{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HIV5TGHYKIEOOUNLG777IK5IJ7","short_pith_number":"pith:HIV5TGHY","canonical_record":{"source":{"id":"1810.10242","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-24T08:33:08Z","cross_cats_sorted":[],"title_canon_sha256":"76a7fc6f5fac63c3e3fb6043b828af3789bce9c02215eec09740515032e43004","abstract_canon_sha256":"479685cf74c565a2adc4a162b7cbba5020c01a83df5f0403958ef0f5b425e561"},"schema_version":"1.0"},"canonical_sha256":"3a2bd998f85208e751ab37fff42ba84fc2e02b3a6576d258a0adc2899c514463","source":{"kind":"arxiv","id":"1810.10242","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.10242","created_at":"2026-05-18T00:02:23Z"},{"alias_kind":"arxiv_version","alias_value":"1810.10242v1","created_at":"2026-05-18T00:02:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10242","created_at":"2026-05-18T00:02:23Z"},{"alias_kind":"pith_short_12","alias_value":"HIV5TGHYKIEO","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HIV5TGHYKIEOOUNL","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HIV5TGHY","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HIV5TGHYKIEOOUNLG777IK5IJ7","target":"record","payload":{"canonical_record":{"source":{"id":"1810.10242","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-24T08:33:08Z","cross_cats_sorted":[],"title_canon_sha256":"76a7fc6f5fac63c3e3fb6043b828af3789bce9c02215eec09740515032e43004","abstract_canon_sha256":"479685cf74c565a2adc4a162b7cbba5020c01a83df5f0403958ef0f5b425e561"},"schema_version":"1.0"},"canonical_sha256":"3a2bd998f85208e751ab37fff42ba84fc2e02b3a6576d258a0adc2899c514463","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:23.791999Z","signature_b64":"uzBlWy9ADYVRWVXpgLCy+BZQRMh53Mf1rCw32j+GZT+bwDpHkjkB6zPhLsNU81ey/VYpT0S8+GJetWlc7/fMCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a2bd998f85208e751ab37fff42ba84fc2e02b3a6576d258a0adc2899c514463","last_reissued_at":"2026-05-18T00:02:23.791490Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:23.791490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.10242","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":"2026-05-18T00:02:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qs6TLe74xKtkzYYh+jRiKC/5C1ilpGC6mX+zWjo0xFGm8x0Yp6LrmY+H/8QspL69S5F8yyTjG5cXf7ZXLAeRAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T08:31:12.400495Z"},"content_sha256":"5a736db1ff35b0c2aeda96458f937d5ed668f7d651c164417b059b3bf18cc15b","schema_version":"1.0","event_id":"sha256:5a736db1ff35b0c2aeda96458f937d5ed668f7d651c164417b059b3bf18cc15b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HIV5TGHYKIEOOUNLG777IK5IJ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Doss almost periodic functions, Besicovitch-Doss almost periodic functions and convolution products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Marko Kostic","submitted_at":"2018-10-24T08:33:08Z","abstract_excerpt":"In the paper under review, we analyze the invariance of Doss almost periodicity and Besicovitch-Doss almost periodicity under the actions of convolution products. We thus continue our recent research studies \\cite{fedorov-novi} and \\cite{NSJOM-besik} by investigating the case in which the solution operator family $(R(t))_{t>0}$ under our consideration has special growth rates at zero and infinity. In contrast to \\cite{NSJOM-besik}, the results obtained in this paper can be incorporated in the qualitative analysis of solutions to abstract (degenerate) inhomogeneous fractional differential equat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10242","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":"2026-05-18T00:02:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6o+TPBKoQcV4TMY7Y/LAlN+PMis4IKOUZ20dKE4tPaYe3Fw+GtFVydtr2nm25eH6XKY19lwYgZ48K6Y8HGj6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T08:31:12.400843Z"},"content_sha256":"cbb2e0fa928c9782d0882d23035ab717d768bcdb48de32f1e6e9d71986f50b22","schema_version":"1.0","event_id":"sha256:cbb2e0fa928c9782d0882d23035ab717d768bcdb48de32f1e6e9d71986f50b22"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HIV5TGHYKIEOOUNLG777IK5IJ7/bundle.json","state_url":"https://pith.science/pith/HIV5TGHYKIEOOUNLG777IK5IJ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HIV5TGHYKIEOOUNLG777IK5IJ7/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":"2026-06-22T08:31:12Z","links":{"resolver":"https://pith.science/pith/HIV5TGHYKIEOOUNLG777IK5IJ7","bundle":"https://pith.science/pith/HIV5TGHYKIEOOUNLG777IK5IJ7/bundle.json","state":"https://pith.science/pith/HIV5TGHYKIEOOUNLG777IK5IJ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HIV5TGHYKIEOOUNLG777IK5IJ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HIV5TGHYKIEOOUNLG777IK5IJ7","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":"479685cf74c565a2adc4a162b7cbba5020c01a83df5f0403958ef0f5b425e561","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-24T08:33:08Z","title_canon_sha256":"76a7fc6f5fac63c3e3fb6043b828af3789bce9c02215eec09740515032e43004"},"schema_version":"1.0","source":{"id":"1810.10242","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.10242","created_at":"2026-05-18T00:02:23Z"},{"alias_kind":"arxiv_version","alias_value":"1810.10242v1","created_at":"2026-05-18T00:02:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10242","created_at":"2026-05-18T00:02:23Z"},{"alias_kind":"pith_short_12","alias_value":"HIV5TGHYKIEO","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HIV5TGHYKIEOOUNL","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HIV5TGHY","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:cbb2e0fa928c9782d0882d23035ab717d768bcdb48de32f1e6e9d71986f50b22","target":"graph","created_at":"2026-05-18T00:02:23Z","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 the paper under review, we analyze the invariance of Doss almost periodicity and Besicovitch-Doss almost periodicity under the actions of convolution products. We thus continue our recent research studies \\cite{fedorov-novi} and \\cite{NSJOM-besik} by investigating the case in which the solution operator family $(R(t))_{t>0}$ under our consideration has special growth rates at zero and infinity. In contrast to \\cite{NSJOM-besik}, the results obtained in this paper can be incorporated in the qualitative analysis of solutions to abstract (degenerate) inhomogeneous fractional differential equat","authors_text":"Marko Kostic","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-24T08:33:08Z","title":"Doss almost periodic functions, Besicovitch-Doss almost periodic functions and convolution products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10242","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":"sha256:5a736db1ff35b0c2aeda96458f937d5ed668f7d651c164417b059b3bf18cc15b","target":"record","created_at":"2026-05-18T00:02:23Z","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":"479685cf74c565a2adc4a162b7cbba5020c01a83df5f0403958ef0f5b425e561","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-24T08:33:08Z","title_canon_sha256":"76a7fc6f5fac63c3e3fb6043b828af3789bce9c02215eec09740515032e43004"},"schema_version":"1.0","source":{"id":"1810.10242","kind":"arxiv","version":1}},"canonical_sha256":"3a2bd998f85208e751ab37fff42ba84fc2e02b3a6576d258a0adc2899c514463","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a2bd998f85208e751ab37fff42ba84fc2e02b3a6576d258a0adc2899c514463","first_computed_at":"2026-05-18T00:02:23.791490Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:23.791490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uzBlWy9ADYVRWVXpgLCy+BZQRMh53Mf1rCw32j+GZT+bwDpHkjkB6zPhLsNU81ey/VYpT0S8+GJetWlc7/fMCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:23.791999Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.10242","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a736db1ff35b0c2aeda96458f937d5ed668f7d651c164417b059b3bf18cc15b","sha256:cbb2e0fa928c9782d0882d23035ab717d768bcdb48de32f1e6e9d71986f50b22"],"state_sha256":"28912a1ff3d0f35d6a43d23aa8d57035ccd229954558a8631190e9433f8b8e11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nkXdhkllICXU+7J6zLPs/xBqijl/UKcNQfZ4uY+bHmhsrRemC8I7rgl/SsCsqoJnK9a0L7mdBmOIou1mOUAMAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T08:31:12.402782Z","bundle_sha256":"a2c8c7d9a29942089437b27aae5b6b65d30b328b3e1f79e434c2e360c3bbad90"}}