{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:TPZQI5OCDFHE4JBV5GTQ4N4QWV","short_pith_number":"pith:TPZQI5OC","schema_version":"1.0","canonical_sha256":"9bf30475c2194e4e2435e9a70e3790b559f5dc6cd4cc99b8d663e1c0a8a4a590","source":{"kind":"arxiv","id":"1603.07026","version":2},"attestation_state":"computed","paper":{"title":"Exponential decay estimates and smoothness of the moduli space of pseudoholomorphic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Hiroshi Ohta, Kaoru Ono, Kenji Fukaya, Yong-Geun Oh","submitted_at":"2016-03-22T23:18:00Z","abstract_excerpt":"In this paper, we examine the dependence of standard gluing process for pseudoholomorphic curves under the change of the length $T$ of the neck-region with respect to the cylindrical metrics associated to the given analytic coordinates near the punctures in the setting of bordered open Riemann surface with boundary punctures. We establish exponential decay of the $T$-derivatives of the $T$-dependent family of glued solutions under the change of the length $T$ of the neck-region in a precise manner. This exponential decay estimate is an important ingredient to prove the smoothness of the Kurani"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1603.07026","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-03-22T23:18:00Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"30f1fa8cf371d4519f011c5a996663ee6b3e3adbae839dea1f83cb5b5dc5dba0","abstract_canon_sha256":"4dbd6b95c7aa0c595daa44513b1eca82e8efb0dc1d1728492ff3430ecf127523"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:29:10.956047Z","signature_b64":"JFEC6erYykuTWqJztreZ7dBwSD5m4GfEU325T90gXKLPiHvFg88V+nzxRaKg7KrAWQPPoNmp0b6X3rRgU3/WAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9bf30475c2194e4e2435e9a70e3790b559f5dc6cd4cc99b8d663e1c0a8a4a590","last_reissued_at":"2026-07-05T08:29:10.955602Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:29:10.955602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exponential decay estimates and smoothness of the moduli space of pseudoholomorphic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Hiroshi Ohta, Kaoru Ono, Kenji Fukaya, Yong-Geun Oh","submitted_at":"2016-03-22T23:18:00Z","abstract_excerpt":"In this paper, we examine the dependence of standard gluing process for pseudoholomorphic curves under the change of the length $T$ of the neck-region with respect to the cylindrical metrics associated to the given analytic coordinates near the punctures in the setting of bordered open Riemann surface with boundary punctures. We establish exponential decay of the $T$-derivatives of the $T$-dependent family of glued solutions under the change of the length $T$ of the neck-region in a precise manner. This exponential decay estimate is an important ingredient to prove the smoothness of the Kurani"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07026","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1603.07026/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1603.07026","created_at":"2026-07-05T08:29:10.955665+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.07026v2","created_at":"2026-07-05T08:29:10.955665+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07026","created_at":"2026-07-05T08:29:10.955665+00:00"},{"alias_kind":"pith_short_12","alias_value":"TPZQI5OCDFHE","created_at":"2026-07-05T08:29:10.955665+00:00"},{"alias_kind":"pith_short_16","alias_value":"TPZQI5OCDFHE4JBV","created_at":"2026-07-05T08:29:10.955665+00:00"},{"alias_kind":"pith_short_8","alias_value":"TPZQI5OC","created_at":"2026-07-05T08:29:10.955665+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.12257","citing_title":"Quantum cohomology and split generation in Lagrangian Floer theory","ref_index":39,"is_internal_anchor":false},{"citing_arxiv_id":"2501.04687","citing_title":"Open-closed Deligne-Mumford field theories: geometric foundations","ref_index":4,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TPZQI5OCDFHE4JBV5GTQ4N4QWV","json":"https://pith.science/pith/TPZQI5OCDFHE4JBV5GTQ4N4QWV.json","graph_json":"https://pith.science/api/pith-number/TPZQI5OCDFHE4JBV5GTQ4N4QWV/graph.json","events_json":"https://pith.science/api/pith-number/TPZQI5OCDFHE4JBV5GTQ4N4QWV/events.json","paper":"https://pith.science/paper/TPZQI5OC"},"agent_actions":{"view_html":"https://pith.science/pith/TPZQI5OCDFHE4JBV5GTQ4N4QWV","download_json":"https://pith.science/pith/TPZQI5OCDFHE4JBV5GTQ4N4QWV.json","view_paper":"https://pith.science/paper/TPZQI5OC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.07026&json=true","fetch_graph":"https://pith.science/api/pith-number/TPZQI5OCDFHE4JBV5GTQ4N4QWV/graph.json","fetch_events":"https://pith.science/api/pith-number/TPZQI5OCDFHE4JBV5GTQ4N4QWV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TPZQI5OCDFHE4JBV5GTQ4N4QWV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TPZQI5OCDFHE4JBV5GTQ4N4QWV/action/storage_attestation","attest_author":"https://pith.science/pith/TPZQI5OCDFHE4JBV5GTQ4N4QWV/action/author_attestation","sign_citation":"https://pith.science/pith/TPZQI5OCDFHE4JBV5GTQ4N4QWV/action/citation_signature","submit_replication":"https://pith.science/pith/TPZQI5OCDFHE4JBV5GTQ4N4QWV/action/replication_record"}},"created_at":"2026-07-05T08:29:10.955665+00:00","updated_at":"2026-07-05T08:29:10.955665+00:00"}