{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:HO4SH4VIDWO5MW5S54E7EWID6T","short_pith_number":"pith:HO4SH4VI","canonical_record":{"source":{"id":"2607.05693","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-06T23:21:51Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"fe268b7ef4a44ec1932e905d0e053da39c29cb30515954327b2e3a977176c3a5","abstract_canon_sha256":"ca8a978e25c161041471798e8b578be32ba515c8f3757da429d5d75ba0390e64"},"schema_version":"1.0"},"canonical_sha256":"3bb923f2a81d9dd65bb2ef09f25903f4e811fcad879aa7c2725b0d52de79b479","source":{"kind":"arxiv","id":"2607.05693","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.05693","created_at":"2026-07-08T01:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"2607.05693v1","created_at":"2026-07-08T01:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.05693","created_at":"2026-07-08T01:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"HO4SH4VIDWO5","created_at":"2026-07-08T01:18:41Z"},{"alias_kind":"pith_short_16","alias_value":"HO4SH4VIDWO5MW5S","created_at":"2026-07-08T01:18:41Z"},{"alias_kind":"pith_short_8","alias_value":"HO4SH4VI","created_at":"2026-07-08T01:18:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:HO4SH4VIDWO5MW5S54E7EWID6T","target":"record","payload":{"canonical_record":{"source":{"id":"2607.05693","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-06T23:21:51Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"fe268b7ef4a44ec1932e905d0e053da39c29cb30515954327b2e3a977176c3a5","abstract_canon_sha256":"ca8a978e25c161041471798e8b578be32ba515c8f3757da429d5d75ba0390e64"},"schema_version":"1.0"},"canonical_sha256":"3bb923f2a81d9dd65bb2ef09f25903f4e811fcad879aa7c2725b0d52de79b479","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-08T01:18:41.730417Z","signature_b64":"YYJmJA1yOkYQUdkW7/FSX5NwxVRU+/TX68NuaAG6+2xQPLKOYTVctBkjQ+TVA13k5jWClu6A35w4boRDyLeoDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bb923f2a81d9dd65bb2ef09f25903f4e811fcad879aa7c2725b0d52de79b479","last_reissued_at":"2026-07-08T01:18:41.729968Z","signature_status":"signed_v1","first_computed_at":"2026-07-08T01:18:41.729968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.05693","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":"2026-07-08T01:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q8MqFXN6GP2zoRpGcOK0L6iReDQCkWsiWpNZOyQxRsVDdZz49kmiRnsemTz8dNPVQWpWTGcyz++COx0sdQ0aAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T10:41:26.870726Z"},"content_sha256":"cbdfd628aa7bed16cb5887f06bb535ca3517c2b9ae3406479fdf60432882a61b","schema_version":"1.0","event_id":"sha256:cbdfd628aa7bed16cb5887f06bb535ca3517c2b9ae3406479fdf60432882a61b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:HO4SH4VIDWO5MW5S54E7EWID6T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Free Multiplicative Convolution and Erlang Moments in Monitored Quantum Transport","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"math.PR","authors_text":"Joon Hyung Lee","submitted_at":"2026-07-06T23:21:51Z","abstract_excerpt":"We study the transmission eigenvalues of monitored Haar products \\[\n  B_L=(PS_L)(PS_{L-1})\\cdots(PS_1), \\] where the $S_i$ are independent Haar unitaries and $P$ is a deterministic projection. For fixed $L$, we prove that the empirical eigenvalue distribution of $B_L^\\dagger B_L$ converges to $\\nu_c^{\\boxtimes L}$, where $\\nu_c=(1-c)\\delta_1+c\\delta_0$. We then take the free small-loss limit and identify the limiting law by \\[\n  S_{\\mu_\\tau}(z)=\\exp\\left(\\frac{\\tau}{1+z}\\right). \\] Lagrange inversion gives explicit Erlang-type moments, explaining the polynomials appearing in Beenakker's recurs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05693","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/2607.05693/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":"2026-07-08T01:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DxqnDxST+oa0BwZk87BUv1hGgGeStKjb2foDa6IYQtOIUckAo1ytIdRh5Gr8aj4/Prh/z3sUqOaHsBBHfVvEDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T10:41:26.871638Z"},"content_sha256":"2744467ae571b4bb4ca967bc95127c31e56c00fcbf8dee0df950671f3c7b8de8","schema_version":"1.0","event_id":"sha256:2744467ae571b4bb4ca967bc95127c31e56c00fcbf8dee0df950671f3c7b8de8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HO4SH4VIDWO5MW5S54E7EWID6T/bundle.json","state_url":"https://pith.science/pith/HO4SH4VIDWO5MW5S54E7EWID6T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HO4SH4VIDWO5MW5S54E7EWID6T/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":"2026-08-15T10:41:26Z","links":{"resolver":"https://pith.science/pith/HO4SH4VIDWO5MW5S54E7EWID6T","bundle":"https://pith.science/pith/HO4SH4VIDWO5MW5S54E7EWID6T/bundle.json","state":"https://pith.science/pith/HO4SH4VIDWO5MW5S54E7EWID6T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HO4SH4VIDWO5MW5S54E7EWID6T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HO4SH4VIDWO5MW5S54E7EWID6T","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":"ca8a978e25c161041471798e8b578be32ba515c8f3757da429d5d75ba0390e64","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-06T23:21:51Z","title_canon_sha256":"fe268b7ef4a44ec1932e905d0e053da39c29cb30515954327b2e3a977176c3a5"},"schema_version":"1.0","source":{"id":"2607.05693","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.05693","created_at":"2026-07-08T01:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"2607.05693v1","created_at":"2026-07-08T01:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.05693","created_at":"2026-07-08T01:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"HO4SH4VIDWO5","created_at":"2026-07-08T01:18:41Z"},{"alias_kind":"pith_short_16","alias_value":"HO4SH4VIDWO5MW5S","created_at":"2026-07-08T01:18:41Z"},{"alias_kind":"pith_short_8","alias_value":"HO4SH4VI","created_at":"2026-07-08T01:18:41Z"}],"graph_snapshots":[{"event_id":"sha256:2744467ae571b4bb4ca967bc95127c31e56c00fcbf8dee0df950671f3c7b8de8","target":"graph","created_at":"2026-07-08T01:18:41Z","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/2607.05693/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the transmission eigenvalues of monitored Haar products \\[\n  B_L=(PS_L)(PS_{L-1})\\cdots(PS_1), \\] where the $S_i$ are independent Haar unitaries and $P$ is a deterministic projection. For fixed $L$, we prove that the empirical eigenvalue distribution of $B_L^\\dagger B_L$ converges to $\\nu_c^{\\boxtimes L}$, where $\\nu_c=(1-c)\\delta_1+c\\delta_0$. We then take the free small-loss limit and identify the limiting law by \\[\n  S_{\\mu_\\tau}(z)=\\exp\\left(\\frac{\\tau}{1+z}\\right). \\] Lagrange inversion gives explicit Erlang-type moments, explaining the polynomials appearing in Beenakker's recurs","authors_text":"Joon Hyung Lee","cross_cats":["math-ph","math.MP","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-06T23:21:51Z","title":"Free Multiplicative Convolution and Erlang Moments in Monitored Quantum Transport"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05693","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:cbdfd628aa7bed16cb5887f06bb535ca3517c2b9ae3406479fdf60432882a61b","target":"record","created_at":"2026-07-08T01:18:41Z","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":"ca8a978e25c161041471798e8b578be32ba515c8f3757da429d5d75ba0390e64","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-06T23:21:51Z","title_canon_sha256":"fe268b7ef4a44ec1932e905d0e053da39c29cb30515954327b2e3a977176c3a5"},"schema_version":"1.0","source":{"id":"2607.05693","kind":"arxiv","version":1}},"canonical_sha256":"3bb923f2a81d9dd65bb2ef09f25903f4e811fcad879aa7c2725b0d52de79b479","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bb923f2a81d9dd65bb2ef09f25903f4e811fcad879aa7c2725b0d52de79b479","first_computed_at":"2026-07-08T01:18:41.729968Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-08T01:18:41.729968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YYJmJA1yOkYQUdkW7/FSX5NwxVRU+/TX68NuaAG6+2xQPLKOYTVctBkjQ+TVA13k5jWClu6A35w4boRDyLeoDQ==","signature_status":"signed_v1","signed_at":"2026-07-08T01:18:41.730417Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.05693","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbdfd628aa7bed16cb5887f06bb535ca3517c2b9ae3406479fdf60432882a61b","sha256:2744467ae571b4bb4ca967bc95127c31e56c00fcbf8dee0df950671f3c7b8de8"],"state_sha256":"4ad625158c1ec1d6b4c27105de4cc023b1f8eac9671e972527ab87c55986d0fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kwRoiF1W3vWD+eAXuKA9YZ1W2rMLVnxAlZJ1tg4+IgqNGIsf70YuboFHj2UaHXHwR2gRijnthJKZeDOUrYLoAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T10:41:26.878283Z","bundle_sha256":"42dfa5aa6eab05a7be8ff8150116e8093bdf34d8dc6924d5ac9fb4688ac4de66"}}