{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:5FOBO3Z64GFBZYBSEZY5JXHB67","short_pith_number":"pith:5FOBO3Z6","canonical_record":{"source":{"id":"1111.6325","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-28T01:04:56Z","cross_cats_sorted":["math.AP","math.CA","math.MP"],"title_canon_sha256":"21dbe5b308f1febfd343c1ef582653ae3e5c5a12155b2264189836e7b7daf513","abstract_canon_sha256":"e48f2a6799dfc743aaaeb66ec3f1c657100c244927af7b67de8b09b4c3618de9"},"schema_version":"1.0"},"canonical_sha256":"e95c176f3ee18a1ce0322671d4dce1f7ceb2e04625b4087acfdd1b41db22061c","source":{"kind":"arxiv","id":"1111.6325","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.6325","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"arxiv_version","alias_value":"1111.6325v2","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6325","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"pith_short_12","alias_value":"5FOBO3Z64GFB","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5FOBO3Z64GFBZYBS","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5FOBO3Z6","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:5FOBO3Z64GFBZYBSEZY5JXHB67","target":"record","payload":{"canonical_record":{"source":{"id":"1111.6325","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-28T01:04:56Z","cross_cats_sorted":["math.AP","math.CA","math.MP"],"title_canon_sha256":"21dbe5b308f1febfd343c1ef582653ae3e5c5a12155b2264189836e7b7daf513","abstract_canon_sha256":"e48f2a6799dfc743aaaeb66ec3f1c657100c244927af7b67de8b09b4c3618de9"},"schema_version":"1.0"},"canonical_sha256":"e95c176f3ee18a1ce0322671d4dce1f7ceb2e04625b4087acfdd1b41db22061c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:39.470504Z","signature_b64":"t17gflHBsJ7lZSkl0YVecguzRjvZZ/0sMZ345cinpqCgTIv8RAiy0Mp/W+b3Rn3iZMsdTAMZfVaXj8IkdtU2Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e95c176f3ee18a1ce0322671d4dce1f7ceb2e04625b4087acfdd1b41db22061c","last_reissued_at":"2026-05-18T03:58:39.470037Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:39.470037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.6325","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":"2026-05-18T03:58:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1gL023M0nSmkk+zta+re/vYh3IUw0/NJ9elkj2NO3Y+U8dLLX7fLmVIO+JCfhvePCS/k4ZhxDQ6ZmAhGTu7lAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T13:51:44.750993Z"},"content_sha256":"16875965c5ae949ac3e15289e3adb2452b566fd10d1ea074ced68a6db5cd20e3","schema_version":"1.0","event_id":"sha256:16875965c5ae949ac3e15289e3adb2452b566fd10d1ea074ced68a6db5cd20e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:5FOBO3Z64GFBZYBSEZY5JXHB67","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Microlocal properties of sheaves and complex WKB","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA","math.MP"],"primary_cat":"math-ph","authors_text":"Alexander Getmanenko, Dmitry Tamarkin","submitted_at":"2011-11-28T01:04:56Z","abstract_excerpt":"Kashiwara-Schapira style sheaf theory is used to justify analytic continuability of solutions of a Laplace transformed Schroedinger equation with a small parameter. This partially proves the description of the Stokes phenomenon for WKB asymptotics predicted by Voros in 1983."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6325","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":"2026-05-18T03:58:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mEEYtPngclW9ObCPFAv6fn+t36Pd6ZxYlwFxizT1wdaHk01vfyxHZg0AMmpSJFVliGUlQU+aM9FMwAkwqKQpBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T13:51:44.751347Z"},"content_sha256":"1e9559cb3c2cbc2fb2b4a16873a6c7409c3ae29fc8d793a6fa47ea4c00e6820b","schema_version":"1.0","event_id":"sha256:1e9559cb3c2cbc2fb2b4a16873a6c7409c3ae29fc8d793a6fa47ea4c00e6820b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5FOBO3Z64GFBZYBSEZY5JXHB67/bundle.json","state_url":"https://pith.science/pith/5FOBO3Z64GFBZYBSEZY5JXHB67/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5FOBO3Z64GFBZYBSEZY5JXHB67/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":"2026-07-01T13:51:44Z","links":{"resolver":"https://pith.science/pith/5FOBO3Z64GFBZYBSEZY5JXHB67","bundle":"https://pith.science/pith/5FOBO3Z64GFBZYBSEZY5JXHB67/bundle.json","state":"https://pith.science/pith/5FOBO3Z64GFBZYBSEZY5JXHB67/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5FOBO3Z64GFBZYBSEZY5JXHB67/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5FOBO3Z64GFBZYBSEZY5JXHB67","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":"e48f2a6799dfc743aaaeb66ec3f1c657100c244927af7b67de8b09b4c3618de9","cross_cats_sorted":["math.AP","math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-28T01:04:56Z","title_canon_sha256":"21dbe5b308f1febfd343c1ef582653ae3e5c5a12155b2264189836e7b7daf513"},"schema_version":"1.0","source":{"id":"1111.6325","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.6325","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"arxiv_version","alias_value":"1111.6325v2","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6325","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"pith_short_12","alias_value":"5FOBO3Z64GFB","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5FOBO3Z64GFBZYBS","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5FOBO3Z6","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:1e9559cb3c2cbc2fb2b4a16873a6c7409c3ae29fc8d793a6fa47ea4c00e6820b","target":"graph","created_at":"2026-05-18T03:58:39Z","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":"Kashiwara-Schapira style sheaf theory is used to justify analytic continuability of solutions of a Laplace transformed Schroedinger equation with a small parameter. This partially proves the description of the Stokes phenomenon for WKB asymptotics predicted by Voros in 1983.","authors_text":"Alexander Getmanenko, Dmitry Tamarkin","cross_cats":["math.AP","math.CA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-28T01:04:56Z","title":"Microlocal properties of sheaves and complex WKB"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6325","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":"sha256:16875965c5ae949ac3e15289e3adb2452b566fd10d1ea074ced68a6db5cd20e3","target":"record","created_at":"2026-05-18T03:58:39Z","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":"e48f2a6799dfc743aaaeb66ec3f1c657100c244927af7b67de8b09b4c3618de9","cross_cats_sorted":["math.AP","math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-28T01:04:56Z","title_canon_sha256":"21dbe5b308f1febfd343c1ef582653ae3e5c5a12155b2264189836e7b7daf513"},"schema_version":"1.0","source":{"id":"1111.6325","kind":"arxiv","version":2}},"canonical_sha256":"e95c176f3ee18a1ce0322671d4dce1f7ceb2e04625b4087acfdd1b41db22061c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e95c176f3ee18a1ce0322671d4dce1f7ceb2e04625b4087acfdd1b41db22061c","first_computed_at":"2026-05-18T03:58:39.470037Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:39.470037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t17gflHBsJ7lZSkl0YVecguzRjvZZ/0sMZ345cinpqCgTIv8RAiy0Mp/W+b3Rn3iZMsdTAMZfVaXj8IkdtU2Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:39.470504Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.6325","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16875965c5ae949ac3e15289e3adb2452b566fd10d1ea074ced68a6db5cd20e3","sha256:1e9559cb3c2cbc2fb2b4a16873a6c7409c3ae29fc8d793a6fa47ea4c00e6820b"],"state_sha256":"a10dc75627ff907fdb5d48bbb661ea9f17fd24e78f93770d7450b8d6ca135dfc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n+fOiRSpqA8msQ733Bd0r7CcFkK33joec9J5HHqWzt89Q3r0y7iGtdX6OoJ7ii2j9XLAYYnAAfDHhGxJnfH6AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T13:51:44.753219Z","bundle_sha256":"09d2988153c6fab46b9723cab8d2d19ca113f8298234c6ad389a12a84b9d345e"}}