{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UTCEG4QIZBYIHPYGOJ76BKMXZV","short_pith_number":"pith:UTCEG4QI","canonical_record":{"source":{"id":"1709.00854","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-09-04T08:08:41Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"6eb5d7859b643dfbd6de6facd4042b03e538dfc58228042c54076090434c775d","abstract_canon_sha256":"ad427f753688defe79cb9da25e845fd028c03192d27ea331ae2caf0200c889a1"},"schema_version":"1.0"},"canonical_sha256":"a4c4437208c87083bf06727fe0a997cd4a91aa92ae89f7b0ba76a53a1319f4d6","source":{"kind":"arxiv","id":"1709.00854","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.00854","created_at":"2026-05-18T00:25:55Z"},{"alias_kind":"arxiv_version","alias_value":"1709.00854v1","created_at":"2026-05-18T00:25:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.00854","created_at":"2026-05-18T00:25:55Z"},{"alias_kind":"pith_short_12","alias_value":"UTCEG4QIZBYI","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UTCEG4QIZBYIHPYG","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UTCEG4QI","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UTCEG4QIZBYIHPYGOJ76BKMXZV","target":"record","payload":{"canonical_record":{"source":{"id":"1709.00854","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-09-04T08:08:41Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"6eb5d7859b643dfbd6de6facd4042b03e538dfc58228042c54076090434c775d","abstract_canon_sha256":"ad427f753688defe79cb9da25e845fd028c03192d27ea331ae2caf0200c889a1"},"schema_version":"1.0"},"canonical_sha256":"a4c4437208c87083bf06727fe0a997cd4a91aa92ae89f7b0ba76a53a1319f4d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:55.241447Z","signature_b64":"4C654HXVSMpxkYpdMbEEiE/DL/my/Sy/yoQXbN6sWGQ7j9vI/wCfWQQw/XQrAnB+EXdoaKjRisB4hKP4TQZsDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4c4437208c87083bf06727fe0a997cd4a91aa92ae89f7b0ba76a53a1319f4d6","last_reissued_at":"2026-05-18T00:25:55.240825Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:55.240825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.00854","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":"2026-05-18T00:25:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4eCVJewUXznoeMWH+vbPYqy3+TSK6J31DjTF2ftY2lH8SiJKOqS6pkessuPqoak/Cy3POXFMAkXMfrN2VxLKDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T22:30:35.392721Z"},"content_sha256":"68d88c8c2ecd8c0cd05147381ec84cdcda9c17fabc6720b18695afb949f174f6","schema_version":"1.0","event_id":"sha256:68d88c8c2ecd8c0cd05147381ec84cdcda9c17fabc6720b18695afb949f174f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UTCEG4QIZBYIHPYGOJ76BKMXZV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"High order perturbation theory for difference equations and Borel summability of quantum mirror curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"hep-th","authors_text":"Jie Gu, Tin Sulejmanpasic","submitted_at":"2017-09-04T08:08:41Z","abstract_excerpt":"We adapt the Bender-Wu algorithm to solve perturbatively but very efficiently the eigenvalue problem of \"relativistic\" quantum mechanical problems whose Hamiltonians are difference operators of the exponential-polynomial type. We implement the algorithm in the function BWDifference in the updated Mathematica package BenderWu. With the help of BWDifference, we survey quantum mirror curves of toric fano Calabi-Yau threefolds, and find strong evidence that not only are the perturbative eigenenergies of the associated 1d quantum mechanical problems Borel summable, but also that the Borel sums are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00854","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":"2026-05-18T00:25:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xpOeVjmMO1hvsDLgZjDqNjXwNBAXedVcnNHU1h4kFEt/xDUB/vAVszwV1DrbO6khXcva7REg7h611nR6XONKBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T22:30:35.393414Z"},"content_sha256":"25eff43df28f9ef79fa6c004fa91ae9c735f547cce19da1c02eb213673729c96","schema_version":"1.0","event_id":"sha256:25eff43df28f9ef79fa6c004fa91ae9c735f547cce19da1c02eb213673729c96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UTCEG4QIZBYIHPYGOJ76BKMXZV/bundle.json","state_url":"https://pith.science/pith/UTCEG4QIZBYIHPYGOJ76BKMXZV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UTCEG4QIZBYIHPYGOJ76BKMXZV/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":"2026-05-23T22:30:35Z","links":{"resolver":"https://pith.science/pith/UTCEG4QIZBYIHPYGOJ76BKMXZV","bundle":"https://pith.science/pith/UTCEG4QIZBYIHPYGOJ76BKMXZV/bundle.json","state":"https://pith.science/pith/UTCEG4QIZBYIHPYGOJ76BKMXZV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UTCEG4QIZBYIHPYGOJ76BKMXZV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UTCEG4QIZBYIHPYGOJ76BKMXZV","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":"ad427f753688defe79cb9da25e845fd028c03192d27ea331ae2caf0200c889a1","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-09-04T08:08:41Z","title_canon_sha256":"6eb5d7859b643dfbd6de6facd4042b03e538dfc58228042c54076090434c775d"},"schema_version":"1.0","source":{"id":"1709.00854","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.00854","created_at":"2026-05-18T00:25:55Z"},{"alias_kind":"arxiv_version","alias_value":"1709.00854v1","created_at":"2026-05-18T00:25:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.00854","created_at":"2026-05-18T00:25:55Z"},{"alias_kind":"pith_short_12","alias_value":"UTCEG4QIZBYI","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UTCEG4QIZBYIHPYG","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UTCEG4QI","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:25eff43df28f9ef79fa6c004fa91ae9c735f547cce19da1c02eb213673729c96","target":"graph","created_at":"2026-05-18T00:25:55Z","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 adapt the Bender-Wu algorithm to solve perturbatively but very efficiently the eigenvalue problem of \"relativistic\" quantum mechanical problems whose Hamiltonians are difference operators of the exponential-polynomial type. We implement the algorithm in the function BWDifference in the updated Mathematica package BenderWu. With the help of BWDifference, we survey quantum mirror curves of toric fano Calabi-Yau threefolds, and find strong evidence that not only are the perturbative eigenenergies of the associated 1d quantum mechanical problems Borel summable, but also that the Borel sums are ","authors_text":"Jie Gu, Tin Sulejmanpasic","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-09-04T08:08:41Z","title":"High order perturbation theory for difference equations and Borel summability of quantum mirror curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00854","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":"sha256:68d88c8c2ecd8c0cd05147381ec84cdcda9c17fabc6720b18695afb949f174f6","target":"record","created_at":"2026-05-18T00:25:55Z","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":"ad427f753688defe79cb9da25e845fd028c03192d27ea331ae2caf0200c889a1","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-09-04T08:08:41Z","title_canon_sha256":"6eb5d7859b643dfbd6de6facd4042b03e538dfc58228042c54076090434c775d"},"schema_version":"1.0","source":{"id":"1709.00854","kind":"arxiv","version":1}},"canonical_sha256":"a4c4437208c87083bf06727fe0a997cd4a91aa92ae89f7b0ba76a53a1319f4d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4c4437208c87083bf06727fe0a997cd4a91aa92ae89f7b0ba76a53a1319f4d6","first_computed_at":"2026-05-18T00:25:55.240825Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:55.240825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4C654HXVSMpxkYpdMbEEiE/DL/my/Sy/yoQXbN6sWGQ7j9vI/wCfWQQw/XQrAnB+EXdoaKjRisB4hKP4TQZsDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:55.241447Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.00854","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68d88c8c2ecd8c0cd05147381ec84cdcda9c17fabc6720b18695afb949f174f6","sha256:25eff43df28f9ef79fa6c004fa91ae9c735f547cce19da1c02eb213673729c96"],"state_sha256":"5fb2728d3482e2d846410600b11ac0a56a2d77dc9716ede2cc508067dac9c8d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x9Ud2usGRV20dkmUU2vAouFOgpZHbJ98RL+ZZ5Jq8HdGoBL9JSUlbTw+q6QjYrpBE4yJIyJrOMraW/TVsr5VAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T22:30:35.396947Z","bundle_sha256":"247699fdaba080e7a6e27cb2937d6721ce678e9bfbea7580272e0ba6c82258fc"}}