{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FMVVVG7KCU32XVH4GKI6FTV5UJ","short_pith_number":"pith:FMVVVG7K","canonical_record":{"source":{"id":"1805.01734","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-05-04T12:09:05Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"1979b5f02f0c533d0c4dceb6561315446d6cbf9fa12c8417b2f950025c30ce97","abstract_canon_sha256":"deb3173f50748c0243218861ee05513d5ee80a4833487c3c3a75e380a2e10754"},"schema_version":"1.0"},"canonical_sha256":"2b2b5a9bea1537abd4fc3291e2cebda24991aad089b58bcb7fe73f1b8754b0bc","source":{"kind":"arxiv","id":"1805.01734","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.01734","created_at":"2026-05-17T23:48:01Z"},{"alias_kind":"arxiv_version","alias_value":"1805.01734v2","created_at":"2026-05-17T23:48:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01734","created_at":"2026-05-17T23:48:01Z"},{"alias_kind":"pith_short_12","alias_value":"FMVVVG7KCU32","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FMVVVG7KCU32XVH4","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FMVVVG7K","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FMVVVG7KCU32XVH4GKI6FTV5UJ","target":"record","payload":{"canonical_record":{"source":{"id":"1805.01734","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-05-04T12:09:05Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"1979b5f02f0c533d0c4dceb6561315446d6cbf9fa12c8417b2f950025c30ce97","abstract_canon_sha256":"deb3173f50748c0243218861ee05513d5ee80a4833487c3c3a75e380a2e10754"},"schema_version":"1.0"},"canonical_sha256":"2b2b5a9bea1537abd4fc3291e2cebda24991aad089b58bcb7fe73f1b8754b0bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:01.783776Z","signature_b64":"BbanRvPfGw0NySwNLzMozqzAU0aPmT9CNR2uMkB6AM4hN7OYqem37fVMwyvO2A4/D21xBBo1VXltJFx+YaDUAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b2b5a9bea1537abd4fc3291e2cebda24991aad089b58bcb7fe73f1b8754b0bc","last_reissued_at":"2026-05-17T23:48:01.783010Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:01.783010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.01734","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IPLchTqImYjkMpMZ6M44v/f8ewtJ7hjvzWuqThsroDQKYQGwU5Wyes8VFXYkWunK4x+fq/GMawPrH88Ot1TpCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:36:32.582069Z"},"content_sha256":"ee6a671fde1ffec450880629d32f396dcac233a74d556957d3ecdd4de61e7a52","schema_version":"1.0","event_id":"sha256:ee6a671fde1ffec450880629d32f396dcac233a74d556957d3ecdd4de61e7a52"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FMVVVG7KCU32XVH4GKI6FTV5UJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite-Part Integration of the Generalized Stieltjes Transform and its dominant asymptotic behavior for small values of the parameter. II. Non-integer orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Christian D. Tica, Eric A. Galapon","submitted_at":"2018-05-04T12:09:05Z","abstract_excerpt":"The paper constitutes the second part on the subject of finite part integration of the generalized Stieltjes transform $S_{\\lambda}[f]=\\int_0^{\\infty} f(x) (\\omega+x)^{-\\lambda}\\mathrm{d}x$ about $\\omega = 0$ where now $\\lambda$ is a non-integer positive real number. Divergent integrals with singularities at the origin are induced by writing $(\\omega+x)^{-\\lambda}$ as a binomial expansion about $\\omega = 0$ and interchanging the order of operations of integration and summation. The prescription of finite part integration is then implemented by interpreting these divergent integrals as finite p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01734","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":""},"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":"2026-05-17T23:48:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o420lFnPXRhxtCpyzMPOWoRtRc6xyL39A4bq/7mQ5sD/i/h88ZFdoiv1yBs8xtkMgFwmqxYW2DMl5fwq+Vf9Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:36:32.582776Z"},"content_sha256":"6833b448b1c893fa49b7a9645d7cbfcd0ca0410e11b44ea4de0a1923c8350d7e","schema_version":"1.0","event_id":"sha256:6833b448b1c893fa49b7a9645d7cbfcd0ca0410e11b44ea4de0a1923c8350d7e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FMVVVG7KCU32XVH4GKI6FTV5UJ/bundle.json","state_url":"https://pith.science/pith/FMVVVG7KCU32XVH4GKI6FTV5UJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FMVVVG7KCU32XVH4GKI6FTV5UJ/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":"2026-06-09T19:36:32Z","links":{"resolver":"https://pith.science/pith/FMVVVG7KCU32XVH4GKI6FTV5UJ","bundle":"https://pith.science/pith/FMVVVG7KCU32XVH4GKI6FTV5UJ/bundle.json","state":"https://pith.science/pith/FMVVVG7KCU32XVH4GKI6FTV5UJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FMVVVG7KCU32XVH4GKI6FTV5UJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FMVVVG7KCU32XVH4GKI6FTV5UJ","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":"deb3173f50748c0243218861ee05513d5ee80a4833487c3c3a75e380a2e10754","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-05-04T12:09:05Z","title_canon_sha256":"1979b5f02f0c533d0c4dceb6561315446d6cbf9fa12c8417b2f950025c30ce97"},"schema_version":"1.0","source":{"id":"1805.01734","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.01734","created_at":"2026-05-17T23:48:01Z"},{"alias_kind":"arxiv_version","alias_value":"1805.01734v2","created_at":"2026-05-17T23:48:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01734","created_at":"2026-05-17T23:48:01Z"},{"alias_kind":"pith_short_12","alias_value":"FMVVVG7KCU32","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FMVVVG7KCU32XVH4","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FMVVVG7K","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:6833b448b1c893fa49b7a9645d7cbfcd0ca0410e11b44ea4de0a1923c8350d7e","target":"graph","created_at":"2026-05-17T23:48:01Z","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":"The paper constitutes the second part on the subject of finite part integration of the generalized Stieltjes transform $S_{\\lambda}[f]=\\int_0^{\\infty} f(x) (\\omega+x)^{-\\lambda}\\mathrm{d}x$ about $\\omega = 0$ where now $\\lambda$ is a non-integer positive real number. Divergent integrals with singularities at the origin are induced by writing $(\\omega+x)^{-\\lambda}$ as a binomial expansion about $\\omega = 0$ and interchanging the order of operations of integration and summation. The prescription of finite part integration is then implemented by interpreting these divergent integrals as finite p","authors_text":"Christian D. Tica, Eric A. Galapon","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-05-04T12:09:05Z","title":"Finite-Part Integration of the Generalized Stieltjes Transform and its dominant asymptotic behavior for small values of the parameter. II. Non-integer orders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01734","kind":"arxiv","version":2},"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:ee6a671fde1ffec450880629d32f396dcac233a74d556957d3ecdd4de61e7a52","target":"record","created_at":"2026-05-17T23:48:01Z","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":"deb3173f50748c0243218861ee05513d5ee80a4833487c3c3a75e380a2e10754","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-05-04T12:09:05Z","title_canon_sha256":"1979b5f02f0c533d0c4dceb6561315446d6cbf9fa12c8417b2f950025c30ce97"},"schema_version":"1.0","source":{"id":"1805.01734","kind":"arxiv","version":2}},"canonical_sha256":"2b2b5a9bea1537abd4fc3291e2cebda24991aad089b58bcb7fe73f1b8754b0bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b2b5a9bea1537abd4fc3291e2cebda24991aad089b58bcb7fe73f1b8754b0bc","first_computed_at":"2026-05-17T23:48:01.783010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:01.783010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BbanRvPfGw0NySwNLzMozqzAU0aPmT9CNR2uMkB6AM4hN7OYqem37fVMwyvO2A4/D21xBBo1VXltJFx+YaDUAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:01.783776Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.01734","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee6a671fde1ffec450880629d32f396dcac233a74d556957d3ecdd4de61e7a52","sha256:6833b448b1c893fa49b7a9645d7cbfcd0ca0410e11b44ea4de0a1923c8350d7e"],"state_sha256":"51ab0806b6b87531a9f0c1c1d93aa4066ac9e6d0367edc8a831c229ae1e736c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A51jdOdAVrCNHksLT86BpfTTWYO7HOrIqSEqKMRZnftRmCxKMKRs4WzOSugIkpwi2PC8qhcM1s0ysU7x2Y2iDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:36:32.586885Z","bundle_sha256":"03138a0feb1f9085bc01254e38cf53997aa02974422921d7575ed76ddaacd562"}}