{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DU3TQYCOVCNZMJIBLLYO433YMC","short_pith_number":"pith:DU3TQYCO","canonical_record":{"source":{"id":"1309.5661","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-22T22:33:38Z","cross_cats_sorted":["math.AG","math.AT","math.DG"],"title_canon_sha256":"9a1257f79d6eaa0e6ebc5506452b91ac8791a456dd31ee32b42535bd20a75189","abstract_canon_sha256":"65f9c6b2cb8b98dff472ae14200b450c206855656e39a111e348bacfb512aa94"},"schema_version":"1.0"},"canonical_sha256":"1d3738604ea89b9625015af0ee6f7860909c8fdb669fd4879de6018f1456275d","source":{"kind":"arxiv","id":"1309.5661","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5661","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5661v1","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5661","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"pith_short_12","alias_value":"DU3TQYCOVCNZ","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DU3TQYCOVCNZMJIB","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DU3TQYCO","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DU3TQYCOVCNZMJIBLLYO433YMC","target":"record","payload":{"canonical_record":{"source":{"id":"1309.5661","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-22T22:33:38Z","cross_cats_sorted":["math.AG","math.AT","math.DG"],"title_canon_sha256":"9a1257f79d6eaa0e6ebc5506452b91ac8791a456dd31ee32b42535bd20a75189","abstract_canon_sha256":"65f9c6b2cb8b98dff472ae14200b450c206855656e39a111e348bacfb512aa94"},"schema_version":"1.0"},"canonical_sha256":"1d3738604ea89b9625015af0ee6f7860909c8fdb669fd4879de6018f1456275d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:35.593203Z","signature_b64":"a82oHthf4g+pAosjvWG1pGk5pj3eBKalnYT+not2Mx2uqsZtlKoBKJIvB339j2KrU7L5Sy2MlAdpxHmym/OfAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d3738604ea89b9625015af0ee6f7860909c8fdb669fd4879de6018f1456275d","last_reissued_at":"2026-05-18T03:12:35.592382Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:35.592382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.5661","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":"2026-05-18T03:12:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cufeKQv1sBC1fLNOWhDK6GLjG97r2nLYgEvGY2v5osfXcREWFvZhM38OadxqBs9OKAF80jFFxYTS32B7493TBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:16:48.544932Z"},"content_sha256":"9e472e69c05819aed0b820b2d1371dee751419929b6f61d08553d95f88890eb2","schema_version":"1.0","event_id":"sha256:9e472e69c05819aed0b820b2d1371dee751419929b6f61d08553d95f88890eb2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DU3TQYCOVCNZMJIBLLYO433YMC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gap probabilities and applications to geometry and random topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT","math.DG"],"primary_cat":"math.PR","authors_text":"Antonio Lerario, Erik Lundberg","submitted_at":"2013-09-22T22:33:38Z","abstract_excerpt":"We give an exact formula for the value of the derivative at zero of the gap probability in finite n x n Gaussian ensembles. As n goes to infinity our computation provides an asymptotic (with an explicit constant) of the order n^(1/2).\n  As a first application, we consider the set of n x n (Real, Complex or Quaternionic) Hermitian matrices with Frobenius norm one and determinant zero. We give an exact formula for the intrinsic volume of this set and as n goes to infinity its asymptotic (with an explicit constant) is of the order n^(1/2).\n  As a second application we consider the problem of comp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5661","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":""},"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":"2026-05-18T03:12:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NvuhxuTgvLxFwpiwzwzEIlnamneB3PUbDrY5Alcpc4jaqAVTVZAOqlhI02iO06yoz64pTTL80GBXHK+sQZvKAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:16:48.545542Z"},"content_sha256":"2cc964fbb88b3dfc18646586637c1f2f7945b680b079fac14404c6eb512a3f59","schema_version":"1.0","event_id":"sha256:2cc964fbb88b3dfc18646586637c1f2f7945b680b079fac14404c6eb512a3f59"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DU3TQYCOVCNZMJIBLLYO433YMC/bundle.json","state_url":"https://pith.science/pith/DU3TQYCOVCNZMJIBLLYO433YMC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DU3TQYCOVCNZMJIBLLYO433YMC/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":"2026-06-01T00:16:48Z","links":{"resolver":"https://pith.science/pith/DU3TQYCOVCNZMJIBLLYO433YMC","bundle":"https://pith.science/pith/DU3TQYCOVCNZMJIBLLYO433YMC/bundle.json","state":"https://pith.science/pith/DU3TQYCOVCNZMJIBLLYO433YMC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DU3TQYCOVCNZMJIBLLYO433YMC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DU3TQYCOVCNZMJIBLLYO433YMC","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":"65f9c6b2cb8b98dff472ae14200b450c206855656e39a111e348bacfb512aa94","cross_cats_sorted":["math.AG","math.AT","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-22T22:33:38Z","title_canon_sha256":"9a1257f79d6eaa0e6ebc5506452b91ac8791a456dd31ee32b42535bd20a75189"},"schema_version":"1.0","source":{"id":"1309.5661","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5661","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5661v1","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5661","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"pith_short_12","alias_value":"DU3TQYCOVCNZ","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DU3TQYCOVCNZMJIB","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DU3TQYCO","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:2cc964fbb88b3dfc18646586637c1f2f7945b680b079fac14404c6eb512a3f59","target":"graph","created_at":"2026-05-18T03:12:35Z","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"},"paper":{"abstract_excerpt":"We give an exact formula for the value of the derivative at zero of the gap probability in finite n x n Gaussian ensembles. As n goes to infinity our computation provides an asymptotic (with an explicit constant) of the order n^(1/2).\n  As a first application, we consider the set of n x n (Real, Complex or Quaternionic) Hermitian matrices with Frobenius norm one and determinant zero. We give an exact formula for the intrinsic volume of this set and as n goes to infinity its asymptotic (with an explicit constant) is of the order n^(1/2).\n  As a second application we consider the problem of comp","authors_text":"Antonio Lerario, Erik Lundberg","cross_cats":["math.AG","math.AT","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-22T22:33:38Z","title":"Gap probabilities and applications to geometry and random topology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5661","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":"sha256:9e472e69c05819aed0b820b2d1371dee751419929b6f61d08553d95f88890eb2","target":"record","created_at":"2026-05-18T03:12:35Z","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":"65f9c6b2cb8b98dff472ae14200b450c206855656e39a111e348bacfb512aa94","cross_cats_sorted":["math.AG","math.AT","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-22T22:33:38Z","title_canon_sha256":"9a1257f79d6eaa0e6ebc5506452b91ac8791a456dd31ee32b42535bd20a75189"},"schema_version":"1.0","source":{"id":"1309.5661","kind":"arxiv","version":1}},"canonical_sha256":"1d3738604ea89b9625015af0ee6f7860909c8fdb669fd4879de6018f1456275d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d3738604ea89b9625015af0ee6f7860909c8fdb669fd4879de6018f1456275d","first_computed_at":"2026-05-18T03:12:35.592382Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:35.592382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a82oHthf4g+pAosjvWG1pGk5pj3eBKalnYT+not2Mx2uqsZtlKoBKJIvB339j2KrU7L5Sy2MlAdpxHmym/OfAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:35.593203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.5661","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e472e69c05819aed0b820b2d1371dee751419929b6f61d08553d95f88890eb2","sha256:2cc964fbb88b3dfc18646586637c1f2f7945b680b079fac14404c6eb512a3f59"],"state_sha256":"a2f4f90519d2852a47d1bed3dd6d13bd71f3a6a5577f13e064054baa1378c217"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+kzvxRDY3JUJNZhyuOmkZezG82Y63gSQQFNYdOyeoCKvsVQISi8iIUryAX6qLqdqCUZxEJa4vtuoTNrm2HPzBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T00:16:48.548708Z","bundle_sha256":"6d62c960f150e4f624bab33d925bb7785ba67e186ea61f9555aecadc8264d4f5"}}