{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JMLSRLJIZZRXZLLUO2PRZLCXAD","short_pith_number":"pith:JMLSRLJI","canonical_record":{"source":{"id":"1602.00099","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-30T10:17:48Z","cross_cats_sorted":[],"title_canon_sha256":"d4a7b9895c9bdcb4149f238e935d12bd547784fdd7fa1186616c6e6b554468ad","abstract_canon_sha256":"480ec9cee6660bb300c6a93a61c77b53dd65910e9002c6c0db9b341586730080"},"schema_version":"1.0"},"canonical_sha256":"4b1728ad28ce637cad74769f1cac5700c6fbb0f86a470a0a290d43b078e86dda","source":{"kind":"arxiv","id":"1602.00099","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.00099","created_at":"2026-05-18T01:21:36Z"},{"alias_kind":"arxiv_version","alias_value":"1602.00099v1","created_at":"2026-05-18T01:21:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00099","created_at":"2026-05-18T01:21:36Z"},{"alias_kind":"pith_short_12","alias_value":"JMLSRLJIZZRX","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JMLSRLJIZZRXZLLU","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JMLSRLJI","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JMLSRLJIZZRXZLLUO2PRZLCXAD","target":"record","payload":{"canonical_record":{"source":{"id":"1602.00099","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-30T10:17:48Z","cross_cats_sorted":[],"title_canon_sha256":"d4a7b9895c9bdcb4149f238e935d12bd547784fdd7fa1186616c6e6b554468ad","abstract_canon_sha256":"480ec9cee6660bb300c6a93a61c77b53dd65910e9002c6c0db9b341586730080"},"schema_version":"1.0"},"canonical_sha256":"4b1728ad28ce637cad74769f1cac5700c6fbb0f86a470a0a290d43b078e86dda","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:36.325303Z","signature_b64":"j3IzWlgIu5+Vnwmcm+z6JwUgwUJgrTz9wndsWWfBhTXi+CvPWr1MgtpIAP3CTEcSLWMeDGVejHeLtF4SVIhDAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b1728ad28ce637cad74769f1cac5700c6fbb0f86a470a0a290d43b078e86dda","last_reissued_at":"2026-05-18T01:21:36.324685Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:36.324685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.00099","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":"2026-05-18T01:21:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mZeH+NuFExu45YH1ornU5qC5Q6XLIkVyB06mf0NxG2gJe18zRaiOTOkNjQVjH7MqhZ8T0t0EQj47Yhvu057lDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:35:31.799842Z"},"content_sha256":"9e4d44820432bc6356e855e45f148e7ede93a4923c5ce197d5b17ae6f1bb04de","schema_version":"1.0","event_id":"sha256:9e4d44820432bc6356e855e45f148e7ede93a4923c5ce197d5b17ae6f1bb04de"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JMLSRLJIZZRXZLLUO2PRZLCXAD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Stokes phenomenon and the Lerch zeta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"R B Paris","submitted_at":"2016-01-30T10:17:48Z","abstract_excerpt":"We examine the exponentially improved asymptotic expansion of the Lerch zeta function $L(\\lambda,a,s)=\\sum_{n=1}^\\infty \\exp (2\\pi ni\\lambda)/(n+a)^s$ for large complex values of $a$, with $\\lambda$ and $s$ regarded as parameters. It is shown that an infinite number of subdominant exponential terms switch on across the Stokes lines $\\arg\\,a=\\pm\\pi/2$. In addition, it is found that the transition across the upper and lower imaginary $a$-axes is associated, in general, with unequal scales. Numerical calculations are presented to confirm the theoretical predictions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00099","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":"2026-05-18T01:21:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NPIJ8pq8knyWA5WmExfpSEvm1UeFVMFT5Yhs6svmf41j9ojpTuq7ZPGhPqV82hWi3+6rrKsF2ygSleDASm/QBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:35:31.800213Z"},"content_sha256":"6817de09247503cbe877b38f1f69000c90979cfb9238464d501437cd689cfe70","schema_version":"1.0","event_id":"sha256:6817de09247503cbe877b38f1f69000c90979cfb9238464d501437cd689cfe70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JMLSRLJIZZRXZLLUO2PRZLCXAD/bundle.json","state_url":"https://pith.science/pith/JMLSRLJIZZRXZLLUO2PRZLCXAD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JMLSRLJIZZRXZLLUO2PRZLCXAD/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":"2026-06-12T00:35:31Z","links":{"resolver":"https://pith.science/pith/JMLSRLJIZZRXZLLUO2PRZLCXAD","bundle":"https://pith.science/pith/JMLSRLJIZZRXZLLUO2PRZLCXAD/bundle.json","state":"https://pith.science/pith/JMLSRLJIZZRXZLLUO2PRZLCXAD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JMLSRLJIZZRXZLLUO2PRZLCXAD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JMLSRLJIZZRXZLLUO2PRZLCXAD","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":"480ec9cee6660bb300c6a93a61c77b53dd65910e9002c6c0db9b341586730080","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-30T10:17:48Z","title_canon_sha256":"d4a7b9895c9bdcb4149f238e935d12bd547784fdd7fa1186616c6e6b554468ad"},"schema_version":"1.0","source":{"id":"1602.00099","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.00099","created_at":"2026-05-18T01:21:36Z"},{"alias_kind":"arxiv_version","alias_value":"1602.00099v1","created_at":"2026-05-18T01:21:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00099","created_at":"2026-05-18T01:21:36Z"},{"alias_kind":"pith_short_12","alias_value":"JMLSRLJIZZRX","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JMLSRLJIZZRXZLLU","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JMLSRLJI","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:6817de09247503cbe877b38f1f69000c90979cfb9238464d501437cd689cfe70","target":"graph","created_at":"2026-05-18T01:21:36Z","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 examine the exponentially improved asymptotic expansion of the Lerch zeta function $L(\\lambda,a,s)=\\sum_{n=1}^\\infty \\exp (2\\pi ni\\lambda)/(n+a)^s$ for large complex values of $a$, with $\\lambda$ and $s$ regarded as parameters. It is shown that an infinite number of subdominant exponential terms switch on across the Stokes lines $\\arg\\,a=\\pm\\pi/2$. In addition, it is found that the transition across the upper and lower imaginary $a$-axes is associated, in general, with unequal scales. Numerical calculations are presented to confirm the theoretical predictions.","authors_text":"R B Paris","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-30T10:17:48Z","title":"The Stokes phenomenon and the Lerch zeta function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00099","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":"sha256:9e4d44820432bc6356e855e45f148e7ede93a4923c5ce197d5b17ae6f1bb04de","target":"record","created_at":"2026-05-18T01:21:36Z","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":"480ec9cee6660bb300c6a93a61c77b53dd65910e9002c6c0db9b341586730080","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-30T10:17:48Z","title_canon_sha256":"d4a7b9895c9bdcb4149f238e935d12bd547784fdd7fa1186616c6e6b554468ad"},"schema_version":"1.0","source":{"id":"1602.00099","kind":"arxiv","version":1}},"canonical_sha256":"4b1728ad28ce637cad74769f1cac5700c6fbb0f86a470a0a290d43b078e86dda","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b1728ad28ce637cad74769f1cac5700c6fbb0f86a470a0a290d43b078e86dda","first_computed_at":"2026-05-18T01:21:36.324685Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:36.324685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j3IzWlgIu5+Vnwmcm+z6JwUgwUJgrTz9wndsWWfBhTXi+CvPWr1MgtpIAP3CTEcSLWMeDGVejHeLtF4SVIhDAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:36.325303Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.00099","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e4d44820432bc6356e855e45f148e7ede93a4923c5ce197d5b17ae6f1bb04de","sha256:6817de09247503cbe877b38f1f69000c90979cfb9238464d501437cd689cfe70"],"state_sha256":"fa7ff70490b28374c5ef47b06b795e11630b20f148b3df3a6763d5e911cf7aaa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mody0zuVeKOjGDXoK/P4yQYCgtyW4DbEOwbGcUnohj4CAFRLpynoD4of6ZLNsM2QCF6Y/UjKUKjUYXH0LE3DBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T00:35:31.802409Z","bundle_sha256":"9c53ef4c9a8ed179b41d22dcd4fcb231abbc4093131c92398facf3a8efa85b1a"}}