{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:PDIUDDUPQAEJCQLAWU4WJXICLA","short_pith_number":"pith:PDIUDDUP","canonical_record":{"source":{"id":"1312.1927","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-06T16:58:56Z","cross_cats_sorted":[],"title_canon_sha256":"a2ec19a752c0f5aafc2b852b234531f5d2e4bff7f45cb618f9a59365ab0e7452","abstract_canon_sha256":"f88bab240e56c495009ecf660fc4a437b99e58986bfb743df0c4c43ee85e10f9"},"schema_version":"1.0"},"canonical_sha256":"78d1418e8f8008914160b53964dd0258166f9f8909c394f09698ab0ac6a45e63","source":{"kind":"arxiv","id":"1312.1927","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1927","created_at":"2026-05-18T03:05:19Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1927v1","created_at":"2026-05-18T03:05:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1927","created_at":"2026-05-18T03:05:19Z"},{"alias_kind":"pith_short_12","alias_value":"PDIUDDUPQAEJ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PDIUDDUPQAEJCQLA","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PDIUDDUP","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:PDIUDDUPQAEJCQLAWU4WJXICLA","target":"record","payload":{"canonical_record":{"source":{"id":"1312.1927","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-06T16:58:56Z","cross_cats_sorted":[],"title_canon_sha256":"a2ec19a752c0f5aafc2b852b234531f5d2e4bff7f45cb618f9a59365ab0e7452","abstract_canon_sha256":"f88bab240e56c495009ecf660fc4a437b99e58986bfb743df0c4c43ee85e10f9"},"schema_version":"1.0"},"canonical_sha256":"78d1418e8f8008914160b53964dd0258166f9f8909c394f09698ab0ac6a45e63","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:19.407222Z","signature_b64":"Wg3dbB+TPs3v2ZetXfxQzQ5BBhF9JUzAr2P9IPqE/uTn1Pl3e/dzr89J0EkQuV03FBeMMt/mQfLkb3/iunXJDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78d1418e8f8008914160b53964dd0258166f9f8909c394f09698ab0ac6a45e63","last_reissued_at":"2026-05-18T03:05:19.406764Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:19.406764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.1927","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":"2026-05-18T03:05:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mw+bLBUDaHf8GeKizvbxV1XJo/620OvvLMf7HWsTiLcQT7U/gleqkKde5My89lrEIaykrr4IBs+RPzCp6vLbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T09:46:16.100811Z"},"content_sha256":"a5a21e54ada9555b2643eda34b60eb17fa659a1919a9db88e3418a9b05943573","schema_version":"1.0","event_id":"sha256:a5a21e54ada9555b2643eda34b60eb17fa659a1919a9db88e3418a9b05943573"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:PDIUDDUPQAEJCQLAWU4WJXICLA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New inversion, convolution and Titchmarsh's theorems for the half-Hilbert transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Semyon Yakubovich","submitted_at":"2013-12-06T16:58:56Z","abstract_excerpt":"While exploiting the generalized Parseval equality for the Mellin transform, we derive the reciprocal inverse operator in the weighted L_2-space related to the Hilbert transform on the nonnegative half-axis. Moreover, employing the convolution method, which is based on the Mellin-Barnes integrals, we prove the corresponding convolution and Titchmarsh's theorems for the half-Hilbert transform. Some applications to the solvability of a new class of singular integral equations are demonstrated. Our technique does not require the use of methods of the Riemann-Hilbert boundary value problems for an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1927","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":"2026-05-18T03:05:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"doVLpz1IUzCZ7m5uET0pota/cM9CLErgOEXKuWKcrAr88jqxoAYv/U0juTzPa1iTHdKN9EC9q36uPqu8xHyZCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T09:46:16.101149Z"},"content_sha256":"0328d24b3fdb6378c29deaa86de7f643de64b9426d43266604ca8c5ad79da1b8","schema_version":"1.0","event_id":"sha256:0328d24b3fdb6378c29deaa86de7f643de64b9426d43266604ca8c5ad79da1b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PDIUDDUPQAEJCQLAWU4WJXICLA/bundle.json","state_url":"https://pith.science/pith/PDIUDDUPQAEJCQLAWU4WJXICLA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PDIUDDUPQAEJCQLAWU4WJXICLA/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":"2026-06-26T09:46:16Z","links":{"resolver":"https://pith.science/pith/PDIUDDUPQAEJCQLAWU4WJXICLA","bundle":"https://pith.science/pith/PDIUDDUPQAEJCQLAWU4WJXICLA/bundle.json","state":"https://pith.science/pith/PDIUDDUPQAEJCQLAWU4WJXICLA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PDIUDDUPQAEJCQLAWU4WJXICLA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PDIUDDUPQAEJCQLAWU4WJXICLA","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":"f88bab240e56c495009ecf660fc4a437b99e58986bfb743df0c4c43ee85e10f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-06T16:58:56Z","title_canon_sha256":"a2ec19a752c0f5aafc2b852b234531f5d2e4bff7f45cb618f9a59365ab0e7452"},"schema_version":"1.0","source":{"id":"1312.1927","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1927","created_at":"2026-05-18T03:05:19Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1927v1","created_at":"2026-05-18T03:05:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1927","created_at":"2026-05-18T03:05:19Z"},{"alias_kind":"pith_short_12","alias_value":"PDIUDDUPQAEJ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PDIUDDUPQAEJCQLA","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PDIUDDUP","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:0328d24b3fdb6378c29deaa86de7f643de64b9426d43266604ca8c5ad79da1b8","target":"graph","created_at":"2026-05-18T03:05:19Z","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":"While exploiting the generalized Parseval equality for the Mellin transform, we derive the reciprocal inverse operator in the weighted L_2-space related to the Hilbert transform on the nonnegative half-axis. Moreover, employing the convolution method, which is based on the Mellin-Barnes integrals, we prove the corresponding convolution and Titchmarsh's theorems for the half-Hilbert transform. Some applications to the solvability of a new class of singular integral equations are demonstrated. Our technique does not require the use of methods of the Riemann-Hilbert boundary value problems for an","authors_text":"Semyon Yakubovich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-06T16:58:56Z","title":"New inversion, convolution and Titchmarsh's theorems for the half-Hilbert transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1927","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:a5a21e54ada9555b2643eda34b60eb17fa659a1919a9db88e3418a9b05943573","target":"record","created_at":"2026-05-18T03:05:19Z","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":"f88bab240e56c495009ecf660fc4a437b99e58986bfb743df0c4c43ee85e10f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-06T16:58:56Z","title_canon_sha256":"a2ec19a752c0f5aafc2b852b234531f5d2e4bff7f45cb618f9a59365ab0e7452"},"schema_version":"1.0","source":{"id":"1312.1927","kind":"arxiv","version":1}},"canonical_sha256":"78d1418e8f8008914160b53964dd0258166f9f8909c394f09698ab0ac6a45e63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78d1418e8f8008914160b53964dd0258166f9f8909c394f09698ab0ac6a45e63","first_computed_at":"2026-05-18T03:05:19.406764Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:19.406764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wg3dbB+TPs3v2ZetXfxQzQ5BBhF9JUzAr2P9IPqE/uTn1Pl3e/dzr89J0EkQuV03FBeMMt/mQfLkb3/iunXJDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:19.407222Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1927","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5a21e54ada9555b2643eda34b60eb17fa659a1919a9db88e3418a9b05943573","sha256:0328d24b3fdb6378c29deaa86de7f643de64b9426d43266604ca8c5ad79da1b8"],"state_sha256":"ae5977ab8896d5e5a9232e6731b440992ec3e3112e544fc90abc5059b51b52ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u189ob7YniOkQYhXyfbG5cfe2StOz+pfPGQd0WkT6Gbu2czrV/i/GPn7cPoQqKcbzT21uRTTCYlPzwXvYuE4CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T09:46:16.103067Z","bundle_sha256":"94080736a314cc5bd43a83cfcad8f6a5d7b66d15f3b6ce43b76c9ff8a91ea85f"}}