{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZOXG5UWN5IYXMOY2MAJWKB7JE6","short_pith_number":"pith:ZOXG5UWN","canonical_record":{"source":{"id":"1304.0198","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-03-31T12:53:42Z","cross_cats_sorted":[],"title_canon_sha256":"fe113d8bfe48250264b8fd5b8b92dbb2c0dcb78635d5536f412cbf649318dc91","abstract_canon_sha256":"323c4a56534853679bb1c1859b4fd5c2b8e8d5279d422e9e4609bc845b868cfb"},"schema_version":"1.0"},"canonical_sha256":"cbae6ed2cdea31763b1a60136507e927888ba469462cad604ef7427f58c9c278","source":{"kind":"arxiv","id":"1304.0198","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0198","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0198v1","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0198","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"pith_short_12","alias_value":"ZOXG5UWN5IYX","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZOXG5UWN5IYXMOY2","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZOXG5UWN","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZOXG5UWN5IYXMOY2MAJWKB7JE6","target":"record","payload":{"canonical_record":{"source":{"id":"1304.0198","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-03-31T12:53:42Z","cross_cats_sorted":[],"title_canon_sha256":"fe113d8bfe48250264b8fd5b8b92dbb2c0dcb78635d5536f412cbf649318dc91","abstract_canon_sha256":"323c4a56534853679bb1c1859b4fd5c2b8e8d5279d422e9e4609bc845b868cfb"},"schema_version":"1.0"},"canonical_sha256":"cbae6ed2cdea31763b1a60136507e927888ba469462cad604ef7427f58c9c278","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:25.737642Z","signature_b64":"C4p1SXjyC1usvkgDyk/PQs6DjloxZVOwfNdEGMLAvVEqYOe3ow+1hVvWtXh1CTbsnxbzBiMLLWQs+nyRzU2rCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbae6ed2cdea31763b1a60136507e927888ba469462cad604ef7427f58c9c278","last_reissued_at":"2026-05-18T03:29:25.736762Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:25.736762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.0198","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":"2026-05-18T03:29:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nSl2gqvCzDB8WvXP3j/PFCEskJIP2aJ2ntqxC4KxMX7ocv799zTiTdyriXVqBxS9+cMYPKrsoLzjeLQFB5AABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:07:09.746481Z"},"content_sha256":"32b7789fd40aa2e2e82145d57ad09385a17aa7ae5663b67330b3d5193a78f6c8","schema_version":"1.0","event_id":"sha256:32b7789fd40aa2e2e82145d57ad09385a17aa7ae5663b67330b3d5193a78f6c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZOXG5UWN5IYXMOY2MAJWKB7JE6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Defects of Algebraic Function Fields, Completion Defects and Defect Quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Asim Naseem, Franz-Viktor Kuhlmann","submitted_at":"2013-03-31T12:53:42Z","abstract_excerpt":"The {\\it defect} (also called {\\it ramification deficiency}) of valued field extensions is a major stumbling block in deep open problems of valuation theory in positive characteristic. For a detailed analysis, we define and investigate two weaker notions of defect: the {\\it completion defect} and the {\\it defect quotient}. We define them for finite extensions as well as for certain valued function fields (those with \"Abhyankar valuations\" that are nontrivial on the ground field). We investigate both defects and present analogues of the results that hold for the usual defect."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0198","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:29:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eYT4n3rtuuFGfQx0kowiwAZbtq37RoHrfUCJeL+l7E+cNnSmSoNr4iH6o9x9frwx2IoARY1Q0i97lsyLHjWHAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:07:09.747180Z"},"content_sha256":"69ad955df65d67c4678637e8b796d4d86471a3fdfa3cb1660f85b53b8aa71af9","schema_version":"1.0","event_id":"sha256:69ad955df65d67c4678637e8b796d4d86471a3fdfa3cb1660f85b53b8aa71af9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZOXG5UWN5IYXMOY2MAJWKB7JE6/bundle.json","state_url":"https://pith.science/pith/ZOXG5UWN5IYXMOY2MAJWKB7JE6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZOXG5UWN5IYXMOY2MAJWKB7JE6/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":"2026-06-08T17:07:09Z","links":{"resolver":"https://pith.science/pith/ZOXG5UWN5IYXMOY2MAJWKB7JE6","bundle":"https://pith.science/pith/ZOXG5UWN5IYXMOY2MAJWKB7JE6/bundle.json","state":"https://pith.science/pith/ZOXG5UWN5IYXMOY2MAJWKB7JE6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZOXG5UWN5IYXMOY2MAJWKB7JE6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZOXG5UWN5IYXMOY2MAJWKB7JE6","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":"323c4a56534853679bb1c1859b4fd5c2b8e8d5279d422e9e4609bc845b868cfb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-03-31T12:53:42Z","title_canon_sha256":"fe113d8bfe48250264b8fd5b8b92dbb2c0dcb78635d5536f412cbf649318dc91"},"schema_version":"1.0","source":{"id":"1304.0198","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0198","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0198v1","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0198","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"pith_short_12","alias_value":"ZOXG5UWN5IYX","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZOXG5UWN5IYXMOY2","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZOXG5UWN","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:69ad955df65d67c4678637e8b796d4d86471a3fdfa3cb1660f85b53b8aa71af9","target":"graph","created_at":"2026-05-18T03:29:25Z","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"},"paper":{"abstract_excerpt":"The {\\it defect} (also called {\\it ramification deficiency}) of valued field extensions is a major stumbling block in deep open problems of valuation theory in positive characteristic. For a detailed analysis, we define and investigate two weaker notions of defect: the {\\it completion defect} and the {\\it defect quotient}. We define them for finite extensions as well as for certain valued function fields (those with \"Abhyankar valuations\" that are nontrivial on the ground field). We investigate both defects and present analogues of the results that hold for the usual defect.","authors_text":"Asim Naseem, Franz-Viktor Kuhlmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-03-31T12:53:42Z","title":"Defects of Algebraic Function Fields, Completion Defects and Defect Quotients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0198","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":"sha256:32b7789fd40aa2e2e82145d57ad09385a17aa7ae5663b67330b3d5193a78f6c8","target":"record","created_at":"2026-05-18T03:29:25Z","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":"323c4a56534853679bb1c1859b4fd5c2b8e8d5279d422e9e4609bc845b868cfb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-03-31T12:53:42Z","title_canon_sha256":"fe113d8bfe48250264b8fd5b8b92dbb2c0dcb78635d5536f412cbf649318dc91"},"schema_version":"1.0","source":{"id":"1304.0198","kind":"arxiv","version":1}},"canonical_sha256":"cbae6ed2cdea31763b1a60136507e927888ba469462cad604ef7427f58c9c278","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbae6ed2cdea31763b1a60136507e927888ba469462cad604ef7427f58c9c278","first_computed_at":"2026-05-18T03:29:25.736762Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:25.736762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C4p1SXjyC1usvkgDyk/PQs6DjloxZVOwfNdEGMLAvVEqYOe3ow+1hVvWtXh1CTbsnxbzBiMLLWQs+nyRzU2rCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:25.737642Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0198","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32b7789fd40aa2e2e82145d57ad09385a17aa7ae5663b67330b3d5193a78f6c8","sha256:69ad955df65d67c4678637e8b796d4d86471a3fdfa3cb1660f85b53b8aa71af9"],"state_sha256":"940357d38a88cd24dc75a1ff7180b32acf9e37b35bf5bc4bb926bfc0dd053223"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hawpqNV8QpNQNUHyjwYy4CCj3ct5VwhawJjdWDI1QYE/+lR8h3MQoSM66kdCvGPBSu0QZouDHH4CUqW5gpXmBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:07:09.751811Z","bundle_sha256":"eb5a47fa73d6dc17088de999f710babdae6a15c5ff6413d5753a8ab6e35def86"}}