{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:6KGEXRBGGTER6BKZLI77HEKL43","short_pith_number":"pith:6KGEXRBG","canonical_record":{"source":{"id":"2608.06576","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-08-06T20:38:06Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"a1652166b59a6951af69af4cdd0ec172d1891596931beedda57cf0e42cf9b661","abstract_canon_sha256":"1d5cff571dfaa708878f1d5232f533594998aeff0698aea32b578b3014ac2163"},"schema_version":"1.0"},"canonical_sha256":"f28c4bc42634c91f05595a3ff3914be6fe3a6e82f291cd2656010f48082c57bf","source":{"kind":"arxiv","id":"2608.06576","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.06576","created_at":"2026-08-10T01:11:19Z"},{"alias_kind":"arxiv_version","alias_value":"2608.06576v1","created_at":"2026-08-10T01:11:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.06576","created_at":"2026-08-10T01:11:19Z"},{"alias_kind":"pith_short_12","alias_value":"6KGEXRBGGTER","created_at":"2026-08-10T01:11:19Z"},{"alias_kind":"pith_short_16","alias_value":"6KGEXRBGGTER6BKZ","created_at":"2026-08-10T01:11:19Z"},{"alias_kind":"pith_short_8","alias_value":"6KGEXRBG","created_at":"2026-08-10T01:11:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:6KGEXRBGGTER6BKZLI77HEKL43","target":"record","payload":{"canonical_record":{"source":{"id":"2608.06576","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-08-06T20:38:06Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"a1652166b59a6951af69af4cdd0ec172d1891596931beedda57cf0e42cf9b661","abstract_canon_sha256":"1d5cff571dfaa708878f1d5232f533594998aeff0698aea32b578b3014ac2163"},"schema_version":"1.0"},"canonical_sha256":"f28c4bc42634c91f05595a3ff3914be6fe3a6e82f291cd2656010f48082c57bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-10T01:11:19.809124Z","signature_b64":"mBdzU+cjOn/l3HBeOI41g2SfyoUEPQDmzlUqftFcW8KQz3m9Zx61M4kmLHCjosl8qgaQb1f8RLLiMQZp898nBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f28c4bc42634c91f05595a3ff3914be6fe3a6e82f291cd2656010f48082c57bf","last_reissued_at":"2026-08-10T01:11:19.806624Z","signature_status":"signed_v1","first_computed_at":"2026-08-10T01:11:19.806624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.06576","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":"2026-08-10T01:11:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uxQo8AsBeh93IqEcVqEfCq80hgz5o67YHwLcJiJp3aqkKJZD4I0GyLIR9zxXVeRAdqThAMAu7b7a4KqkF1n/DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T22:50:02.063635Z"},"content_sha256":"310954ef7da18da4a717116b86c7005d9c368961ed16e5747d94541f5352488b","schema_version":"1.0","event_id":"sha256:310954ef7da18da4a717116b86c7005d9c368961ed16e5747d94541f5352488b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:6KGEXRBGGTER6BKZLI77HEKL43","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universality for Random $p$-adic Polynomials and Random Matrices Via the Resultant Distribution Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.PR","authors_text":"Jiahe Shen","submitted_at":"2026-08-06T20:38:06Z","abstract_excerpt":"We prove universality results for zeros of random $p$-adic polynomials with independent, sufficiently non-concentrated coefficients. We show that when the degree goes to infinity, the limiting joint root statistics in arbitrary finite extensions of $\\mathbb{Q}_p$ are universal and coincide with those of the Haar coefficient model, whose limiting root statistics were determined by Caruso (arXiv:2110.03942). In particular, our results extend the Haar-model formulas to a broad class of coefficient distributions and to general joint root statistics over finite extensions of $\\mathbb{Q}_p$.\n  Our a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06576","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/2608.06576/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":"2026-08-10T01:11:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dsRaVzRLoPxRAVI2dk/CWZvMem/JJsdEufz6kz7xcT9JhYZX/wVT4jyJMFgOf4wcoq1f9xrOM7lqnKRZ8wgcBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T22:50:02.064550Z"},"content_sha256":"d5791cf172579b25c93282f4afbf1bada40b2982bf9beae2050004ad7bde3cfe","schema_version":"1.0","event_id":"sha256:d5791cf172579b25c93282f4afbf1bada40b2982bf9beae2050004ad7bde3cfe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6KGEXRBGGTER6BKZLI77HEKL43/bundle.json","state_url":"https://pith.science/pith/6KGEXRBGGTER6BKZLI77HEKL43/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6KGEXRBGGTER6BKZLI77HEKL43/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":"2026-08-23T22:50:02Z","links":{"resolver":"https://pith.science/pith/6KGEXRBGGTER6BKZLI77HEKL43","bundle":"https://pith.science/pith/6KGEXRBGGTER6BKZLI77HEKL43/bundle.json","state":"https://pith.science/pith/6KGEXRBGGTER6BKZLI77HEKL43/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6KGEXRBGGTER6BKZLI77HEKL43/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6KGEXRBGGTER6BKZLI77HEKL43","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":"1d5cff571dfaa708878f1d5232f533594998aeff0698aea32b578b3014ac2163","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-08-06T20:38:06Z","title_canon_sha256":"a1652166b59a6951af69af4cdd0ec172d1891596931beedda57cf0e42cf9b661"},"schema_version":"1.0","source":{"id":"2608.06576","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.06576","created_at":"2026-08-10T01:11:19Z"},{"alias_kind":"arxiv_version","alias_value":"2608.06576v1","created_at":"2026-08-10T01:11:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.06576","created_at":"2026-08-10T01:11:19Z"},{"alias_kind":"pith_short_12","alias_value":"6KGEXRBGGTER","created_at":"2026-08-10T01:11:19Z"},{"alias_kind":"pith_short_16","alias_value":"6KGEXRBGGTER6BKZ","created_at":"2026-08-10T01:11:19Z"},{"alias_kind":"pith_short_8","alias_value":"6KGEXRBG","created_at":"2026-08-10T01:11:19Z"}],"graph_snapshots":[{"event_id":"sha256:d5791cf172579b25c93282f4afbf1bada40b2982bf9beae2050004ad7bde3cfe","target":"graph","created_at":"2026-08-10T01:11:19Z","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/2608.06576/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove universality results for zeros of random $p$-adic polynomials with independent, sufficiently non-concentrated coefficients. We show that when the degree goes to infinity, the limiting joint root statistics in arbitrary finite extensions of $\\mathbb{Q}_p$ are universal and coincide with those of the Haar coefficient model, whose limiting root statistics were determined by Caruso (arXiv:2110.03942). In particular, our results extend the Haar-model formulas to a broad class of coefficient distributions and to general joint root statistics over finite extensions of $\\mathbb{Q}_p$.\n  Our a","authors_text":"Jiahe Shen","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-08-06T20:38:06Z","title":"Universality for Random $p$-adic Polynomials and Random Matrices Via the Resultant Distribution Method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06576","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":"sha256:310954ef7da18da4a717116b86c7005d9c368961ed16e5747d94541f5352488b","target":"record","created_at":"2026-08-10T01:11:19Z","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":"1d5cff571dfaa708878f1d5232f533594998aeff0698aea32b578b3014ac2163","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-08-06T20:38:06Z","title_canon_sha256":"a1652166b59a6951af69af4cdd0ec172d1891596931beedda57cf0e42cf9b661"},"schema_version":"1.0","source":{"id":"2608.06576","kind":"arxiv","version":1}},"canonical_sha256":"f28c4bc42634c91f05595a3ff3914be6fe3a6e82f291cd2656010f48082c57bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f28c4bc42634c91f05595a3ff3914be6fe3a6e82f291cd2656010f48082c57bf","first_computed_at":"2026-08-10T01:11:19.806624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-10T01:11:19.806624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mBdzU+cjOn/l3HBeOI41g2SfyoUEPQDmzlUqftFcW8KQz3m9Zx61M4kmLHCjosl8qgaQb1f8RLLiMQZp898nBA==","signature_status":"signed_v1","signed_at":"2026-08-10T01:11:19.809124Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.06576","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:310954ef7da18da4a717116b86c7005d9c368961ed16e5747d94541f5352488b","sha256:d5791cf172579b25c93282f4afbf1bada40b2982bf9beae2050004ad7bde3cfe"],"state_sha256":"637e6eec3112272eadabdc86540d35540f861f84ead6404cc70833f793ede835"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dGdkV3bA6zow+wZn2SUO6J1afm+7KxvDe8sGGAJEkWCfmKpp2MLUii9k6MUWhn6E6xGhebhNUBFhaKgFLGLeCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T22:50:02.069562Z","bundle_sha256":"7d731bfba1b60c68a8d79222e4193889c4ae9dd681177b4cf12a0905c3b75776"}}