{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XBJEOUVWZLFXG6NE4QCKCEOSEH","short_pith_number":"pith:XBJEOUVW","canonical_record":{"source":{"id":"1505.01679","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-05-07T12:27:31Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"4e6d5be36fb9b50aac1495df3691c6fd97d9ab45363b581a8265662ee42c3246","abstract_canon_sha256":"8eaf28f980697fd795df7ea41c8b502c6d72da8a86a192db622b650792075f01"},"schema_version":"1.0"},"canonical_sha256":"b8524752b6cacb7379a4e404a111d221dbf1dfa018955d4e717f95bd4ed9662d","source":{"kind":"arxiv","id":"1505.01679","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.01679","created_at":"2026-05-18T02:16:40Z"},{"alias_kind":"arxiv_version","alias_value":"1505.01679v1","created_at":"2026-05-18T02:16:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.01679","created_at":"2026-05-18T02:16:40Z"},{"alias_kind":"pith_short_12","alias_value":"XBJEOUVWZLFX","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XBJEOUVWZLFXG6NE","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XBJEOUVW","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XBJEOUVWZLFXG6NE4QCKCEOSEH","target":"record","payload":{"canonical_record":{"source":{"id":"1505.01679","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-05-07T12:27:31Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"4e6d5be36fb9b50aac1495df3691c6fd97d9ab45363b581a8265662ee42c3246","abstract_canon_sha256":"8eaf28f980697fd795df7ea41c8b502c6d72da8a86a192db622b650792075f01"},"schema_version":"1.0"},"canonical_sha256":"b8524752b6cacb7379a4e404a111d221dbf1dfa018955d4e717f95bd4ed9662d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:40.302783Z","signature_b64":"/KUL9NLD7qCwkAoe+3zBIY2uf2DkFOSr723Z1/D1tfWjn20p1EBbAEvoKfV5qIgbR1JNyoy3xA+UV1ro7syrAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8524752b6cacb7379a4e404a111d221dbf1dfa018955d4e717f95bd4ed9662d","last_reissued_at":"2026-05-18T02:16:40.302077Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:40.302077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.01679","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":"2026-05-18T02:16:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v7ireI5ikjoyavNhZ9AhVWLixsfkCOjq+0gidQz2VXP2wenyqUKCHMUyIAhBwCuRfmqf8D+7ezOsTHqukNNwDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:45:08.357557Z"},"content_sha256":"d97b945b5e4ac4ac1a3d1eccd82ff8ac264ea3adf8aba5ee4e4aff9a3582d209","schema_version":"1.0","event_id":"sha256:d97b945b5e4ac4ac1a3d1eccd82ff8ac264ea3adf8aba5ee4e4aff9a3582d209"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XBJEOUVWZLFXG6NE4QCKCEOSEH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variational problems for Holderian functions with free terminal point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.DS","authors_text":"Nat\\'alia Martins, Ricardo Almeida","submitted_at":"2015-05-07T12:27:31Z","abstract_excerpt":"We develop the new variational calculus introduced in 2011 by J. Cresson and I. Greff, where the classical derivative is substituted by a new complex operator called the scale derivative. In this paper we consider several nondifferentiable variational problems with free terminal point: with and without constraints, of first and higher-order type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01679","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":"2026-05-18T02:16:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FzVFT2dbiPGOqOc3R44e+GRG7uXJy/4IJtUcaH7ADLFg/dLMFulcyLEu2aVKXgb/K8pKCZnwlFZ5vMZi4WBJAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:45:08.357905Z"},"content_sha256":"4557810b9e5d24b9a6783bda42875761e705550719e99bb7970832c3d81d082e","schema_version":"1.0","event_id":"sha256:4557810b9e5d24b9a6783bda42875761e705550719e99bb7970832c3d81d082e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XBJEOUVWZLFXG6NE4QCKCEOSEH/bundle.json","state_url":"https://pith.science/pith/XBJEOUVWZLFXG6NE4QCKCEOSEH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XBJEOUVWZLFXG6NE4QCKCEOSEH/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":"2026-06-03T04:45:08Z","links":{"resolver":"https://pith.science/pith/XBJEOUVWZLFXG6NE4QCKCEOSEH","bundle":"https://pith.science/pith/XBJEOUVWZLFXG6NE4QCKCEOSEH/bundle.json","state":"https://pith.science/pith/XBJEOUVWZLFXG6NE4QCKCEOSEH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XBJEOUVWZLFXG6NE4QCKCEOSEH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XBJEOUVWZLFXG6NE4QCKCEOSEH","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":"8eaf28f980697fd795df7ea41c8b502c6d72da8a86a192db622b650792075f01","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-05-07T12:27:31Z","title_canon_sha256":"4e6d5be36fb9b50aac1495df3691c6fd97d9ab45363b581a8265662ee42c3246"},"schema_version":"1.0","source":{"id":"1505.01679","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.01679","created_at":"2026-05-18T02:16:40Z"},{"alias_kind":"arxiv_version","alias_value":"1505.01679v1","created_at":"2026-05-18T02:16:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.01679","created_at":"2026-05-18T02:16:40Z"},{"alias_kind":"pith_short_12","alias_value":"XBJEOUVWZLFX","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XBJEOUVWZLFXG6NE","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XBJEOUVW","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:4557810b9e5d24b9a6783bda42875761e705550719e99bb7970832c3d81d082e","target":"graph","created_at":"2026-05-18T02:16:40Z","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":"We develop the new variational calculus introduced in 2011 by J. Cresson and I. Greff, where the classical derivative is substituted by a new complex operator called the scale derivative. In this paper we consider several nondifferentiable variational problems with free terminal point: with and without constraints, of first and higher-order type.","authors_text":"Nat\\'alia Martins, Ricardo Almeida","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-05-07T12:27:31Z","title":"Variational problems for Holderian functions with free terminal point"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01679","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:d97b945b5e4ac4ac1a3d1eccd82ff8ac264ea3adf8aba5ee4e4aff9a3582d209","target":"record","created_at":"2026-05-18T02:16:40Z","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":"8eaf28f980697fd795df7ea41c8b502c6d72da8a86a192db622b650792075f01","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-05-07T12:27:31Z","title_canon_sha256":"4e6d5be36fb9b50aac1495df3691c6fd97d9ab45363b581a8265662ee42c3246"},"schema_version":"1.0","source":{"id":"1505.01679","kind":"arxiv","version":1}},"canonical_sha256":"b8524752b6cacb7379a4e404a111d221dbf1dfa018955d4e717f95bd4ed9662d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8524752b6cacb7379a4e404a111d221dbf1dfa018955d4e717f95bd4ed9662d","first_computed_at":"2026-05-18T02:16:40.302077Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:40.302077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/KUL9NLD7qCwkAoe+3zBIY2uf2DkFOSr723Z1/D1tfWjn20p1EBbAEvoKfV5qIgbR1JNyoy3xA+UV1ro7syrAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:40.302783Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.01679","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d97b945b5e4ac4ac1a3d1eccd82ff8ac264ea3adf8aba5ee4e4aff9a3582d209","sha256:4557810b9e5d24b9a6783bda42875761e705550719e99bb7970832c3d81d082e"],"state_sha256":"fc92d0a24c6fa9bcc030a12f8a919aca65d484beac27810cea8b6e577a6f0913"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eAFl7nehBmAEkXf3+NZXadonAtYMN/YmOv+StC0nhWpxdoTeMTMYcK9xPXIr733mwI1fbs08vP+x58/73mDNDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T04:45:08.360240Z","bundle_sha256":"e71010a758028130ce079493b4bdda74f800ca501e299a82f8bfeb32e86bff7c"}}