{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:3MHKELGFIW3BMJCIEFHONAIVSU","short_pith_number":"pith:3MHKELGF","canonical_record":{"source":{"id":"2605.20983","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CA","submitted_at":"2026-05-20T10:14:17Z","cross_cats_sorted":[],"title_canon_sha256":"0885592be85138a069b309e96cc1749b717f8c8760605ed1103a4063fcef918b","abstract_canon_sha256":"4d7e950076a85287b9389cd4ec78c6ac943203b266cdcb7e82693f28d39221b3"},"schema_version":"1.0"},"canonical_sha256":"db0ea22cc545b6162448214ee681159502561f84a9875f1f65bb5151d05f31f8","source":{"kind":"arxiv","id":"2605.20983","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20983","created_at":"2026-05-21T01:05:30Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20983v1","created_at":"2026-05-21T01:05:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20983","created_at":"2026-05-21T01:05:30Z"},{"alias_kind":"pith_short_12","alias_value":"3MHKELGFIW3B","created_at":"2026-05-21T01:05:30Z"},{"alias_kind":"pith_short_16","alias_value":"3MHKELGFIW3BMJCI","created_at":"2026-05-21T01:05:30Z"},{"alias_kind":"pith_short_8","alias_value":"3MHKELGF","created_at":"2026-05-21T01:05:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:3MHKELGFIW3BMJCIEFHONAIVSU","target":"record","payload":{"canonical_record":{"source":{"id":"2605.20983","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CA","submitted_at":"2026-05-20T10:14:17Z","cross_cats_sorted":[],"title_canon_sha256":"0885592be85138a069b309e96cc1749b717f8c8760605ed1103a4063fcef918b","abstract_canon_sha256":"4d7e950076a85287b9389cd4ec78c6ac943203b266cdcb7e82693f28d39221b3"},"schema_version":"1.0"},"canonical_sha256":"db0ea22cc545b6162448214ee681159502561f84a9875f1f65bb5151d05f31f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:05:30.980090Z","signature_b64":"fxJhE8Meet3vhKDvAr+dRV5f0gCklsDgQhSq85juDAdSuzVNt8PZS6Zf21Ghvszs1rSQQJl7ppP04brgb8RvCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db0ea22cc545b6162448214ee681159502561f84a9875f1f65bb5151d05f31f8","last_reissued_at":"2026-05-21T01:05:30.979325Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:05:30.979325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.20983","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":"2026-05-21T01:05:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7XGwCb8DXVuUKrltDYq6EMiXC8OLtQZPj/uWpeVXLGz9Dh/t/QMTmGD26AYmeahn3sGXdQEVkXgPROi5P52QDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:35:55.851485Z"},"content_sha256":"00b14b5e228197e96c79f8be793101886270e156e8fddd4d9defb12ef583e0a9","schema_version":"1.0","event_id":"sha256:00b14b5e228197e96c79f8be793101886270e156e8fddd4d9defb12ef583e0a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:3MHKELGFIW3BMJCIEFHONAIVSU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weighted Uniform Endpoint Majorants for Integrals Involving Modified Bessel Functions","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Yaoran Yang, Yutong Zhang","submitted_at":"2026-05-20T10:14:17Z","abstract_excerpt":"We give an affirmative full-range solution to Gaunt's 2019 Open Problem~2.10. The problem asks whether, for every \\(\\nu>-1/2\\) and \\(0<\\gamma<1\\), the reciprocal-power integral \\(\\int_0^x e^{-\\gamma t}I_\\nu(t)t^{-\\nu}\\,\\dd t\\) is bounded by a constant multiple of \\(e^{-\\gamma x}I_{\\nu+1}(x)x^{-\\nu}\\), uniformly for all \\(x>0\\). Earlier exponential-tilt estimates proved such endpoint majorants only under an additional smallness condition on \\(\\gamma\\). We prove the estimate throughout the natural range \\(0<\\gamma<1\\), with an explicit admissible constant. More generally, if \\(\\mu>-1\\), \\(q>-1\\)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20983","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.20983/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-21T01:05:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mrpGY/Dzrg8hu1Ebgx+knOfYwM2SyPIsxx7PEdjgj0V1kMUgZFfQTlWHwOnGhXuFjKEciADLx4NUfzjdYNH9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:35:55.851862Z"},"content_sha256":"6183a951f23c047bc85ca3c5708094c5c5b3f3958c1f0a9c3653f085fbb57861","schema_version":"1.0","event_id":"sha256:6183a951f23c047bc85ca3c5708094c5c5b3f3958c1f0a9c3653f085fbb57861"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3MHKELGFIW3BMJCIEFHONAIVSU/bundle.json","state_url":"https://pith.science/pith/3MHKELGFIW3BMJCIEFHONAIVSU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3MHKELGFIW3BMJCIEFHONAIVSU/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":"2026-06-03T06:35:55Z","links":{"resolver":"https://pith.science/pith/3MHKELGFIW3BMJCIEFHONAIVSU","bundle":"https://pith.science/pith/3MHKELGFIW3BMJCIEFHONAIVSU/bundle.json","state":"https://pith.science/pith/3MHKELGFIW3BMJCIEFHONAIVSU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3MHKELGFIW3BMJCIEFHONAIVSU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3MHKELGFIW3BMJCIEFHONAIVSU","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":"4d7e950076a85287b9389cd4ec78c6ac943203b266cdcb7e82693f28d39221b3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CA","submitted_at":"2026-05-20T10:14:17Z","title_canon_sha256":"0885592be85138a069b309e96cc1749b717f8c8760605ed1103a4063fcef918b"},"schema_version":"1.0","source":{"id":"2605.20983","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20983","created_at":"2026-05-21T01:05:30Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20983v1","created_at":"2026-05-21T01:05:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20983","created_at":"2026-05-21T01:05:30Z"},{"alias_kind":"pith_short_12","alias_value":"3MHKELGFIW3B","created_at":"2026-05-21T01:05:30Z"},{"alias_kind":"pith_short_16","alias_value":"3MHKELGFIW3BMJCI","created_at":"2026-05-21T01:05:30Z"},{"alias_kind":"pith_short_8","alias_value":"3MHKELGF","created_at":"2026-05-21T01:05:30Z"}],"graph_snapshots":[{"event_id":"sha256:6183a951f23c047bc85ca3c5708094c5c5b3f3958c1f0a9c3653f085fbb57861","target":"graph","created_at":"2026-05-21T01:05:30Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.20983/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give an affirmative full-range solution to Gaunt's 2019 Open Problem~2.10. The problem asks whether, for every \\(\\nu>-1/2\\) and \\(0<\\gamma<1\\), the reciprocal-power integral \\(\\int_0^x e^{-\\gamma t}I_\\nu(t)t^{-\\nu}\\,\\dd t\\) is bounded by a constant multiple of \\(e^{-\\gamma x}I_{\\nu+1}(x)x^{-\\nu}\\), uniformly for all \\(x>0\\). Earlier exponential-tilt estimates proved such endpoint majorants only under an additional smallness condition on \\(\\gamma\\). We prove the estimate throughout the natural range \\(0<\\gamma<1\\), with an explicit admissible constant. More generally, if \\(\\mu>-1\\), \\(q>-1\\)","authors_text":"Yaoran Yang, Yutong Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CA","submitted_at":"2026-05-20T10:14:17Z","title":"Weighted Uniform Endpoint Majorants for Integrals Involving Modified Bessel Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20983","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":"sha256:00b14b5e228197e96c79f8be793101886270e156e8fddd4d9defb12ef583e0a9","target":"record","created_at":"2026-05-21T01:05:30Z","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":"4d7e950076a85287b9389cd4ec78c6ac943203b266cdcb7e82693f28d39221b3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CA","submitted_at":"2026-05-20T10:14:17Z","title_canon_sha256":"0885592be85138a069b309e96cc1749b717f8c8760605ed1103a4063fcef918b"},"schema_version":"1.0","source":{"id":"2605.20983","kind":"arxiv","version":1}},"canonical_sha256":"db0ea22cc545b6162448214ee681159502561f84a9875f1f65bb5151d05f31f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db0ea22cc545b6162448214ee681159502561f84a9875f1f65bb5151d05f31f8","first_computed_at":"2026-05-21T01:05:30.979325Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:05:30.979325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fxJhE8Meet3vhKDvAr+dRV5f0gCklsDgQhSq85juDAdSuzVNt8PZS6Zf21Ghvszs1rSQQJl7ppP04brgb8RvCA==","signature_status":"signed_v1","signed_at":"2026-05-21T01:05:30.980090Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.20983","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00b14b5e228197e96c79f8be793101886270e156e8fddd4d9defb12ef583e0a9","sha256:6183a951f23c047bc85ca3c5708094c5c5b3f3958c1f0a9c3653f085fbb57861"],"state_sha256":"6b4bdfbb8ab33b8ae2508ababe2687ce70dcc09cd16fde7a4308b0b45142f535"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/PuJKFbYOol+Rovjv/tASqlW5flKFJ+nlN51q72mCTVos8ILPnNRI18dKDtNrWRT6Aa9V1SZLMddidvQVaWZCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T06:35:55.853909Z","bundle_sha256":"237ba6ce68399ae8988c52504f798713ebc24d62b80fc0c79810653ef026c480"}}