{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:34KJ63MNA4W5O2ZP56UDQH3DGL","short_pith_number":"pith:34KJ63MN","canonical_record":{"source":{"id":"math/0204304","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"2002-04-24T18:33:21Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"59e79709fa13d39d3db85b9597289c003204facb653a577ddb4a66e3f2b414c2","abstract_canon_sha256":"7899c0730703af4644da33884967993564cb953e4841f44936f8f5d2ca156dd7"},"schema_version":"1.0"},"canonical_sha256":"df149f6d8d072dd76b2fefa8381f6332fe060b884d4a22556d944bde5d404b78","source":{"kind":"arxiv","id":"math/0204304","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0204304","created_at":"2026-07-04T16:35:03Z"},{"alias_kind":"arxiv_version","alias_value":"math/0204304v1","created_at":"2026-07-04T16:35:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0204304","created_at":"2026-07-04T16:35:03Z"},{"alias_kind":"pith_short_12","alias_value":"34KJ63MNA4W5","created_at":"2026-07-04T16:35:03Z"},{"alias_kind":"pith_short_16","alias_value":"34KJ63MNA4W5O2ZP","created_at":"2026-07-04T16:35:03Z"},{"alias_kind":"pith_short_8","alias_value":"34KJ63MN","created_at":"2026-07-04T16:35:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:34KJ63MNA4W5O2ZP56UDQH3DGL","target":"record","payload":{"canonical_record":{"source":{"id":"math/0204304","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"2002-04-24T18:33:21Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"59e79709fa13d39d3db85b9597289c003204facb653a577ddb4a66e3f2b414c2","abstract_canon_sha256":"7899c0730703af4644da33884967993564cb953e4841f44936f8f5d2ca156dd7"},"schema_version":"1.0"},"canonical_sha256":"df149f6d8d072dd76b2fefa8381f6332fe060b884d4a22556d944bde5d404b78","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:35:03.504484Z","signature_b64":"J2X97kgJkL1mISeiq76+OpO/lv2fGke7dpGe4YB4KqcUQeabT55lbLd0V/U6SvVLR76Wct7S1wa+Td977MByCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df149f6d8d072dd76b2fefa8381f6332fe060b884d4a22556d944bde5d404b78","last_reissued_at":"2026-07-04T16:35:03.504010Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:35:03.504010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0204304","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":"2026-07-04T16:35:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bOc155IhrzLSzsoq98s7jb/R3u5MKZLc/R1/GGMwwbxI4EEJnSM0Gj1t1ywGwlpwD1EUssSSWd8ULbnS6jbXDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T05:17:35.672197Z"},"content_sha256":"9fa29c5e3def0637466ef08114d959f0f08dce1d5b5f48301b634c1372664b07","schema_version":"1.0","event_id":"sha256:9fa29c5e3def0637466ef08114d959f0f08dce1d5b5f48301b634c1372664b07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:34KJ63MNA4W5O2ZP56UDQH3DGL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotics of determinants of Bessel operators","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.FA","authors_text":"Estelle L. Basor, Torsten Ehrhardt","submitted_at":"2002-04-24T18:33:21Z","abstract_excerpt":"In this paper we determine the asymptotics of the determinant of Bessel operators for sufficiently smooth generating functions. These operators are similar to Wiener-Hopf operators with the Fourier transform replaced by the Hankel transform and thus the asymptotics of the determinanst are similar to the well-known Szeg\\\"o-Akhiezer-Kac formula for truncated Wiener-Hopf determinants. In order to compute the above, we also show that the Bessel operators differ from the Wiener-Hopf by a Hilbert-Schmidt operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0204304","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/math/0204304/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":"2026-07-04T16:35:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8K345JMqdoJ+VKdWrkg6N151rYSafQghZt4vI1aB+4djlXqsu+pq9msL3exRebMvaP78mPX5MHV79CHK3iwoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T05:17:35.672674Z"},"content_sha256":"9f37ab4e914f4397af27a3b03e0315b079430f6f098f7eaf4f04f2cde036dc1b","schema_version":"1.0","event_id":"sha256:9f37ab4e914f4397af27a3b03e0315b079430f6f098f7eaf4f04f2cde036dc1b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/34KJ63MNA4W5O2ZP56UDQH3DGL/bundle.json","state_url":"https://pith.science/pith/34KJ63MNA4W5O2ZP56UDQH3DGL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/34KJ63MNA4W5O2ZP56UDQH3DGL/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":"2026-08-05T05:17:35Z","links":{"resolver":"https://pith.science/pith/34KJ63MNA4W5O2ZP56UDQH3DGL","bundle":"https://pith.science/pith/34KJ63MNA4W5O2ZP56UDQH3DGL/bundle.json","state":"https://pith.science/pith/34KJ63MNA4W5O2ZP56UDQH3DGL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/34KJ63MNA4W5O2ZP56UDQH3DGL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:34KJ63MNA4W5O2ZP56UDQH3DGL","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":"7899c0730703af4644da33884967993564cb953e4841f44936f8f5d2ca156dd7","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.FA","submitted_at":"2002-04-24T18:33:21Z","title_canon_sha256":"59e79709fa13d39d3db85b9597289c003204facb653a577ddb4a66e3f2b414c2"},"schema_version":"1.0","source":{"id":"math/0204304","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0204304","created_at":"2026-07-04T16:35:03Z"},{"alias_kind":"arxiv_version","alias_value":"math/0204304v1","created_at":"2026-07-04T16:35:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0204304","created_at":"2026-07-04T16:35:03Z"},{"alias_kind":"pith_short_12","alias_value":"34KJ63MNA4W5","created_at":"2026-07-04T16:35:03Z"},{"alias_kind":"pith_short_16","alias_value":"34KJ63MNA4W5O2ZP","created_at":"2026-07-04T16:35:03Z"},{"alias_kind":"pith_short_8","alias_value":"34KJ63MN","created_at":"2026-07-04T16:35:03Z"}],"graph_snapshots":[{"event_id":"sha256:9f37ab4e914f4397af27a3b03e0315b079430f6f098f7eaf4f04f2cde036dc1b","target":"graph","created_at":"2026-07-04T16:35:03Z","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/math/0204304/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we determine the asymptotics of the determinant of Bessel operators for sufficiently smooth generating functions. These operators are similar to Wiener-Hopf operators with the Fourier transform replaced by the Hankel transform and thus the asymptotics of the determinanst are similar to the well-known Szeg\\\"o-Akhiezer-Kac formula for truncated Wiener-Hopf determinants. In order to compute the above, we also show that the Bessel operators differ from the Wiener-Hopf by a Hilbert-Schmidt operator.","authors_text":"Estelle L. Basor, Torsten Ehrhardt","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"2002-04-24T18:33:21Z","title":"Asymptotics of determinants of Bessel operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0204304","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":"sha256:9fa29c5e3def0637466ef08114d959f0f08dce1d5b5f48301b634c1372664b07","target":"record","created_at":"2026-07-04T16:35:03Z","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":"7899c0730703af4644da33884967993564cb953e4841f44936f8f5d2ca156dd7","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.FA","submitted_at":"2002-04-24T18:33:21Z","title_canon_sha256":"59e79709fa13d39d3db85b9597289c003204facb653a577ddb4a66e3f2b414c2"},"schema_version":"1.0","source":{"id":"math/0204304","kind":"arxiv","version":1}},"canonical_sha256":"df149f6d8d072dd76b2fefa8381f6332fe060b884d4a22556d944bde5d404b78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df149f6d8d072dd76b2fefa8381f6332fe060b884d4a22556d944bde5d404b78","first_computed_at":"2026-07-04T16:35:03.504010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:35:03.504010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J2X97kgJkL1mISeiq76+OpO/lv2fGke7dpGe4YB4KqcUQeabT55lbLd0V/U6SvVLR76Wct7S1wa+Td977MByCA==","signature_status":"signed_v1","signed_at":"2026-07-04T16:35:03.504484Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0204304","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9fa29c5e3def0637466ef08114d959f0f08dce1d5b5f48301b634c1372664b07","sha256:9f37ab4e914f4397af27a3b03e0315b079430f6f098f7eaf4f04f2cde036dc1b"],"state_sha256":"d65ab2cc87d4a51a999959f7da204a1de8be2676cbba3b525ba98e0887bbcf91"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2EiT+aYyVa4QXQpyGoeO3iG+kFioSSC1p5salumV4Ce+cKh3OJOE1V5zDMH3u8AS9PdwlxVBnKLYrCSW+i0PDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T05:17:35.676235Z","bundle_sha256":"c3a8fbae055aed998db399ff74d7f38e52717527e4fd74dbdc47a19346b6c4b3"}}