{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:3RLQDMTUHPF45S7EYBN2CFVTLX","short_pith_number":"pith:3RLQDMTU","canonical_record":{"source":{"id":"0809.0180","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-09-01T07:07:20Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"e1c085f4a958987e4620d1bfc7e6e76efe2fd869ae86d9fd98b7c4de15595d64","abstract_canon_sha256":"639f0723cc7e7d91efebe742c3ec9815649888587da79a1b1ce2193b4cbd110e"},"schema_version":"1.0"},"canonical_sha256":"dc5701b2743bcbcecbe4c05ba116b35df0951a4d4c56ac6c910e7289fe2a4680","source":{"kind":"arxiv","id":"0809.0180","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.0180","created_at":"2026-05-18T04:33:48Z"},{"alias_kind":"arxiv_version","alias_value":"0809.0180v2","created_at":"2026-05-18T04:33:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.0180","created_at":"2026-05-18T04:33:48Z"},{"alias_kind":"pith_short_12","alias_value":"3RLQDMTUHPF4","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"3RLQDMTUHPF45S7E","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"3RLQDMTU","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:3RLQDMTUHPF45S7EYBN2CFVTLX","target":"record","payload":{"canonical_record":{"source":{"id":"0809.0180","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-09-01T07:07:20Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"e1c085f4a958987e4620d1bfc7e6e76efe2fd869ae86d9fd98b7c4de15595d64","abstract_canon_sha256":"639f0723cc7e7d91efebe742c3ec9815649888587da79a1b1ce2193b4cbd110e"},"schema_version":"1.0"},"canonical_sha256":"dc5701b2743bcbcecbe4c05ba116b35df0951a4d4c56ac6c910e7289fe2a4680","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:48.585268Z","signature_b64":"tAVzZ2SkiNY4UufDYYYGJOHjXF3LWz0F6QJhTQCFf/06HB+YgfF4N7XnuScv3pwC486myCnlFplKHaOG0Ch5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc5701b2743bcbcecbe4c05ba116b35df0951a4d4c56ac6c910e7289fe2a4680","last_reissued_at":"2026-05-18T04:33:48.584768Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:48.584768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0809.0180","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:33:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N5llTZnbAPbg2QtuRRYeCzikQZv2dxIv1t1n3YLI21GqT+GbNiNzOS8P0Q25o78FtWKQA+A/Co7xgHaMD6xZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T02:45:08.562031Z"},"content_sha256":"d3d53d161f00d1e9942a5a14680f1c3b5176451888cbe5a73275a7e1eb22abbc","schema_version":"1.0","event_id":"sha256:d3d53d161f00d1e9942a5a14680f1c3b5176451888cbe5a73275a7e1eb22abbc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:3RLQDMTUHPF45S7EYBN2CFVTLX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local Fourier transform and epsilon factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Ahmed Abbes, Takeshi Saito","submitted_at":"2008-09-01T07:07:20Z","abstract_excerpt":"Laumon introduced the local Fourier transform for $\\ell$-adic Galois representations of local fields, of equal characteristic $p$ different from $\\ell$, as a powerful tool to study the Fourier-Deligne transform of $\\ell$-adic sheaves over the affine line. In this article, we compute explicitly the local Fourier transform of monomial representations satisfying a certain ramification condition, and deduce Laumon's formula relating the epsilon factor to the determinant of the local Fourier transform under the same condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.0180","kind":"arxiv","version":2},"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":"2026-05-18T04:33:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mVFeuVf9xrW220n6EcOsaohw9lDGNpKFSK646grqWuygtFp93nlL64PbTt9RrIvHLUFoyYIDjscPm8d8vnDvCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T02:45:08.562694Z"},"content_sha256":"9ad8641fbbc1b77cd6279d5226639852290e8eee705f7dc984da6d584e82ba36","schema_version":"1.0","event_id":"sha256:9ad8641fbbc1b77cd6279d5226639852290e8eee705f7dc984da6d584e82ba36"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3RLQDMTUHPF45S7EYBN2CFVTLX/bundle.json","state_url":"https://pith.science/pith/3RLQDMTUHPF45S7EYBN2CFVTLX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3RLQDMTUHPF45S7EYBN2CFVTLX/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":"2026-06-06T02:45:08Z","links":{"resolver":"https://pith.science/pith/3RLQDMTUHPF45S7EYBN2CFVTLX","bundle":"https://pith.science/pith/3RLQDMTUHPF45S7EYBN2CFVTLX/bundle.json","state":"https://pith.science/pith/3RLQDMTUHPF45S7EYBN2CFVTLX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3RLQDMTUHPF45S7EYBN2CFVTLX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:3RLQDMTUHPF45S7EYBN2CFVTLX","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":"639f0723cc7e7d91efebe742c3ec9815649888587da79a1b1ce2193b4cbd110e","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-09-01T07:07:20Z","title_canon_sha256":"e1c085f4a958987e4620d1bfc7e6e76efe2fd869ae86d9fd98b7c4de15595d64"},"schema_version":"1.0","source":{"id":"0809.0180","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.0180","created_at":"2026-05-18T04:33:48Z"},{"alias_kind":"arxiv_version","alias_value":"0809.0180v2","created_at":"2026-05-18T04:33:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.0180","created_at":"2026-05-18T04:33:48Z"},{"alias_kind":"pith_short_12","alias_value":"3RLQDMTUHPF4","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"3RLQDMTUHPF45S7E","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"3RLQDMTU","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:9ad8641fbbc1b77cd6279d5226639852290e8eee705f7dc984da6d584e82ba36","target":"graph","created_at":"2026-05-18T04:33:48Z","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":"Laumon introduced the local Fourier transform for $\\ell$-adic Galois representations of local fields, of equal characteristic $p$ different from $\\ell$, as a powerful tool to study the Fourier-Deligne transform of $\\ell$-adic sheaves over the affine line. In this article, we compute explicitly the local Fourier transform of monomial representations satisfying a certain ramification condition, and deduce Laumon's formula relating the epsilon factor to the determinant of the local Fourier transform under the same condition.","authors_text":"Ahmed Abbes, Takeshi Saito","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-09-01T07:07:20Z","title":"Local Fourier transform and epsilon factors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.0180","kind":"arxiv","version":2},"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:d3d53d161f00d1e9942a5a14680f1c3b5176451888cbe5a73275a7e1eb22abbc","target":"record","created_at":"2026-05-18T04:33:48Z","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":"639f0723cc7e7d91efebe742c3ec9815649888587da79a1b1ce2193b4cbd110e","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-09-01T07:07:20Z","title_canon_sha256":"e1c085f4a958987e4620d1bfc7e6e76efe2fd869ae86d9fd98b7c4de15595d64"},"schema_version":"1.0","source":{"id":"0809.0180","kind":"arxiv","version":2}},"canonical_sha256":"dc5701b2743bcbcecbe4c05ba116b35df0951a4d4c56ac6c910e7289fe2a4680","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc5701b2743bcbcecbe4c05ba116b35df0951a4d4c56ac6c910e7289fe2a4680","first_computed_at":"2026-05-18T04:33:48.584768Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:48.584768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tAVzZ2SkiNY4UufDYYYGJOHjXF3LWz0F6QJhTQCFf/06HB+YgfF4N7XnuScv3pwC486myCnlFplKHaOG0Ch5Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:48.585268Z","signed_message":"canonical_sha256_bytes"},"source_id":"0809.0180","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3d53d161f00d1e9942a5a14680f1c3b5176451888cbe5a73275a7e1eb22abbc","sha256:9ad8641fbbc1b77cd6279d5226639852290e8eee705f7dc984da6d584e82ba36"],"state_sha256":"fcd35da9298e276c8604283d8bf200b175bfab8f30de043d928c49dd1c4ae512"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Z14155f9r9DnIWi1zn7ivgT5UB0UJ19IE+p5btpnKall6Zl05jEbnLO3FiqnaIkuFRsL70eDW5nk5l/caNcBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T02:45:08.565907Z","bundle_sha256":"4ff0a14a9c324e406acd17976ac08e5b87beb955a9faf55347d5364895a2731b"}}