{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:BMEGPOUXEZVUI3OEZ676WDN7UL","short_pith_number":"pith:BMEGPOUX","canonical_record":{"source":{"id":"2606.08928","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-08T02:09:51Z","cross_cats_sorted":[],"title_canon_sha256":"d8260dcafb62ab498a3739ed35a921e5f147de4d354941cc1f34536dcffc783c","abstract_canon_sha256":"dcd58cc9347c4fe3e829a993fec1399eec34d3bbd79e37b35dfbed665dc9f0b4"},"schema_version":"1.0"},"canonical_sha256":"0b0867ba97266b446dc4cfbfeb0dbfa2e17b4ee245af0516011b3f5c644c4588","source":{"kind":"arxiv","id":"2606.08928","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08928","created_at":"2026-06-09T02:07:47Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08928v1","created_at":"2026-06-09T02:07:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08928","created_at":"2026-06-09T02:07:47Z"},{"alias_kind":"pith_short_12","alias_value":"BMEGPOUXEZVU","created_at":"2026-06-09T02:07:47Z"},{"alias_kind":"pith_short_16","alias_value":"BMEGPOUXEZVUI3OE","created_at":"2026-06-09T02:07:47Z"},{"alias_kind":"pith_short_8","alias_value":"BMEGPOUX","created_at":"2026-06-09T02:07:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:BMEGPOUXEZVUI3OEZ676WDN7UL","target":"record","payload":{"canonical_record":{"source":{"id":"2606.08928","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-08T02:09:51Z","cross_cats_sorted":[],"title_canon_sha256":"d8260dcafb62ab498a3739ed35a921e5f147de4d354941cc1f34536dcffc783c","abstract_canon_sha256":"dcd58cc9347c4fe3e829a993fec1399eec34d3bbd79e37b35dfbed665dc9f0b4"},"schema_version":"1.0"},"canonical_sha256":"0b0867ba97266b446dc4cfbfeb0dbfa2e17b4ee245af0516011b3f5c644c4588","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:07:47.802538Z","signature_b64":"94XRvYTDjxCauP1/FnF2AmtR8SnMQmD9NO0a5QwNR9aPp0byeZDDSc2oLxGkLY2LoAGJC28H3lsLcO6lu9BwBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b0867ba97266b446dc4cfbfeb0dbfa2e17b4ee245af0516011b3f5c644c4588","last_reissued_at":"2026-06-09T02:07:47.801650Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:07:47.801650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.08928","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":"2026-06-09T02:07:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yaYyFV6m8ZxI1tCq5X515T56Hu8hz6BAIESsn14P5q8gj+LCyklWgkRNltehURqBMYpKDl4pptYXPccXlUufDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T17:09:45.408373Z"},"content_sha256":"77e1c48c8a066ad81530a7634add2bc974c92c806795db9772ded2c1df89585a","schema_version":"1.0","event_id":"sha256:77e1c48c8a066ad81530a7634add2bc974c92c806795db9772ded2c1df89585a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:BMEGPOUXEZVUI3OEZ676WDN7UL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Singular Values of L\\'evy's Area Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Danilo Jr Dela Cruz, Harald Oberhauser","submitted_at":"2026-06-08T02:09:51Z","abstract_excerpt":"The matrix of L\\'evy's areas of $d$-dimensional Brownian motion is a fundamental object in stochastic analysis. In this article, we study the singular values of this $d \\times d$ skew-symmetric random matrix. First, we derive an explicit formula for the density of the singular values and, en passant, present a new short proof of the characteristic function of L\\'evy's area when $d \\ge 3$. This also allows us to extend the well-known formula for the density of L\\'evy's area to $d \\ge 3$. Next, we use these results to characterise the singular spectrum as a determinantal point process with its k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08928","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/2606.08928/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":"2026-06-09T02:07:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"14EMazCnpNO/sCoTrgRkhDDMY96gEo+ef22hydB3Xg1BX4VRRtWDPhKZhcQVU0Ctz7xP+D9DtygBfL0VnTcEDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T17:09:45.408747Z"},"content_sha256":"a891b923f7e58dfd2e2e2a03a0d8c92f95a0e29fdefc3014845dad30064a1d14","schema_version":"1.0","event_id":"sha256:a891b923f7e58dfd2e2e2a03a0d8c92f95a0e29fdefc3014845dad30064a1d14"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BMEGPOUXEZVUI3OEZ676WDN7UL/bundle.json","state_url":"https://pith.science/pith/BMEGPOUXEZVUI3OEZ676WDN7UL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BMEGPOUXEZVUI3OEZ676WDN7UL/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":"2026-06-28T17:09:45Z","links":{"resolver":"https://pith.science/pith/BMEGPOUXEZVUI3OEZ676WDN7UL","bundle":"https://pith.science/pith/BMEGPOUXEZVUI3OEZ676WDN7UL/bundle.json","state":"https://pith.science/pith/BMEGPOUXEZVUI3OEZ676WDN7UL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BMEGPOUXEZVUI3OEZ676WDN7UL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BMEGPOUXEZVUI3OEZ676WDN7UL","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":"dcd58cc9347c4fe3e829a993fec1399eec34d3bbd79e37b35dfbed665dc9f0b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-08T02:09:51Z","title_canon_sha256":"d8260dcafb62ab498a3739ed35a921e5f147de4d354941cc1f34536dcffc783c"},"schema_version":"1.0","source":{"id":"2606.08928","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08928","created_at":"2026-06-09T02:07:47Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08928v1","created_at":"2026-06-09T02:07:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08928","created_at":"2026-06-09T02:07:47Z"},{"alias_kind":"pith_short_12","alias_value":"BMEGPOUXEZVU","created_at":"2026-06-09T02:07:47Z"},{"alias_kind":"pith_short_16","alias_value":"BMEGPOUXEZVUI3OE","created_at":"2026-06-09T02:07:47Z"},{"alias_kind":"pith_short_8","alias_value":"BMEGPOUX","created_at":"2026-06-09T02:07:47Z"}],"graph_snapshots":[{"event_id":"sha256:a891b923f7e58dfd2e2e2a03a0d8c92f95a0e29fdefc3014845dad30064a1d14","target":"graph","created_at":"2026-06-09T02:07:47Z","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/2606.08928/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The matrix of L\\'evy's areas of $d$-dimensional Brownian motion is a fundamental object in stochastic analysis. In this article, we study the singular values of this $d \\times d$ skew-symmetric random matrix. First, we derive an explicit formula for the density of the singular values and, en passant, present a new short proof of the characteristic function of L\\'evy's area when $d \\ge 3$. This also allows us to extend the well-known formula for the density of L\\'evy's area to $d \\ge 3$. Next, we use these results to characterise the singular spectrum as a determinantal point process with its k","authors_text":"Danilo Jr Dela Cruz, Harald Oberhauser","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-08T02:09:51Z","title":"The Singular Values of L\\'evy's Area Matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08928","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":"sha256:77e1c48c8a066ad81530a7634add2bc974c92c806795db9772ded2c1df89585a","target":"record","created_at":"2026-06-09T02:07:47Z","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":"dcd58cc9347c4fe3e829a993fec1399eec34d3bbd79e37b35dfbed665dc9f0b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-08T02:09:51Z","title_canon_sha256":"d8260dcafb62ab498a3739ed35a921e5f147de4d354941cc1f34536dcffc783c"},"schema_version":"1.0","source":{"id":"2606.08928","kind":"arxiv","version":1}},"canonical_sha256":"0b0867ba97266b446dc4cfbfeb0dbfa2e17b4ee245af0516011b3f5c644c4588","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b0867ba97266b446dc4cfbfeb0dbfa2e17b4ee245af0516011b3f5c644c4588","first_computed_at":"2026-06-09T02:07:47.801650Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:07:47.801650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"94XRvYTDjxCauP1/FnF2AmtR8SnMQmD9NO0a5QwNR9aPp0byeZDDSc2oLxGkLY2LoAGJC28H3lsLcO6lu9BwBg==","signature_status":"signed_v1","signed_at":"2026-06-09T02:07:47.802538Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.08928","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77e1c48c8a066ad81530a7634add2bc974c92c806795db9772ded2c1df89585a","sha256:a891b923f7e58dfd2e2e2a03a0d8c92f95a0e29fdefc3014845dad30064a1d14"],"state_sha256":"1a0192635dbe6e92031f886bf427f302a02a3c73ac539d2b4ad4824f96f1f9ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Iw5UyEnS1/rRSk1dXkw8JUgODVpeA/Ddg5Xyx+HH5zeULQVj5RP4dac3NjKCJRIg8xW0mXsJQ64WcRhjbrFsCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T17:09:45.410800Z","bundle_sha256":"901a9abe03e476dabae088b0b2c60d8b1de790fac00114b074610b29295b5db5"}}