{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:K26XEXRU2FBJPN3KVNTDVX6VRL","short_pith_number":"pith:K26XEXRU","canonical_record":{"source":{"id":"0706.3570","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2007-06-25T06:56:08Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"ba8f7813667a2c06799688624951da61c02edccc4c93d286f969564d537c9211","abstract_canon_sha256":"60b4be4ba9064f47f79debc5be0d2f30c3907d7d684f8aa5e7557f60b5e3c822"},"schema_version":"1.0"},"canonical_sha256":"56bd725e34d14297b76aab663adfd58ac02756a6b71d23cc019aab31a0d4357e","source":{"kind":"arxiv","id":"0706.3570","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.3570","created_at":"2026-05-18T04:32:20Z"},{"alias_kind":"arxiv_version","alias_value":"0706.3570v2","created_at":"2026-05-18T04:32:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.3570","created_at":"2026-05-18T04:32:20Z"},{"alias_kind":"pith_short_12","alias_value":"K26XEXRU2FBJ","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"K26XEXRU2FBJPN3K","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"K26XEXRU","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:K26XEXRU2FBJPN3KVNTDVX6VRL","target":"record","payload":{"canonical_record":{"source":{"id":"0706.3570","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2007-06-25T06:56:08Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"ba8f7813667a2c06799688624951da61c02edccc4c93d286f969564d537c9211","abstract_canon_sha256":"60b4be4ba9064f47f79debc5be0d2f30c3907d7d684f8aa5e7557f60b5e3c822"},"schema_version":"1.0"},"canonical_sha256":"56bd725e34d14297b76aab663adfd58ac02756a6b71d23cc019aab31a0d4357e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:20.344445Z","signature_b64":"H8owxFir1AMneFSaOiT/aqbQiIrWcY5lRHHVW8dQGo9nr7f8MaOHtthgKe1XCKD2GuYt0AyNhIr42EGDA4m5Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56bd725e34d14297b76aab663adfd58ac02756a6b71d23cc019aab31a0d4357e","last_reissued_at":"2026-05-18T04:32:20.343737Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:20.343737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0706.3570","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":"2026-05-18T04:32:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3ypVsfUcqbA0bdGHXBuj2I/ssznsinsHLO929vdVDp9IQw0ze5/ZqMUP3zMboDHVuQoFf2JEpgKp5AqC5w1ODQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:59:08.804662Z"},"content_sha256":"4e571c642e503a66dfb973055b5512e8596abe49ee57b1ddc11125a2807a35ee","schema_version":"1.0","event_id":"sha256:4e571c642e503a66dfb973055b5512e8596abe49ee57b1ddc11125a2807a35ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:K26XEXRU2FBJPN3KVNTDVX6VRL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An explicit stationary phase formula for the local formal Fourier-Laplace transform","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Claude Sabbah","submitted_at":"2007-06-25T06:56:08Z","abstract_excerpt":"We give an explicit formula (i.e., a formal stationary phase formula) for the local Fourier-Laplace transform of a formal germ of meromorphic connection of one complex variable with a possibly irregular singularity. This is a complex analogue of the formulas in the preprint math/0702436v1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.3570","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":"2026-05-18T04:32:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tSa8I29zpQWIUqEyNA+GC3t5ysL0tkRkMBFv8ik/JP/ZRECvf4cU5NgIga0jRZ4nDDlNpks0G7BMeieKEY4kBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:59:08.805006Z"},"content_sha256":"5f9b8bff237e750e6baf2b0b82e1e0e680747bc76036734331cbcbb451576c19","schema_version":"1.0","event_id":"sha256:5f9b8bff237e750e6baf2b0b82e1e0e680747bc76036734331cbcbb451576c19"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K26XEXRU2FBJPN3KVNTDVX6VRL/bundle.json","state_url":"https://pith.science/pith/K26XEXRU2FBJPN3KVNTDVX6VRL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K26XEXRU2FBJPN3KVNTDVX6VRL/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":"2026-06-24T04:59:08Z","links":{"resolver":"https://pith.science/pith/K26XEXRU2FBJPN3KVNTDVX6VRL","bundle":"https://pith.science/pith/K26XEXRU2FBJPN3KVNTDVX6VRL/bundle.json","state":"https://pith.science/pith/K26XEXRU2FBJPN3KVNTDVX6VRL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K26XEXRU2FBJPN3KVNTDVX6VRL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:K26XEXRU2FBJPN3KVNTDVX6VRL","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":"60b4be4ba9064f47f79debc5be0d2f30c3907d7d684f8aa5e7557f60b5e3c822","cross_cats_sorted":["math.CV"],"license":"","primary_cat":"math.AG","submitted_at":"2007-06-25T06:56:08Z","title_canon_sha256":"ba8f7813667a2c06799688624951da61c02edccc4c93d286f969564d537c9211"},"schema_version":"1.0","source":{"id":"0706.3570","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.3570","created_at":"2026-05-18T04:32:20Z"},{"alias_kind":"arxiv_version","alias_value":"0706.3570v2","created_at":"2026-05-18T04:32:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.3570","created_at":"2026-05-18T04:32:20Z"},{"alias_kind":"pith_short_12","alias_value":"K26XEXRU2FBJ","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"K26XEXRU2FBJPN3K","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"K26XEXRU","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:5f9b8bff237e750e6baf2b0b82e1e0e680747bc76036734331cbcbb451576c19","target":"graph","created_at":"2026-05-18T04:32:20Z","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":"We give an explicit formula (i.e., a formal stationary phase formula) for the local Fourier-Laplace transform of a formal germ of meromorphic connection of one complex variable with a possibly irregular singularity. This is a complex analogue of the formulas in the preprint math/0702436v1.","authors_text":"Claude Sabbah","cross_cats":["math.CV"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2007-06-25T06:56:08Z","title":"An explicit stationary phase formula for the local formal Fourier-Laplace transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.3570","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":"sha256:4e571c642e503a66dfb973055b5512e8596abe49ee57b1ddc11125a2807a35ee","target":"record","created_at":"2026-05-18T04:32:20Z","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":"60b4be4ba9064f47f79debc5be0d2f30c3907d7d684f8aa5e7557f60b5e3c822","cross_cats_sorted":["math.CV"],"license":"","primary_cat":"math.AG","submitted_at":"2007-06-25T06:56:08Z","title_canon_sha256":"ba8f7813667a2c06799688624951da61c02edccc4c93d286f969564d537c9211"},"schema_version":"1.0","source":{"id":"0706.3570","kind":"arxiv","version":2}},"canonical_sha256":"56bd725e34d14297b76aab663adfd58ac02756a6b71d23cc019aab31a0d4357e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56bd725e34d14297b76aab663adfd58ac02756a6b71d23cc019aab31a0d4357e","first_computed_at":"2026-05-18T04:32:20.343737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:20.343737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H8owxFir1AMneFSaOiT/aqbQiIrWcY5lRHHVW8dQGo9nr7f8MaOHtthgKe1XCKD2GuYt0AyNhIr42EGDA4m5Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:20.344445Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.3570","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e571c642e503a66dfb973055b5512e8596abe49ee57b1ddc11125a2807a35ee","sha256:5f9b8bff237e750e6baf2b0b82e1e0e680747bc76036734331cbcbb451576c19"],"state_sha256":"467ff14f79308604583f8176800d7ec0d68bbcb4f4d74044711b6d1996085ebd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1wphqrPqDlJ4xQ5wkVGBS0mWa83+tTA9on3TRRsXtej4NpbopXtcxT8VeX5R30BpXsdKDnMJp6t3/7Va/RmMAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T04:59:08.806938Z","bundle_sha256":"dad53e3498ca5ee040e3b6a21188eebb241a1ae7e1de8d3304178baf8788cc54"}}