{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JE7JCXYIXTQ6PIN74SIMTGZMB3","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":"c9f64acd41ebf57f8210afcd3e4e5d0c885b7beada6144cd143cfe3e9a758a20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-09T00:51:16Z","title_canon_sha256":"89152bc371a2a5de83f7242b695967dea3a0f6dd848c8a283a8ec32418bf3f40"},"schema_version":"1.0","source":{"id":"1612.02876","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02876","created_at":"2026-05-18T00:55:28Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02876v1","created_at":"2026-05-18T00:55:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02876","created_at":"2026-05-18T00:55:28Z"},{"alias_kind":"pith_short_12","alias_value":"JE7JCXYIXTQ6","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JE7JCXYIXTQ6PIN7","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JE7JCXYI","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:c88a1ded9f5a38b51aef285ba2addc13e6045177d6f33589422562d4331dacf5","target":"graph","created_at":"2026-05-18T00:55:28Z","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":"In this article we point out interesting connections among Lah numbers, Laguerre polynomials of order negative one, and exponential polynomials. We also discuss several different expressions for the higher order derivatives of exp (1/x). A new representation of these derivatives is given in terms of exponential polynomials","authors_text":"Ada, Khristo N. Boyadzhiev (Department of Mathematics, OH), Ohio Northern University, Statistics","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-09T00:51:16Z","title":"Lah numbers and Laguerre polynomials of order negative one"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02876","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:fd5d1952a53be65b580e984ed3bd6d530dddf22337d833003e986f9e928cffc6","target":"record","created_at":"2026-05-18T00:55:28Z","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":"c9f64acd41ebf57f8210afcd3e4e5d0c885b7beada6144cd143cfe3e9a758a20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-09T00:51:16Z","title_canon_sha256":"89152bc371a2a5de83f7242b695967dea3a0f6dd848c8a283a8ec32418bf3f40"},"schema_version":"1.0","source":{"id":"1612.02876","kind":"arxiv","version":1}},"canonical_sha256":"493e915f08bce1e7a1bfe490c99b2c0ed1be70d29f3341db4a43d5bb8d3de0af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"493e915f08bce1e7a1bfe490c99b2c0ed1be70d29f3341db4a43d5bb8d3de0af","first_computed_at":"2026-05-18T00:55:28.084269Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:28.084269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HbAOrlW2odCwW8Ru1BVHuUSCf62tV0DLlxK7hdeev9B7k3q2L0Xx42v1BROCWHMafIPoTF1JGpeqGb8OdM8/DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:28.084757Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.02876","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd5d1952a53be65b580e984ed3bd6d530dddf22337d833003e986f9e928cffc6","sha256:c88a1ded9f5a38b51aef285ba2addc13e6045177d6f33589422562d4331dacf5"],"state_sha256":"6994a99296102ee994449af2cff564b481155073d9dd10fdf0ce2f063b261bcc"}