{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QYZK2NK3PKM3MZKVZJKZCG7PAR","short_pith_number":"pith:QYZK2NK3","canonical_record":{"source":{"id":"1501.02994","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-01-13T13:24:32Z","cross_cats_sorted":[],"title_canon_sha256":"39251d4d1b2da73ce4b79f91227f2f556226ce937477892158b69bfc59101132","abstract_canon_sha256":"d255799e87784f28fffa980269a9b0e0ed3135ef7e1de393847a49cf6961765d"},"schema_version":"1.0"},"canonical_sha256":"8632ad355b7a99b66555ca55911bef04679144d9e3e0a27037a3536dc3edb688","source":{"kind":"arxiv","id":"1501.02994","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02994","created_at":"2026-05-17T23:53:07Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02994v3","created_at":"2026-05-17T23:53:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02994","created_at":"2026-05-17T23:53:07Z"},{"alias_kind":"pith_short_12","alias_value":"QYZK2NK3PKM3","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QYZK2NK3PKM3MZKV","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QYZK2NK3","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QYZK2NK3PKM3MZKVZJKZCG7PAR","target":"record","payload":{"canonical_record":{"source":{"id":"1501.02994","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-01-13T13:24:32Z","cross_cats_sorted":[],"title_canon_sha256":"39251d4d1b2da73ce4b79f91227f2f556226ce937477892158b69bfc59101132","abstract_canon_sha256":"d255799e87784f28fffa980269a9b0e0ed3135ef7e1de393847a49cf6961765d"},"schema_version":"1.0"},"canonical_sha256":"8632ad355b7a99b66555ca55911bef04679144d9e3e0a27037a3536dc3edb688","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:07.006922Z","signature_b64":"JcrhPHNFv0c5xdn8P5BoRm23yh0H/ePmatmhNR7ETV3DzJnWUCkTLTwkUMoSYaYfys0KON8c+bJ0cb+BPYgmAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8632ad355b7a99b66555ca55911bef04679144d9e3e0a27037a3536dc3edb688","last_reissued_at":"2026-05-17T23:53:07.006434Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:07.006434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.02994","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FMt6H+cZS/2K5/HzVuhQCkybAZs74nLNevFYBr/T9GH7RmBwp2Ag+xySS+7QmP6iYD5sbdnSXnHx3yYtQ7FxCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T22:41:37.839172Z"},"content_sha256":"61bac34b404ff371c672ef824eca1b2ab4e8dd095f5798741f72ebd63e31943a","schema_version":"1.0","event_id":"sha256:61bac34b404ff371c672ef824eca1b2ab4e8dd095f5798741f72ebd63e31943a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QYZK2NK3PKM3MZKVZJKZCG7PAR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$q$-Borel-Laplace summation for $q$-difference equations with two slopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Anton Eloy, Thomas Dreyfus","submitted_at":"2015-01-13T13:24:32Z","abstract_excerpt":"In this paper, we consider linear $q$-difference systems with coefficients that are germs of meromorphic functions, with Newton polygon that has two slopes. Then, we explain how to compute similar meromorphic gauge transformations than those appearing in the work of Bugeaud, using a $q$-analogue of the Borel-Laplace summation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02994","kind":"arxiv","version":3},"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":"2026-05-17T23:53:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8iSpEjI7NqEwiYMjt6ygqQfY+jG17Rctfwl5/WPpuRBJckJGAy5AnIr37AaZwnHnRPfu0NpAa7Lt0Vfxpq5OAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T22:41:37.839536Z"},"content_sha256":"17d0aedd553ce3237cf8ba6ee451e3a14d142548910009fb083f8d34b55ea36e","schema_version":"1.0","event_id":"sha256:17d0aedd553ce3237cf8ba6ee451e3a14d142548910009fb083f8d34b55ea36e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QYZK2NK3PKM3MZKVZJKZCG7PAR/bundle.json","state_url":"https://pith.science/pith/QYZK2NK3PKM3MZKVZJKZCG7PAR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QYZK2NK3PKM3MZKVZJKZCG7PAR/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":"2026-06-30T22:41:37Z","links":{"resolver":"https://pith.science/pith/QYZK2NK3PKM3MZKVZJKZCG7PAR","bundle":"https://pith.science/pith/QYZK2NK3PKM3MZKVZJKZCG7PAR/bundle.json","state":"https://pith.science/pith/QYZK2NK3PKM3MZKVZJKZCG7PAR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QYZK2NK3PKM3MZKVZJKZCG7PAR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QYZK2NK3PKM3MZKVZJKZCG7PAR","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":"d255799e87784f28fffa980269a9b0e0ed3135ef7e1de393847a49cf6961765d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-01-13T13:24:32Z","title_canon_sha256":"39251d4d1b2da73ce4b79f91227f2f556226ce937477892158b69bfc59101132"},"schema_version":"1.0","source":{"id":"1501.02994","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02994","created_at":"2026-05-17T23:53:07Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02994v3","created_at":"2026-05-17T23:53:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02994","created_at":"2026-05-17T23:53:07Z"},{"alias_kind":"pith_short_12","alias_value":"QYZK2NK3PKM3","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QYZK2NK3PKM3MZKV","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QYZK2NK3","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:17d0aedd553ce3237cf8ba6ee451e3a14d142548910009fb083f8d34b55ea36e","target":"graph","created_at":"2026-05-17T23:53:07Z","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 paper, we consider linear $q$-difference systems with coefficients that are germs of meromorphic functions, with Newton polygon that has two slopes. Then, we explain how to compute similar meromorphic gauge transformations than those appearing in the work of Bugeaud, using a $q$-analogue of the Borel-Laplace summation.","authors_text":"Anton Eloy, Thomas Dreyfus","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-01-13T13:24:32Z","title":"$q$-Borel-Laplace summation for $q$-difference equations with two slopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02994","kind":"arxiv","version":3},"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":"sha256:61bac34b404ff371c672ef824eca1b2ab4e8dd095f5798741f72ebd63e31943a","target":"record","created_at":"2026-05-17T23:53:07Z","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":"d255799e87784f28fffa980269a9b0e0ed3135ef7e1de393847a49cf6961765d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-01-13T13:24:32Z","title_canon_sha256":"39251d4d1b2da73ce4b79f91227f2f556226ce937477892158b69bfc59101132"},"schema_version":"1.0","source":{"id":"1501.02994","kind":"arxiv","version":3}},"canonical_sha256":"8632ad355b7a99b66555ca55911bef04679144d9e3e0a27037a3536dc3edb688","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8632ad355b7a99b66555ca55911bef04679144d9e3e0a27037a3536dc3edb688","first_computed_at":"2026-05-17T23:53:07.006434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:07.006434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JcrhPHNFv0c5xdn8P5BoRm23yh0H/ePmatmhNR7ETV3DzJnWUCkTLTwkUMoSYaYfys0KON8c+bJ0cb+BPYgmAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:07.006922Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.02994","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61bac34b404ff371c672ef824eca1b2ab4e8dd095f5798741f72ebd63e31943a","sha256:17d0aedd553ce3237cf8ba6ee451e3a14d142548910009fb083f8d34b55ea36e"],"state_sha256":"6562f052b86e4bfec735446c3ea0290b280552a6f0f2f136bce68ee789367265"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hIa+J3cgDXT9esB845xPWR+FxpynufehzbPAVvqxVTT7WX1WPy06XC2qWke2A87fC6//EKzWjvXEThu7l3TUAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T22:41:37.841552Z","bundle_sha256":"76a100a4e8eee4e0eb7b52fd8701063cb65e5cb149d8d146724a7dfd3902aeb3"}}