{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:R6I7YIU66XAQTOH2XDM2EGX6NT","short_pith_number":"pith:R6I7YIU6","canonical_record":{"source":{"id":"1405.0356","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-02T07:43:34Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"5986514d41cc79b9e59b7cdf35934eee94e424d7993878616e22e5ddb0f1c43a","abstract_canon_sha256":"4564614444519caa7dc781813bb072659449e60ff3fcfe08780135491e6b1364"},"schema_version":"1.0"},"canonical_sha256":"8f91fc229ef5c109b8fab8d9a21afe6ccad7399fe12d982d1acf7348c50a591b","source":{"kind":"arxiv","id":"1405.0356","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0356","created_at":"2026-05-18T02:52:48Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0356v1","created_at":"2026-05-18T02:52:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0356","created_at":"2026-05-18T02:52:48Z"},{"alias_kind":"pith_short_12","alias_value":"R6I7YIU66XAQ","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"R6I7YIU66XAQTOH2","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"R6I7YIU6","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:R6I7YIU66XAQTOH2XDM2EGX6NT","target":"record","payload":{"canonical_record":{"source":{"id":"1405.0356","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-02T07:43:34Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"5986514d41cc79b9e59b7cdf35934eee94e424d7993878616e22e5ddb0f1c43a","abstract_canon_sha256":"4564614444519caa7dc781813bb072659449e60ff3fcfe08780135491e6b1364"},"schema_version":"1.0"},"canonical_sha256":"8f91fc229ef5c109b8fab8d9a21afe6ccad7399fe12d982d1acf7348c50a591b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:48.141846Z","signature_b64":"781QLAvrLkhoBFkGdmhgT/GNrlOWREgglSt1f1j/7ureMHn/7S+DjEtVYrwb1wnvXj4EfutEHoALfeWIfVK0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f91fc229ef5c109b8fab8d9a21afe6ccad7399fe12d982d1acf7348c50a591b","last_reissued_at":"2026-05-18T02:52:48.141340Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:48.141340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.0356","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":"2026-05-18T02:52:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fZkSOjdoMGVtFGhQjW5MqdBAyJnJ7x+XulUZzMiShc5l2f3SrwxsTkGDehKGCfM2riGg9wgMXpa+V/0Xkh05Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:28:38.421979Z"},"content_sha256":"0a0f9a18f33dbf88acbb5454222da300976726995b5e53b36a14b458c50c3141","schema_version":"1.0","event_id":"sha256:0a0f9a18f33dbf88acbb5454222da300976726995b5e53b36a14b458c50c3141"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:R6I7YIU66XAQTOH2XDM2EGX6NT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Introduction to 1-summability and resurgence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"David Sauzin","submitted_at":"2014-05-02T07:43:34Z","abstract_excerpt":"This text is about the mathematical use of certain divergent power series. The first part is an introduction to 1-summability. The definitions rely on the formal Borel transform and the Laplace transform along an arbitrary direction of the complex plane. Given an arc of directions, if a power series is 1-summable in that arc, then one can attach to it a Borel-Laplace sum, i.e. a holomorphic function defined in a large enough sector and asymptotic to that power series in Gevrey sense. The second part is an introduction to Ecalle's resurgence theory. A power series is said to be resurgent when i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0356","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":"2026-05-18T02:52:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o+EQIOAbHQXYm7eeCcYVnJMAEgn93+B6EbHM2X/lNfSzEouRZA1lF2hH60kmYPObJc3dsonSPYpqG/aXgOHYDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:28:38.422642Z"},"content_sha256":"38df11ea7cc46cd1f32bf40c397f8e90b048499d8315d9c368641a0fbf704133","schema_version":"1.0","event_id":"sha256:38df11ea7cc46cd1f32bf40c397f8e90b048499d8315d9c368641a0fbf704133"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R6I7YIU66XAQTOH2XDM2EGX6NT/bundle.json","state_url":"https://pith.science/pith/R6I7YIU66XAQTOH2XDM2EGX6NT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R6I7YIU66XAQTOH2XDM2EGX6NT/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":"2026-05-26T23:28:38Z","links":{"resolver":"https://pith.science/pith/R6I7YIU66XAQTOH2XDM2EGX6NT","bundle":"https://pith.science/pith/R6I7YIU66XAQTOH2XDM2EGX6NT/bundle.json","state":"https://pith.science/pith/R6I7YIU66XAQTOH2XDM2EGX6NT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R6I7YIU66XAQTOH2XDM2EGX6NT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:R6I7YIU66XAQTOH2XDM2EGX6NT","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":"4564614444519caa7dc781813bb072659449e60ff3fcfe08780135491e6b1364","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-02T07:43:34Z","title_canon_sha256":"5986514d41cc79b9e59b7cdf35934eee94e424d7993878616e22e5ddb0f1c43a"},"schema_version":"1.0","source":{"id":"1405.0356","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0356","created_at":"2026-05-18T02:52:48Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0356v1","created_at":"2026-05-18T02:52:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0356","created_at":"2026-05-18T02:52:48Z"},{"alias_kind":"pith_short_12","alias_value":"R6I7YIU66XAQ","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"R6I7YIU66XAQTOH2","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"R6I7YIU6","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:38df11ea7cc46cd1f32bf40c397f8e90b048499d8315d9c368641a0fbf704133","target":"graph","created_at":"2026-05-18T02:52:48Z","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":"This text is about the mathematical use of certain divergent power series. The first part is an introduction to 1-summability. The definitions rely on the formal Borel transform and the Laplace transform along an arbitrary direction of the complex plane. Given an arc of directions, if a power series is 1-summable in that arc, then one can attach to it a Borel-Laplace sum, i.e. a holomorphic function defined in a large enough sector and asymptotic to that power series in Gevrey sense. The second part is an introduction to Ecalle's resurgence theory. A power series is said to be resurgent when i","authors_text":"David Sauzin","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-02T07:43:34Z","title":"Introduction to 1-summability and resurgence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0356","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":"sha256:0a0f9a18f33dbf88acbb5454222da300976726995b5e53b36a14b458c50c3141","target":"record","created_at":"2026-05-18T02:52:48Z","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":"4564614444519caa7dc781813bb072659449e60ff3fcfe08780135491e6b1364","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-02T07:43:34Z","title_canon_sha256":"5986514d41cc79b9e59b7cdf35934eee94e424d7993878616e22e5ddb0f1c43a"},"schema_version":"1.0","source":{"id":"1405.0356","kind":"arxiv","version":1}},"canonical_sha256":"8f91fc229ef5c109b8fab8d9a21afe6ccad7399fe12d982d1acf7348c50a591b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f91fc229ef5c109b8fab8d9a21afe6ccad7399fe12d982d1acf7348c50a591b","first_computed_at":"2026-05-18T02:52:48.141340Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:48.141340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"781QLAvrLkhoBFkGdmhgT/GNrlOWREgglSt1f1j/7ureMHn/7S+DjEtVYrwb1wnvXj4EfutEHoALfeWIfVK0BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:48.141846Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.0356","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a0f9a18f33dbf88acbb5454222da300976726995b5e53b36a14b458c50c3141","sha256:38df11ea7cc46cd1f32bf40c397f8e90b048499d8315d9c368641a0fbf704133"],"state_sha256":"642f7a4c6d7fd093586c90cdd0fd511e11b0887b1f61624f9258759705af3154"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+a7jlu1oVO/lQSj/U+IHGNMbeb2FX2+PB2JBHFHT3pBDu7PD79XKXqWKrbhXIW+ng5jEamWbbLK4WOOzlxCbAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T23:28:38.425515Z","bundle_sha256":"3daedc01c7343d86e04102e98a89ca97d8aaa64444c50ee18d189de62601c01c"}}