{:}B)\\rangle = (d_A^2-1)(d_B^2-1)\\,\\mathcal{G}(d_A,d_B,d_E)$, where $\\mathcal{G}$ is given by an explicit convergent integral over a Bose--Einstein kernel. The overall factor $(d_A^2-1)(d_B^2-1)=\\dim[\\mathfrak{su}(d_A)]\\cdot\\dim[\\mathfrak{su}(d_B)]$ is exact, not merely asymptotic. The asymptotic expansion of $\\mathcal{G}$ in $1/N$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29725","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.29725/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":"2026-05-29T01:05:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WSGr5LbIgSK9Kc3HFFrpOhC6F0bai+7iO71mKlqzLBE3RVrXIxhDPw+lcm1JiHyow3JQfQ3/vWtNGDnT3EdTCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T16:46:29.036613Z"},"content_sha256":"4cf282cb1d5334e90ad27e9614ba30be29d5fcc317674ed43ce9a2754b0b9444","schema_version":"1.0","event_id":"sha256:4cf282cb1d5334e90ad27e9614ba30be29d5fcc317674ed43ce9a2754b0b9444"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3GOKXDTQDJNH5WCELFW6AT247Z/bundle.json","state_url":"https://pith.science/pith/3GOKXDTQDJNH5WCELFW6AT247Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3GOKXDTQDJNH5WCELFW6AT247Z/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":"2026-07-02T16:46:29Z","links":{"resolver":"https://pith.science/pith/3GOKXDTQDJNH5WCELFW6AT247Z","bundle":"https://pith.science/pith/3GOKXDTQDJNH5WCELFW6AT247Z/bundle.json","state":"https://pith.science/pith/3GOKXDTQDJNH5WCELFW6AT247Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3GOKXDTQDJNH5WCELFW6AT247Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3GOKXDTQDJNH5WCELFW6AT247Z","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":"69d34e1b99a3869c625256a7d31435e95412afe469772546d57563f2e676d303","cross_cats_sorted":["hep-th","math-ph","math.MP","stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-05-28T10:19:40Z","title_canon_sha256":"0a65b43492bc784558ed37e462e1a52891036ba19ebb29df739ea7b791586253"},"schema_version":"1.0","source":{"id":"2605.29725","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.29725","created_at":"2026-05-29T01:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"2605.29725v1","created_at":"2026-05-29T01:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.29725","created_at":"2026-05-29T01:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"3GOKXDTQDJNH","created_at":"2026-05-29T01:05:57Z"},{"alias_kind":"pith_short_16","alias_value":"3GOKXDTQDJNH5WCE","created_at":"2026-05-29T01:05:57Z"},{"alias_kind":"pith_short_8","alias_value":"3GOKXDTQ","created_at":"2026-05-29T01:05:57Z"}],"graph_snapshots":[{"event_id":"sha256:4cf282cb1d5334e90ad27e9614ba30be29d5fcc317674ed43ce9a2754b0b9444","target":"graph","created_at":"2026-05-29T01:05:57Z","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/2605.29725/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The average bipartite quantum mutual information $\\langle I(A{:}B)\\rangle$ of Haar-random pure states can be expressed exactly through Page's formula in terms of digamma functions. We show that this quantity admits a single non-perturbative closed form: $\\langle I(A{:}B)\\rangle = (d_A^2-1)(d_B^2-1)\\,\\mathcal{G}(d_A,d_B,d_E)$, where $\\mathcal{G}$ is given by an explicit convergent integral over a Bose--Einstein kernel. The overall factor $(d_A^2-1)(d_B^2-1)=\\dim[\\mathfrak{su}(d_A)]\\cdot\\dim[\\mathfrak{su}(d_B)]$ is exact, not merely asymptotic. The asymptotic expansion of $\\mathcal{G}$ in $1/N$ ","authors_text":"Pei-Wen Li, Samuel L. Braunstein, Zhi-Wei Wang","cross_cats":["hep-th","math-ph","math.MP","stat.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-05-28T10:19:40Z","title":"Non-Perturbative Closed Form for the Typical Bipartite Mutual Information of Haar-Random States"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29725","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":"sha256:89590f2aaaee85a1b5fdd9592c56ef2660e62b2371f46b64b5f900b505659d1c","target":"record","created_at":"2026-05-29T01:05:57Z","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":"69d34e1b99a3869c625256a7d31435e95412afe469772546d57563f2e676d303","cross_cats_sorted":["hep-th","math-ph","math.MP","stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-05-28T10:19:40Z","title_canon_sha256":"0a65b43492bc784558ed37e462e1a52891036ba19ebb29df739ea7b791586253"},"schema_version":"1.0","source":{"id":"2605.29725","kind":"arxiv","version":1}},"canonical_sha256":"d99cab8e701a5a7ed844596de04f5cfe45e46a1248dbd21065e7d6d32f4325b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d99cab8e701a5a7ed844596de04f5cfe45e46a1248dbd21065e7d6d32f4325b4","first_computed_at":"2026-05-29T01:05:57.022869Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T01:05:57.022869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C8+HmlTRLDo7IZjgS2u6GRxZFR7AYBr1qq3nQq7rIw7B2quI/KLZUNakOaVPjDsKYK84zZdeqkfcxfkv5a/0Dw==","signature_status":"signed_v1","signed_at":"2026-05-29T01:05:57.023325Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.29725","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89590f2aaaee85a1b5fdd9592c56ef2660e62b2371f46b64b5f900b505659d1c","sha256:4cf282cb1d5334e90ad27e9614ba30be29d5fcc317674ed43ce9a2754b0b9444"],"state_sha256":"b049ed30ef8bdcb9eb17ca35c263463a313fd456159c87aacbeabdaf06255c36"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dCVvt3c2h4Su2QVioP9khPgUhlWVMPz5z4pRj6sesI7uHFRmV6QjDY6ik4vluEZWOQqwxOMk9aGglkrMKB4kBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T16:46:29.038937Z","bundle_sha256":"c68e205272d1b160dfc188754f8fb168d7df99e549d34ac4d0532324d13f0620"}}