{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:K7HF2DPIXVGBQ77M3WGAIAGDIM","short_pith_number":"pith:K7HF2DPI","canonical_record":{"source":{"id":"1010.2956","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-10-14T15:39:42Z","cross_cats_sorted":[],"title_canon_sha256":"0fefb608d3cbfb63058c79e8343a8e394cb85ecb0fd1e74d2f3b6e64c0845e83","abstract_canon_sha256":"a48fe2024d83bf0a6585da772e0bb45311928affd28fe517030debb9ff50d284"},"schema_version":"1.0"},"canonical_sha256":"57ce5d0de8bd4c187fecdd8c0400c34311bdab9ad88051f0b9ce06f9ad300a39","source":{"kind":"arxiv","id":"1010.2956","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2956","created_at":"2026-05-18T04:35:48Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2956v1","created_at":"2026-05-18T04:35:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2956","created_at":"2026-05-18T04:35:48Z"},{"alias_kind":"pith_short_12","alias_value":"K7HF2DPIXVGB","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"K7HF2DPIXVGBQ77M","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"K7HF2DPI","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:K7HF2DPIXVGBQ77M3WGAIAGDIM","target":"record","payload":{"canonical_record":{"source":{"id":"1010.2956","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-10-14T15:39:42Z","cross_cats_sorted":[],"title_canon_sha256":"0fefb608d3cbfb63058c79e8343a8e394cb85ecb0fd1e74d2f3b6e64c0845e83","abstract_canon_sha256":"a48fe2024d83bf0a6585da772e0bb45311928affd28fe517030debb9ff50d284"},"schema_version":"1.0"},"canonical_sha256":"57ce5d0de8bd4c187fecdd8c0400c34311bdab9ad88051f0b9ce06f9ad300a39","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:48.781578Z","signature_b64":"j6X48Urrtr0EkrXipIIKpT8p14dqOSC+TEc6J1zbWoO38r9a82SvAZCswmKWIyKNUIY2p3feWAp5qHNM8xUrDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57ce5d0de8bd4c187fecdd8c0400c34311bdab9ad88051f0b9ce06f9ad300a39","last_reissued_at":"2026-05-18T04:35:48.781088Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:48.781088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.2956","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":"2026-05-18T04:35:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wc2fueZIJbd4fSswB0HQ63RJO88MLahdmrtdpnY6xYcA9/QZwbb/JUW5ySyuQa6achbhFLjscsrNAIcE8HqECg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T02:08:53.040517Z"},"content_sha256":"77097feba229627394d3c24318be46474a33a0aee49ba961cb04e9fe8dac651f","schema_version":"1.0","event_id":"sha256:77097feba229627394d3c24318be46474a33a0aee49ba961cb04e9fe8dac651f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:K7HF2DPIXVGBQ77M3WGAIAGDIM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Delta-Nabla Isoperimetric Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Agnieszka B. Malinowska, Delfim F. M. Torres","submitted_at":"2010-10-14T15:39:42Z","abstract_excerpt":"We prove general necessary optimality conditions for delta-nabla isoperimetric problems of the calculus of variations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2956","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":"2026-05-18T04:35:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QP94tqKb6jpcw5NUACtxoYOhHjLuLs5KuIKhPgzPUi63atNXtG/yWKulUWZtgTJSwh46rrx9LXYn747NCbMEDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T02:08:53.040859Z"},"content_sha256":"083c4a5bbbbecb9c12ea10c119717c01c17ab83d5cbba1c2d92daa92cc0f4e59","schema_version":"1.0","event_id":"sha256:083c4a5bbbbecb9c12ea10c119717c01c17ab83d5cbba1c2d92daa92cc0f4e59"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K7HF2DPIXVGBQ77M3WGAIAGDIM/bundle.json","state_url":"https://pith.science/pith/K7HF2DPIXVGBQ77M3WGAIAGDIM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K7HF2DPIXVGBQ77M3WGAIAGDIM/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":"2026-06-26T02:08:53Z","links":{"resolver":"https://pith.science/pith/K7HF2DPIXVGBQ77M3WGAIAGDIM","bundle":"https://pith.science/pith/K7HF2DPIXVGBQ77M3WGAIAGDIM/bundle.json","state":"https://pith.science/pith/K7HF2DPIXVGBQ77M3WGAIAGDIM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K7HF2DPIXVGBQ77M3WGAIAGDIM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:K7HF2DPIXVGBQ77M3WGAIAGDIM","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":"a48fe2024d83bf0a6585da772e0bb45311928affd28fe517030debb9ff50d284","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-10-14T15:39:42Z","title_canon_sha256":"0fefb608d3cbfb63058c79e8343a8e394cb85ecb0fd1e74d2f3b6e64c0845e83"},"schema_version":"1.0","source":{"id":"1010.2956","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2956","created_at":"2026-05-18T04:35:48Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2956v1","created_at":"2026-05-18T04:35:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2956","created_at":"2026-05-18T04:35:48Z"},{"alias_kind":"pith_short_12","alias_value":"K7HF2DPIXVGB","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"K7HF2DPIXVGBQ77M","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"K7HF2DPI","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:083c4a5bbbbecb9c12ea10c119717c01c17ab83d5cbba1c2d92daa92cc0f4e59","target":"graph","created_at":"2026-05-18T04:35:48Z","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 prove general necessary optimality conditions for delta-nabla isoperimetric problems of the calculus of variations.","authors_text":"Agnieszka B. Malinowska, Delfim F. M. Torres","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-10-14T15:39:42Z","title":"Delta-Nabla Isoperimetric Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2956","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":"sha256:77097feba229627394d3c24318be46474a33a0aee49ba961cb04e9fe8dac651f","target":"record","created_at":"2026-05-18T04:35:48Z","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":"a48fe2024d83bf0a6585da772e0bb45311928affd28fe517030debb9ff50d284","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-10-14T15:39:42Z","title_canon_sha256":"0fefb608d3cbfb63058c79e8343a8e394cb85ecb0fd1e74d2f3b6e64c0845e83"},"schema_version":"1.0","source":{"id":"1010.2956","kind":"arxiv","version":1}},"canonical_sha256":"57ce5d0de8bd4c187fecdd8c0400c34311bdab9ad88051f0b9ce06f9ad300a39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57ce5d0de8bd4c187fecdd8c0400c34311bdab9ad88051f0b9ce06f9ad300a39","first_computed_at":"2026-05-18T04:35:48.781088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:48.781088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j6X48Urrtr0EkrXipIIKpT8p14dqOSC+TEc6J1zbWoO38r9a82SvAZCswmKWIyKNUIY2p3feWAp5qHNM8xUrDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:48.781578Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.2956","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77097feba229627394d3c24318be46474a33a0aee49ba961cb04e9fe8dac651f","sha256:083c4a5bbbbecb9c12ea10c119717c01c17ab83d5cbba1c2d92daa92cc0f4e59"],"state_sha256":"c0c6abeca9ceee081da168e7a7a2adbaf83c261ba4ab2f8bf4686a37d1c23612"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AtO3/7uvVR0Ti3gGQ8CmLsbxYD9EQoMs/KqXt+N2Qk9pRrrpn+guSakOtE0v6tqj201uUZSEKcgPHTpIQKtEAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T02:08:53.042838Z","bundle_sha256":"65a120bd0d04326c0339a6c7152fdc028b065ba396ff23f96178016c9f82f9de"}}