{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:ZF5ZI3RC6GWU4654OS5GZVMKEY","short_pith_number":"pith:ZF5ZI3RC","schema_version":"1.0","canonical_sha256":"c97b946e22f1ad4e7bbc74ba6cd58a2615b44fa78d41763b6ddcc460d46491d1","source":{"kind":"arxiv","id":"0708.3128","version":1},"attestation_state":"computed","paper":{"title":"The u-invariant of the function fields of p-adic curves","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"R. Parimala, V. Suresh","submitted_at":"2007-08-23T05:59:29Z","abstract_excerpt":"The u-invariant of a field is the maximum dimension of ansiotropic quadratic forms over the field. It is an open question whether the u-invariant of function fields of p-aidc curves is 8. In this paper, we answer this question in the affirmative for function fields of non-dyadic p-adic curves."},"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":"0708.3128","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2007-08-23T05:59:29Z","cross_cats_sorted":[],"title_canon_sha256":"5a07f88af470fb83ce574678810ae2da31f8b24d6078ee8b955a2ad1776f0a7b","abstract_canon_sha256":"ecd56ccfd8d77fcdd5879fc2b2e48be6a35db7cf828f7ed5ef54b0c4b1aeb01b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:55.348627Z","signature_b64":"RzjXaqcAhEIvyMADhEoWqODGlyhY2LWG5CC1RP/Csk9ORaWmHmcp87LaiU0sZcdWULVcKNVMDjy7pZEZL0xpDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c97b946e22f1ad4e7bbc74ba6cd58a2615b44fa78d41763b6ddcc460d46491d1","last_reissued_at":"2026-05-18T04:04:55.347735Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:55.347735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The u-invariant of the function fields of p-adic curves","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"R. Parimala, V. Suresh","submitted_at":"2007-08-23T05:59:29Z","abstract_excerpt":"The u-invariant of a field is the maximum dimension of ansiotropic quadratic forms over the field. It is an open question whether the u-invariant of function fields of p-aidc curves is 8. In this paper, we answer this question in the affirmative for function fields of non-dyadic p-adic curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.3128","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0708.3128","created_at":"2026-05-18T04:04:55.347874+00:00"},{"alias_kind":"arxiv_version","alias_value":"0708.3128v1","created_at":"2026-05-18T04:04:55.347874+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.3128","created_at":"2026-05-18T04:04:55.347874+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZF5ZI3RC6GWU","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZF5ZI3RC6GWU4654","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZF5ZI3RC","created_at":"2026-05-18T12:25:56.245647+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZF5ZI3RC6GWU4654OS5GZVMKEY","json":"https://pith.science/pith/ZF5ZI3RC6GWU4654OS5GZVMKEY.json","graph_json":"https://pith.science/api/pith-number/ZF5ZI3RC6GWU4654OS5GZVMKEY/graph.json","events_json":"https://pith.science/api/pith-number/ZF5ZI3RC6GWU4654OS5GZVMKEY/events.json","paper":"https://pith.science/paper/ZF5ZI3RC"},"agent_actions":{"view_html":"https://pith.science/pith/ZF5ZI3RC6GWU4654OS5GZVMKEY","download_json":"https://pith.science/pith/ZF5ZI3RC6GWU4654OS5GZVMKEY.json","view_paper":"https://pith.science/paper/ZF5ZI3RC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0708.3128&json=true","fetch_graph":"https://pith.science/api/pith-number/ZF5ZI3RC6GWU4654OS5GZVMKEY/graph.json","fetch_events":"https://pith.science/api/pith-number/ZF5ZI3RC6GWU4654OS5GZVMKEY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZF5ZI3RC6GWU4654OS5GZVMKEY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZF5ZI3RC6GWU4654OS5GZVMKEY/action/storage_attestation","attest_author":"https://pith.science/pith/ZF5ZI3RC6GWU4654OS5GZVMKEY/action/author_attestation","sign_citation":"https://pith.science/pith/ZF5ZI3RC6GWU4654OS5GZVMKEY/action/citation_signature","submit_replication":"https://pith.science/pith/ZF5ZI3RC6GWU4654OS5GZVMKEY/action/replication_record"}},"created_at":"2026-05-18T04:04:55.347874+00:00","updated_at":"2026-05-18T04:04:55.347874+00:00"}