{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:EWB3A676JU75CEOOHYURDIP3XX","short_pith_number":"pith:EWB3A676","schema_version":"1.0","canonical_sha256":"2583b07bfe4d3fd111ce3e2911a1fbbdc1aeb7f3dcc0f838e3cfeddd9afe013f","source":{"kind":"arxiv","id":"2507.12502","version":1},"attestation_state":"computed","paper":{"title":"Quantitative Edge Eigenvector Universality for Random Regular Graphs: Berry-Esseen Bounds with Explicit Constants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO","math.SP"],"primary_cat":"math.PR","authors_text":"Leonhard Nagel","submitted_at":"2025-07-16T05:31:51Z","abstract_excerpt":"We establish the first quantitative Berry-Esseen bounds for edge eigenvector statistics in random regular graphs. For any $d$-regular graph on $N$ vertices with fixed $d \\geq 3$ and deterministic unit vector $\\mathbf{q} \\perp \\mathbf{e}$, we prove that the normalized overlap $\\sqrt{N}\\langle \\mathbf{q}, \\mathbf{u}_2 \\rangle$ satisfies \\[ \\sup_{x \\in \\mathbb{R}} \\left|\\mathbb{P}\\left(\\sqrt{N}\\langle \\mathbf{q}, \\mathbf{u}_2 \\rangle \\leq x\\right) - \\Phi(x)\\right| \\leq C_d N^{-1/6+\\varepsilon} \\] where $\\mathbf{u}_2$ is the second eigenvector and $C_d \\leq \\tilde{C}d^3\\varepsilon^{-10}$ for an ab"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.12502","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-16T05:31:51Z","cross_cats_sorted":["cs.DM","math.CO","math.SP"],"title_canon_sha256":"0ac661a35a91453e86591c006ac4f04a77b1ebad41c185909d5468a28211b8cb","abstract_canon_sha256":"6410bf757d4dfb4319d74d2662c799b4de70d33b0b3f6f3565d1f0da8c0e28a0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:38:33.106898Z","signature_b64":"LtVmdmdwvZwOIsjcJzv9I2jhVbWj9/mYQ9lQSL3og/vIxM/ox2MgJzH5J6bchubcuaQ+4YpTk1Pm2/GZTqd2Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2583b07bfe4d3fd111ce3e2911a1fbbdc1aeb7f3dcc0f838e3cfeddd9afe013f","last_reissued_at":"2026-07-05T11:38:33.106387Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:38:33.106387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantitative Edge Eigenvector Universality for Random Regular Graphs: Berry-Esseen Bounds with Explicit Constants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO","math.SP"],"primary_cat":"math.PR","authors_text":"Leonhard Nagel","submitted_at":"2025-07-16T05:31:51Z","abstract_excerpt":"We establish the first quantitative Berry-Esseen bounds for edge eigenvector statistics in random regular graphs. For any $d$-regular graph on $N$ vertices with fixed $d \\geq 3$ and deterministic unit vector $\\mathbf{q} \\perp \\mathbf{e}$, we prove that the normalized overlap $\\sqrt{N}\\langle \\mathbf{q}, \\mathbf{u}_2 \\rangle$ satisfies \\[ \\sup_{x \\in \\mathbb{R}} \\left|\\mathbb{P}\\left(\\sqrt{N}\\langle \\mathbf{q}, \\mathbf{u}_2 \\rangle \\leq x\\right) - \\Phi(x)\\right| \\leq C_d N^{-1/6+\\varepsilon} \\] where $\\mathbf{u}_2$ is the second eigenvector and $C_d \\leq \\tilde{C}d^3\\varepsilon^{-10}$ for an ab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.12502","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/2507.12502/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2507.12502","created_at":"2026-07-05T11:38:33.106444+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.12502v1","created_at":"2026-07-05T11:38:33.106444+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.12502","created_at":"2026-07-05T11:38:33.106444+00:00"},{"alias_kind":"pith_short_12","alias_value":"EWB3A676JU75","created_at":"2026-07-05T11:38:33.106444+00:00"},{"alias_kind":"pith_short_16","alias_value":"EWB3A676JU75CEOO","created_at":"2026-07-05T11:38:33.106444+00:00"},{"alias_kind":"pith_short_8","alias_value":"EWB3A676","created_at":"2026-07-05T11:38:33.106444+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.14259","citing_title":"Sharp Square Root Bounds for Edge Eigenvector Universality in Sparse Random Regular Graphs","ref_index":12,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EWB3A676JU75CEOOHYURDIP3XX","json":"https://pith.science/pith/EWB3A676JU75CEOOHYURDIP3XX.json","graph_json":"https://pith.science/api/pith-number/EWB3A676JU75CEOOHYURDIP3XX/graph.json","events_json":"https://pith.science/api/pith-number/EWB3A676JU75CEOOHYURDIP3XX/events.json","paper":"https://pith.science/paper/EWB3A676"},"agent_actions":{"view_html":"https://pith.science/pith/EWB3A676JU75CEOOHYURDIP3XX","download_json":"https://pith.science/pith/EWB3A676JU75CEOOHYURDIP3XX.json","view_paper":"https://pith.science/paper/EWB3A676","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.12502&json=true","fetch_graph":"https://pith.science/api/pith-number/EWB3A676JU75CEOOHYURDIP3XX/graph.json","fetch_events":"https://pith.science/api/pith-number/EWB3A676JU75CEOOHYURDIP3XX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EWB3A676JU75CEOOHYURDIP3XX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EWB3A676JU75CEOOHYURDIP3XX/action/storage_attestation","attest_author":"https://pith.science/pith/EWB3A676JU75CEOOHYURDIP3XX/action/author_attestation","sign_citation":"https://pith.science/pith/EWB3A676JU75CEOOHYURDIP3XX/action/citation_signature","submit_replication":"https://pith.science/pith/EWB3A676JU75CEOOHYURDIP3XX/action/replication_record"}},"created_at":"2026-07-05T11:38:33.106444+00:00","updated_at":"2026-07-05T11:38:33.106444+00:00"}