{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GZUOSJE5LQVCQB3I4A7BWK2ZDX","short_pith_number":"pith:GZUOSJE5","canonical_record":{"source":{"id":"1607.06913","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-23T10:27:16Z","cross_cats_sorted":[],"title_canon_sha256":"db04db0e9e7ee2d556da8924479c86d1f5a30788da201c923d167792705bb770","abstract_canon_sha256":"24b547d5a1b119c7ad91e6f568a56f5ecb1bbe99a2c091a8b2bb9026691d5cbd"},"schema_version":"1.0"},"canonical_sha256":"3668e9249d5c2a280768e03e1b2b591ddf09cf1f08fd95e63d3a71df8d51543d","source":{"kind":"arxiv","id":"1607.06913","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06913","created_at":"2026-05-18T01:10:35Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06913v1","created_at":"2026-05-18T01:10:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06913","created_at":"2026-05-18T01:10:35Z"},{"alias_kind":"pith_short_12","alias_value":"GZUOSJE5LQVC","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GZUOSJE5LQVCQB3I","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GZUOSJE5","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GZUOSJE5LQVCQB3I4A7BWK2ZDX","target":"record","payload":{"canonical_record":{"source":{"id":"1607.06913","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-23T10:27:16Z","cross_cats_sorted":[],"title_canon_sha256":"db04db0e9e7ee2d556da8924479c86d1f5a30788da201c923d167792705bb770","abstract_canon_sha256":"24b547d5a1b119c7ad91e6f568a56f5ecb1bbe99a2c091a8b2bb9026691d5cbd"},"schema_version":"1.0"},"canonical_sha256":"3668e9249d5c2a280768e03e1b2b591ddf09cf1f08fd95e63d3a71df8d51543d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:35.467930Z","signature_b64":"vifa1HFh0ASqz8hDlzYlGHXnkiSv/bF/8msKnV4ZOKe3TAZxHGXBTsTcIYrlgsgJy6A06yRapmT40ubqVG0kCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3668e9249d5c2a280768e03e1b2b591ddf09cf1f08fd95e63d3a71df8d51543d","last_reissued_at":"2026-05-18T01:10:35.467276Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:35.467276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.06913","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":"2026-05-18T01:10:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"duEYUekHzlmr+0/SXqAhg58yKWuOxaQrT6BB+l9uAUM7/dMx7MxNvzaxZXsFOtZ1yk+T3OsYSdUvF+2wSt5CAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:30:58.559666Z"},"content_sha256":"bfaee903cd83b3900d0fec1266e859eaaf9a2911bf91156fa126765b627ac9a3","schema_version":"1.0","event_id":"sha256:bfaee903cd83b3900d0fec1266e859eaaf9a2911bf91156fa126765b627ac9a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GZUOSJE5LQVCQB3I4A7BWK2ZDX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional differential equations with dependence on the Caputo-Katugampola derivative","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Agnieszka B. Malinowska, Ricardo Almeida, Tatiana Odzijewicz","submitted_at":"2016-07-23T10:27:16Z","abstract_excerpt":"In this paper we present a new type of fractional operator, the Caputo-Katugampola derivative. The Caputo and the Caputo-Hadamard fractional derivatives are special cases of this new operator. An existence and uniqueness theorem for a fractional Cauchy type problem, with dependence on the Caputo--Katugampola derivative, is proven. A decomposition formula for the Caputo-Katugampola derivative is obtained. This formula allows us to provide a simple numerical procedure to solve the fractional differential equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06913","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":"2026-05-18T01:10:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yCA5YUGVuHAzWh2xN2q9qRxarYA5SoAbNRdOkmcuI6lmrOtLrFaHUGMYF3iXksSKK4Ny/0PPTLNgguBQTq5lAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:30:58.560021Z"},"content_sha256":"d93aeb485122917f7b372dec8956781a1380bcd521b7e9289c278c4ddb4e669f","schema_version":"1.0","event_id":"sha256:d93aeb485122917f7b372dec8956781a1380bcd521b7e9289c278c4ddb4e669f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GZUOSJE5LQVCQB3I4A7BWK2ZDX/bundle.json","state_url":"https://pith.science/pith/GZUOSJE5LQVCQB3I4A7BWK2ZDX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GZUOSJE5LQVCQB3I4A7BWK2ZDX/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":"2026-06-02T19:30:58Z","links":{"resolver":"https://pith.science/pith/GZUOSJE5LQVCQB3I4A7BWK2ZDX","bundle":"https://pith.science/pith/GZUOSJE5LQVCQB3I4A7BWK2ZDX/bundle.json","state":"https://pith.science/pith/GZUOSJE5LQVCQB3I4A7BWK2ZDX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GZUOSJE5LQVCQB3I4A7BWK2ZDX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GZUOSJE5LQVCQB3I4A7BWK2ZDX","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":"24b547d5a1b119c7ad91e6f568a56f5ecb1bbe99a2c091a8b2bb9026691d5cbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-23T10:27:16Z","title_canon_sha256":"db04db0e9e7ee2d556da8924479c86d1f5a30788da201c923d167792705bb770"},"schema_version":"1.0","source":{"id":"1607.06913","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06913","created_at":"2026-05-18T01:10:35Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06913v1","created_at":"2026-05-18T01:10:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06913","created_at":"2026-05-18T01:10:35Z"},{"alias_kind":"pith_short_12","alias_value":"GZUOSJE5LQVC","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GZUOSJE5LQVCQB3I","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GZUOSJE5","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:d93aeb485122917f7b372dec8956781a1380bcd521b7e9289c278c4ddb4e669f","target":"graph","created_at":"2026-05-18T01:10:35Z","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":"In this paper we present a new type of fractional operator, the Caputo-Katugampola derivative. The Caputo and the Caputo-Hadamard fractional derivatives are special cases of this new operator. An existence and uniqueness theorem for a fractional Cauchy type problem, with dependence on the Caputo--Katugampola derivative, is proven. A decomposition formula for the Caputo-Katugampola derivative is obtained. This formula allows us to provide a simple numerical procedure to solve the fractional differential equation.","authors_text":"Agnieszka B. Malinowska, Ricardo Almeida, Tatiana Odzijewicz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-23T10:27:16Z","title":"Fractional differential equations with dependence on the Caputo-Katugampola derivative"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06913","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:bfaee903cd83b3900d0fec1266e859eaaf9a2911bf91156fa126765b627ac9a3","target":"record","created_at":"2026-05-18T01:10:35Z","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":"24b547d5a1b119c7ad91e6f568a56f5ecb1bbe99a2c091a8b2bb9026691d5cbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-23T10:27:16Z","title_canon_sha256":"db04db0e9e7ee2d556da8924479c86d1f5a30788da201c923d167792705bb770"},"schema_version":"1.0","source":{"id":"1607.06913","kind":"arxiv","version":1}},"canonical_sha256":"3668e9249d5c2a280768e03e1b2b591ddf09cf1f08fd95e63d3a71df8d51543d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3668e9249d5c2a280768e03e1b2b591ddf09cf1f08fd95e63d3a71df8d51543d","first_computed_at":"2026-05-18T01:10:35.467276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:35.467276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vifa1HFh0ASqz8hDlzYlGHXnkiSv/bF/8msKnV4ZOKe3TAZxHGXBTsTcIYrlgsgJy6A06yRapmT40ubqVG0kCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:35.467930Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.06913","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfaee903cd83b3900d0fec1266e859eaaf9a2911bf91156fa126765b627ac9a3","sha256:d93aeb485122917f7b372dec8956781a1380bcd521b7e9289c278c4ddb4e669f"],"state_sha256":"85a5ce5b058e9dcf8b2f605e34ccb732a5a2ea92f5e004ccbecf76eb906afcc9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JsC0QAa8vPEjzmGgDHOaW91vGoNcuqcI6VdGiZYD8ip+IJ3gfz+gSyFUVjn6Wnv3qkDO386CoYaMc8U8FfpCAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T19:30:58.561965Z","bundle_sha256":"7fbdd0b35eb87bf0b6bd6e8e98d7ce668406d626da44b7a6625380440b1c0ff7"}}