{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SDYZVVHVH2BKW7PA6LABO2YIO5","short_pith_number":"pith:SDYZVVHV","canonical_record":{"source":{"id":"1710.03712","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-10-10T16:36:09Z","cross_cats_sorted":[],"title_canon_sha256":"69a3a00200f4812c9f15aa0b1ca56c532335144f2389f7078c87c4537e9d4b0b","abstract_canon_sha256":"d09e87da486f370669faf1673aec0962b73cc2d77c278d3d7014a213946c50ed"},"schema_version":"1.0"},"canonical_sha256":"90f19ad4f53e82ab7de0f2c0176b087764d7d89f5c54f364cae88797d4bd8573","source":{"kind":"arxiv","id":"1710.03712","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.03712","created_at":"2026-05-18T00:01:38Z"},{"alias_kind":"arxiv_version","alias_value":"1710.03712v3","created_at":"2026-05-18T00:01:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03712","created_at":"2026-05-18T00:01:38Z"},{"alias_kind":"pith_short_12","alias_value":"SDYZVVHVH2BK","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SDYZVVHVH2BKW7PA","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SDYZVVHV","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SDYZVVHVH2BKW7PA6LABO2YIO5","target":"record","payload":{"canonical_record":{"source":{"id":"1710.03712","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-10-10T16:36:09Z","cross_cats_sorted":[],"title_canon_sha256":"69a3a00200f4812c9f15aa0b1ca56c532335144f2389f7078c87c4537e9d4b0b","abstract_canon_sha256":"d09e87da486f370669faf1673aec0962b73cc2d77c278d3d7014a213946c50ed"},"schema_version":"1.0"},"canonical_sha256":"90f19ad4f53e82ab7de0f2c0176b087764d7d89f5c54f364cae88797d4bd8573","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:38.929685Z","signature_b64":"+vi6pD2ScRJQeszX7WSnonysIo4IOwQrIfeo1EakohSkjz2p5lN/9yV3/N4YIyVw5OZJpe/V51kA1DUxFxxQCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90f19ad4f53e82ab7de0f2c0176b087764d7d89f5c54f364cae88797d4bd8573","last_reissued_at":"2026-05-18T00:01:38.929267Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:38.929267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.03712","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:01:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zVOz6v1yxknLMMn7c9bc4AATBrQVqTPBbHSZbRZYIKH4Z5i9jJsxwkJ8EIqvl+0Sa1q7XHS1yckf87NlUHZrAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:27:10.789076Z"},"content_sha256":"664c3a0d73f72e592de798ad45d3e1919f8c4ab9c106ba9b06bd409ab7540bfa","schema_version":"1.0","event_id":"sha256:664c3a0d73f72e592de798ad45d3e1919f8c4ab9c106ba9b06bd409ab7540bfa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SDYZVVHVH2BKW7PA6LABO2YIO5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the $\\mathbf{\\rm\\Psi}-$fractional integral and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"E. Capelas de Oliveira, J. Vanterler da C. Sousa","submitted_at":"2017-10-10T16:36:09Z","abstract_excerpt":"Motivated by the ${\\rm \\Psi}$-Riemann-Liouville $({\\rm \\Psi-RL})$ fractional derivative and by the ${\\rm \\Psi}$-Hilfer $({\\rm \\Psi-H})$ fractional derivative, we introduced a new fractional operator the so-called $\\rm\\Psi-$fractional integral. We present some important results by means of theorems and in particular, that the $\\rm\\Psi-$fractional integration operator is limited. In this sense, we discuss some examples, in particular, involving the Mittag-Leffler $({\\rm M-L})$ function, of paramount importance in the solution of population growth problem, as approached. On the other hand, we rea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03712","kind":"arxiv","version":3},"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":"2026-05-18T00:01:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6waIED0fCkM/WJCM2YZ+p5h3Hpz03oY1qKukrTIbmasrV07lW/weNfDqBpTNT9JguV5jRjnZnLMHKf9Z3GEfAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:27:10.789439Z"},"content_sha256":"13fa922859881c954f8caf015516026b53e2d0369f0509175b2497af28b44042","schema_version":"1.0","event_id":"sha256:13fa922859881c954f8caf015516026b53e2d0369f0509175b2497af28b44042"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SDYZVVHVH2BKW7PA6LABO2YIO5/bundle.json","state_url":"https://pith.science/pith/SDYZVVHVH2BKW7PA6LABO2YIO5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SDYZVVHVH2BKW7PA6LABO2YIO5/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":"2026-06-03T16:27:10Z","links":{"resolver":"https://pith.science/pith/SDYZVVHVH2BKW7PA6LABO2YIO5","bundle":"https://pith.science/pith/SDYZVVHVH2BKW7PA6LABO2YIO5/bundle.json","state":"https://pith.science/pith/SDYZVVHVH2BKW7PA6LABO2YIO5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SDYZVVHVH2BKW7PA6LABO2YIO5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SDYZVVHVH2BKW7PA6LABO2YIO5","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":"d09e87da486f370669faf1673aec0962b73cc2d77c278d3d7014a213946c50ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-10-10T16:36:09Z","title_canon_sha256":"69a3a00200f4812c9f15aa0b1ca56c532335144f2389f7078c87c4537e9d4b0b"},"schema_version":"1.0","source":{"id":"1710.03712","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.03712","created_at":"2026-05-18T00:01:38Z"},{"alias_kind":"arxiv_version","alias_value":"1710.03712v3","created_at":"2026-05-18T00:01:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03712","created_at":"2026-05-18T00:01:38Z"},{"alias_kind":"pith_short_12","alias_value":"SDYZVVHVH2BK","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SDYZVVHVH2BKW7PA","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SDYZVVHV","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:13fa922859881c954f8caf015516026b53e2d0369f0509175b2497af28b44042","target":"graph","created_at":"2026-05-18T00:01:38Z","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":"Motivated by the ${\\rm \\Psi}$-Riemann-Liouville $({\\rm \\Psi-RL})$ fractional derivative and by the ${\\rm \\Psi}$-Hilfer $({\\rm \\Psi-H})$ fractional derivative, we introduced a new fractional operator the so-called $\\rm\\Psi-$fractional integral. We present some important results by means of theorems and in particular, that the $\\rm\\Psi-$fractional integration operator is limited. In this sense, we discuss some examples, in particular, involving the Mittag-Leffler $({\\rm M-L})$ function, of paramount importance in the solution of population growth problem, as approached. On the other hand, we rea","authors_text":"E. Capelas de Oliveira, J. Vanterler da C. Sousa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-10-10T16:36:09Z","title":"On the $\\mathbf{\\rm\\Psi}-$fractional integral and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03712","kind":"arxiv","version":3},"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":"sha256:664c3a0d73f72e592de798ad45d3e1919f8c4ab9c106ba9b06bd409ab7540bfa","target":"record","created_at":"2026-05-18T00:01:38Z","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":"d09e87da486f370669faf1673aec0962b73cc2d77c278d3d7014a213946c50ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-10-10T16:36:09Z","title_canon_sha256":"69a3a00200f4812c9f15aa0b1ca56c532335144f2389f7078c87c4537e9d4b0b"},"schema_version":"1.0","source":{"id":"1710.03712","kind":"arxiv","version":3}},"canonical_sha256":"90f19ad4f53e82ab7de0f2c0176b087764d7d89f5c54f364cae88797d4bd8573","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90f19ad4f53e82ab7de0f2c0176b087764d7d89f5c54f364cae88797d4bd8573","first_computed_at":"2026-05-18T00:01:38.929267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:38.929267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+vi6pD2ScRJQeszX7WSnonysIo4IOwQrIfeo1EakohSkjz2p5lN/9yV3/N4YIyVw5OZJpe/V51kA1DUxFxxQCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:38.929685Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.03712","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:664c3a0d73f72e592de798ad45d3e1919f8c4ab9c106ba9b06bd409ab7540bfa","sha256:13fa922859881c954f8caf015516026b53e2d0369f0509175b2497af28b44042"],"state_sha256":"2e1edee90e5d3f8c48438cd14b771c78e92d68d93473877324cf30c725ad84a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1NLYARBWnGtp8QrJ95uHz28rb9S6lSCu07AM7v502+YbGudL8JCBAH/fg9YEUTlqncTw9doQZCZwUcLPxGdbBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:27:10.791430Z","bundle_sha256":"e3f86b7b7bd7cbe0887e26a1db6d8c67dc6c1f051bca5a448fc7aa0a6ac98101"}}