{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:IRVJD2MTKGYNZVP3FG6XDUV7MK","short_pith_number":"pith:IRVJD2MT","canonical_record":{"source":{"id":"2512.16118","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-12-18T03:11:48Z","cross_cats_sorted":[],"title_canon_sha256":"d5e3ecc164c1504e80b634481b0405f0cf24653139198af7f4e78604b8ca0e89","abstract_canon_sha256":"4d9333c301e98eea86b80aa887a55e3fdb67b3448f9986a8d918cb99f3180f39"},"schema_version":"1.0"},"canonical_sha256":"446a91e99351b0dcd5fb29bd71d2bf62bc2d2f3239988c052a0b0ad4c4ab115e","source":{"kind":"arxiv","id":"2512.16118","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.16118","created_at":"2026-05-22T02:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"2512.16118v3","created_at":"2026-05-22T02:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.16118","created_at":"2026-05-22T02:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"IRVJD2MTKGYN","created_at":"2026-05-22T02:04:38Z"},{"alias_kind":"pith_short_16","alias_value":"IRVJD2MTKGYNZVP3","created_at":"2026-05-22T02:04:38Z"},{"alias_kind":"pith_short_8","alias_value":"IRVJD2MT","created_at":"2026-05-22T02:04:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:IRVJD2MTKGYNZVP3FG6XDUV7MK","target":"record","payload":{"canonical_record":{"source":{"id":"2512.16118","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-12-18T03:11:48Z","cross_cats_sorted":[],"title_canon_sha256":"d5e3ecc164c1504e80b634481b0405f0cf24653139198af7f4e78604b8ca0e89","abstract_canon_sha256":"4d9333c301e98eea86b80aa887a55e3fdb67b3448f9986a8d918cb99f3180f39"},"schema_version":"1.0"},"canonical_sha256":"446a91e99351b0dcd5fb29bd71d2bf62bc2d2f3239988c052a0b0ad4c4ab115e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T02:04:38.594084Z","signature_b64":"rZKkXMsqiErkHWlsv8ZWoEG5YBpL15HcEUFuquNB6Nc6QbzKVRcSCg3A4kjuxe8y/ZoMnZYEHYdORFLb2FfgAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"446a91e99351b0dcd5fb29bd71d2bf62bc2d2f3239988c052a0b0ad4c4ab115e","last_reissued_at":"2026-05-22T02:04:38.593099Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T02:04:38.593099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2512.16118","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-22T02:04:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sIGE2vuLqiwWXl1StBqXMC/IZMA5qjTUe3fe5HJFOMa8e3o5w4kyeMb2n27li6EUz41IJASW/hHhouLrVuSTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:28:17.826600Z"},"content_sha256":"97a8575047837fbfa407da6ba243e18d3e4f8e49b3b0e0539854c10e46ba1843","schema_version":"1.0","event_id":"sha256:97a8575047837fbfa407da6ba243e18d3e4f8e49b3b0e0539854c10e46ba1843"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:IRVJD2MTKGYNZVP3FG6XDUV7MK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equidistribution of polynomial sequences in function fields: resolution of a conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"J\\'er\\'emy Champagne, Th\\'ai Ho\\`ang L\\^e, Trevor D. Wooley, Yu-Ru Liu, Zhenchao Ge","submitted_at":"2025-12-18T03:11:48Z","abstract_excerpt":"Let $\\mathbb F_q$ be the finite field of $q$ elements having characteristic $p$, and denote by $\\mathbb K_\\infty=\\mathbb F_q((1/t))$ the field of formal Laurent series in $1/t$. We consider the equidistribution in $\\mathbb T=\\mathbb K_\\infty/\\mathbb F_q[t]$ of the values of polynomials $f(u)\\in \\mathbb K_\\infty [u]$ as $u$ varies over $\\mathbb F_q[t]$. Let $\\mathcal K$ be a finite set of positive integers, and suppose that $\\alpha_r\\in \\mathbb K_\\infty$ for $r\\in \\mathcal K\\cup \\{0\\}$. We show that the polynomial $\\sum_{r\\in \\mathcal K\\cup\\{0\\}}\\alpha_ru^r$ is equidistributed in $\\mathbb T$ wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.16118","kind":"arxiv","version":3},"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/2512.16118/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":"2026-05-22T02:04:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w6bdYVWHx4oGtlaHZ17iuNrtqV2kX876hIWPwG/zIr1jvH7v4v0gC4ZgXW/tNTMqMwY0qDKjIZb1Am/ZYWqcAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:28:17.826985Z"},"content_sha256":"2acb83742b5197169ef93d53bbfa2179367f00d29157bf6ab717285dbd8db4d9","schema_version":"1.0","event_id":"sha256:2acb83742b5197169ef93d53bbfa2179367f00d29157bf6ab717285dbd8db4d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IRVJD2MTKGYNZVP3FG6XDUV7MK/bundle.json","state_url":"https://pith.science/pith/IRVJD2MTKGYNZVP3FG6XDUV7MK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IRVJD2MTKGYNZVP3FG6XDUV7MK/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":"2026-06-02T23:28:17Z","links":{"resolver":"https://pith.science/pith/IRVJD2MTKGYNZVP3FG6XDUV7MK","bundle":"https://pith.science/pith/IRVJD2MTKGYNZVP3FG6XDUV7MK/bundle.json","state":"https://pith.science/pith/IRVJD2MTKGYNZVP3FG6XDUV7MK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IRVJD2MTKGYNZVP3FG6XDUV7MK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:IRVJD2MTKGYNZVP3FG6XDUV7MK","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":"4d9333c301e98eea86b80aa887a55e3fdb67b3448f9986a8d918cb99f3180f39","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-12-18T03:11:48Z","title_canon_sha256":"d5e3ecc164c1504e80b634481b0405f0cf24653139198af7f4e78604b8ca0e89"},"schema_version":"1.0","source":{"id":"2512.16118","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.16118","created_at":"2026-05-22T02:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"2512.16118v3","created_at":"2026-05-22T02:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.16118","created_at":"2026-05-22T02:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"IRVJD2MTKGYN","created_at":"2026-05-22T02:04:38Z"},{"alias_kind":"pith_short_16","alias_value":"IRVJD2MTKGYNZVP3","created_at":"2026-05-22T02:04:38Z"},{"alias_kind":"pith_short_8","alias_value":"IRVJD2MT","created_at":"2026-05-22T02:04:38Z"}],"graph_snapshots":[{"event_id":"sha256:2acb83742b5197169ef93d53bbfa2179367f00d29157bf6ab717285dbd8db4d9","target":"graph","created_at":"2026-05-22T02:04:38Z","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/2512.16118/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathbb F_q$ be the finite field of $q$ elements having characteristic $p$, and denote by $\\mathbb K_\\infty=\\mathbb F_q((1/t))$ the field of formal Laurent series in $1/t$. We consider the equidistribution in $\\mathbb T=\\mathbb K_\\infty/\\mathbb F_q[t]$ of the values of polynomials $f(u)\\in \\mathbb K_\\infty [u]$ as $u$ varies over $\\mathbb F_q[t]$. Let $\\mathcal K$ be a finite set of positive integers, and suppose that $\\alpha_r\\in \\mathbb K_\\infty$ for $r\\in \\mathcal K\\cup \\{0\\}$. We show that the polynomial $\\sum_{r\\in \\mathcal K\\cup\\{0\\}}\\alpha_ru^r$ is equidistributed in $\\mathbb T$ wh","authors_text":"J\\'er\\'emy Champagne, Th\\'ai Ho\\`ang L\\^e, Trevor D. Wooley, Yu-Ru Liu, Zhenchao Ge","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-12-18T03:11:48Z","title":"Equidistribution of polynomial sequences in function fields: resolution of a conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.16118","kind":"arxiv","version":3},"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":"sha256:97a8575047837fbfa407da6ba243e18d3e4f8e49b3b0e0539854c10e46ba1843","target":"record","created_at":"2026-05-22T02:04:38Z","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":"4d9333c301e98eea86b80aa887a55e3fdb67b3448f9986a8d918cb99f3180f39","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-12-18T03:11:48Z","title_canon_sha256":"d5e3ecc164c1504e80b634481b0405f0cf24653139198af7f4e78604b8ca0e89"},"schema_version":"1.0","source":{"id":"2512.16118","kind":"arxiv","version":3}},"canonical_sha256":"446a91e99351b0dcd5fb29bd71d2bf62bc2d2f3239988c052a0b0ad4c4ab115e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"446a91e99351b0dcd5fb29bd71d2bf62bc2d2f3239988c052a0b0ad4c4ab115e","first_computed_at":"2026-05-22T02:04:38.593099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T02:04:38.593099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rZKkXMsqiErkHWlsv8ZWoEG5YBpL15HcEUFuquNB6Nc6QbzKVRcSCg3A4kjuxe8y/ZoMnZYEHYdORFLb2FfgAw==","signature_status":"signed_v1","signed_at":"2026-05-22T02:04:38.594084Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.16118","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97a8575047837fbfa407da6ba243e18d3e4f8e49b3b0e0539854c10e46ba1843","sha256:2acb83742b5197169ef93d53bbfa2179367f00d29157bf6ab717285dbd8db4d9"],"state_sha256":"1853086c8599bafc3753ba94b40b671dbb0d3aea9b131904681b12115b8c1cd9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wAc9VyWrItAR5WMdbV3S8iw4JYFvIPxfyMb4lwx5uFKzwGEHhFEet50+W94ZNnMwSNLxzJlwK6HxFxxuUpyKBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:28:17.831980Z","bundle_sha256":"e00dc927150bc928b80b5e5735f48521aab190a1d2afa878466472c315047fa5"}}