{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:BLRDCL4GHYAAD7ZLAWZTGKJNDF","short_pith_number":"pith:BLRDCL4G","canonical_record":{"source":{"id":"2510.23726","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-10-27T18:01:55Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5d3a72096878999742127b6d0627d9a391f6702fde51aad6c59ba41222f4b04f","abstract_canon_sha256":"a05dbd7125d5aa4ba49ec714e63d8af08da85fcf55bdbb33278c13aa5d384dd6"},"schema_version":"1.0"},"canonical_sha256":"0ae2312f863e0001ff2b05b333292d194a1b7ff0d6545e2bc0ce51d641642157","source":{"kind":"arxiv","id":"2510.23726","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.23726","created_at":"2026-07-28T00:21:32Z"},{"alias_kind":"arxiv_version","alias_value":"2510.23726v2","created_at":"2026-07-28T00:21:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.23726","created_at":"2026-07-28T00:21:32Z"},{"alias_kind":"pith_short_12","alias_value":"BLRDCL4GHYAA","created_at":"2026-07-28T00:21:32Z"},{"alias_kind":"pith_short_16","alias_value":"BLRDCL4GHYAAD7ZL","created_at":"2026-07-28T00:21:32Z"},{"alias_kind":"pith_short_8","alias_value":"BLRDCL4G","created_at":"2026-07-28T00:21:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:BLRDCL4GHYAAD7ZLAWZTGKJNDF","target":"record","payload":{"canonical_record":{"source":{"id":"2510.23726","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-10-27T18:01:55Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5d3a72096878999742127b6d0627d9a391f6702fde51aad6c59ba41222f4b04f","abstract_canon_sha256":"a05dbd7125d5aa4ba49ec714e63d8af08da85fcf55bdbb33278c13aa5d384dd6"},"schema_version":"1.0"},"canonical_sha256":"0ae2312f863e0001ff2b05b333292d194a1b7ff0d6545e2bc0ce51d641642157","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T00:21:32.749010Z","signature_b64":"ZEBKE8J0JRM9CAcKAlKt+83tN/uOI19hjghEKjk5EmHLTAZ5pVtraCExR1oBf0Y2QNzdhIr+7u2vSahMhPjXAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ae2312f863e0001ff2b05b333292d194a1b7ff0d6545e2bc0ce51d641642157","last_reissued_at":"2026-07-28T00:21:32.748009Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T00:21:32.748009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2510.23726","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-28T00:21:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RQwTK/sMnBKimo6Jt+rZE1nMqixOXjijDen7rLGq5ffjWkLVkXDfgo3Awd4J6D14s9vSZMevqpKr+0Ce88tEDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T07:05:09.839988Z"},"content_sha256":"eeabd8d2541b5c84a8751be74235134d4997430a612157b18ba456074da48849","schema_version":"1.0","event_id":"sha256:eeabd8d2541b5c84a8751be74235134d4997430a612157b18ba456074da48849"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:BLRDCL4GHYAAD7ZLAWZTGKJNDF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Apparent Universal Behavior in Second Moments of Random Quantum Circuits","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Bryan K. Clark, Daniel Belkin, James Allen","submitted_at":"2025-10-27T18:01:55Z","abstract_excerpt":"Just how fast does the brickwork circuit form an approximate 2-design? Is there any difference between anticoncentration and being a 2-design? Does geometry matter? How deep a circuit will I need in practice? We tell you everything you always wanted to know about second moments of random quantum circuits, but were too afraid to compute. Our answers generally take the form of numerical results for up to 50 qubits. Our first contribution is a strategy to determine explicitly the optimal experiment which distinguishes any given ensemble from the Haar measure. With this formula and some computatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.23726","kind":"arxiv","version":2},"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/2510.23726/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":"2026-07-28T00:21:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jhtCcXEkVW3w4gpM+gg7UAEq1tmZeor8yf/BnPxVjt+5yylOS7r+nrwwMMM/H7qYO74zrOluynHOBVb7AKidBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T07:05:09.840466Z"},"content_sha256":"33c846b59fb5deca0d64be1142ea3bc416e082c5cc2a6e919390b707110baae1","schema_version":"1.0","event_id":"sha256:33c846b59fb5deca0d64be1142ea3bc416e082c5cc2a6e919390b707110baae1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BLRDCL4GHYAAD7ZLAWZTGKJNDF/bundle.json","state_url":"https://pith.science/pith/BLRDCL4GHYAAD7ZLAWZTGKJNDF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BLRDCL4GHYAAD7ZLAWZTGKJNDF/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":"2026-08-05T07:05:09Z","links":{"resolver":"https://pith.science/pith/BLRDCL4GHYAAD7ZLAWZTGKJNDF","bundle":"https://pith.science/pith/BLRDCL4GHYAAD7ZLAWZTGKJNDF/bundle.json","state":"https://pith.science/pith/BLRDCL4GHYAAD7ZLAWZTGKJNDF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BLRDCL4GHYAAD7ZLAWZTGKJNDF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BLRDCL4GHYAAD7ZLAWZTGKJNDF","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":"a05dbd7125d5aa4ba49ec714e63d8af08da85fcf55bdbb33278c13aa5d384dd6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-10-27T18:01:55Z","title_canon_sha256":"5d3a72096878999742127b6d0627d9a391f6702fde51aad6c59ba41222f4b04f"},"schema_version":"1.0","source":{"id":"2510.23726","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.23726","created_at":"2026-07-28T00:21:32Z"},{"alias_kind":"arxiv_version","alias_value":"2510.23726v2","created_at":"2026-07-28T00:21:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.23726","created_at":"2026-07-28T00:21:32Z"},{"alias_kind":"pith_short_12","alias_value":"BLRDCL4GHYAA","created_at":"2026-07-28T00:21:32Z"},{"alias_kind":"pith_short_16","alias_value":"BLRDCL4GHYAAD7ZL","created_at":"2026-07-28T00:21:32Z"},{"alias_kind":"pith_short_8","alias_value":"BLRDCL4G","created_at":"2026-07-28T00:21:32Z"}],"graph_snapshots":[{"event_id":"sha256:33c846b59fb5deca0d64be1142ea3bc416e082c5cc2a6e919390b707110baae1","target":"graph","created_at":"2026-07-28T00:21:32Z","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/2510.23726/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Just how fast does the brickwork circuit form an approximate 2-design? Is there any difference between anticoncentration and being a 2-design? Does geometry matter? How deep a circuit will I need in practice? We tell you everything you always wanted to know about second moments of random quantum circuits, but were too afraid to compute. Our answers generally take the form of numerical results for up to 50 qubits. Our first contribution is a strategy to determine explicitly the optimal experiment which distinguishes any given ensemble from the Haar measure. With this formula and some computatio","authors_text":"Bryan K. Clark, Daniel Belkin, James Allen","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-10-27T18:01:55Z","title":"Apparent Universal Behavior in Second Moments of Random Quantum Circuits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.23726","kind":"arxiv","version":2},"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:eeabd8d2541b5c84a8751be74235134d4997430a612157b18ba456074da48849","target":"record","created_at":"2026-07-28T00:21:32Z","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":"a05dbd7125d5aa4ba49ec714e63d8af08da85fcf55bdbb33278c13aa5d384dd6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-10-27T18:01:55Z","title_canon_sha256":"5d3a72096878999742127b6d0627d9a391f6702fde51aad6c59ba41222f4b04f"},"schema_version":"1.0","source":{"id":"2510.23726","kind":"arxiv","version":2}},"canonical_sha256":"0ae2312f863e0001ff2b05b333292d194a1b7ff0d6545e2bc0ce51d641642157","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ae2312f863e0001ff2b05b333292d194a1b7ff0d6545e2bc0ce51d641642157","first_computed_at":"2026-07-28T00:21:32.748009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-28T00:21:32.748009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZEBKE8J0JRM9CAcKAlKt+83tN/uOI19hjghEKjk5EmHLTAZ5pVtraCExR1oBf0Y2QNzdhIr+7u2vSahMhPjXAw==","signature_status":"signed_v1","signed_at":"2026-07-28T00:21:32.749010Z","signed_message":"canonical_sha256_bytes"},"source_id":"2510.23726","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eeabd8d2541b5c84a8751be74235134d4997430a612157b18ba456074da48849","sha256:33c846b59fb5deca0d64be1142ea3bc416e082c5cc2a6e919390b707110baae1"],"state_sha256":"2073d83fda590128197ef64eee3162a8623414b73d5579961c7974bea8ce5d78"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WhnSJuo1498bok2RPIKxQPwEVyafzumV1o+XDHpoTcgyZhWDkuf8GIQfzOJ7kLruGLGHxEyHA/dhYrfPAjeLAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T07:05:09.843787Z","bundle_sha256":"5fe208ca76ecb09c724c37c3e6fbe103ef6c0d644a031a279a089ab5ffd3e62d"}}