{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:NSQ2MRQSF5JTABMUQS4KCIBHTL","short_pith_number":"pith:NSQ2MRQS","canonical_record":{"source":{"id":"1309.6555","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-25T16:09:51Z","cross_cats_sorted":[],"title_canon_sha256":"b1aa887117a7a53b0801b9562d9b58aea1483c2bd51b2d662c2a41bb56c9d721","abstract_canon_sha256":"81f4c52c557f853a07dbbffcbbc0d1169091cb8f33b600070c6aaeb2482ca7a6"},"schema_version":"1.0"},"canonical_sha256":"6ca1a646122f5330059484b8a120279ad89cb49699887503bdef0e0d5f878fe2","source":{"kind":"arxiv","id":"1309.6555","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6555","created_at":"2026-05-18T03:12:20Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6555v1","created_at":"2026-05-18T03:12:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6555","created_at":"2026-05-18T03:12:20Z"},{"alias_kind":"pith_short_12","alias_value":"NSQ2MRQSF5JT","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NSQ2MRQSF5JTABMU","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NSQ2MRQS","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:NSQ2MRQSF5JTABMUQS4KCIBHTL","target":"record","payload":{"canonical_record":{"source":{"id":"1309.6555","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-25T16:09:51Z","cross_cats_sorted":[],"title_canon_sha256":"b1aa887117a7a53b0801b9562d9b58aea1483c2bd51b2d662c2a41bb56c9d721","abstract_canon_sha256":"81f4c52c557f853a07dbbffcbbc0d1169091cb8f33b600070c6aaeb2482ca7a6"},"schema_version":"1.0"},"canonical_sha256":"6ca1a646122f5330059484b8a120279ad89cb49699887503bdef0e0d5f878fe2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:20.692305Z","signature_b64":"pW7xlFJHfXY6hMrnAlqvYPBGEAnzBb3Idec+jEr4/dje1S9d6pg8pzGLtg6AWk0GpUivQICCOqBosTsXf7BwCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ca1a646122f5330059484b8a120279ad89cb49699887503bdef0e0d5f878fe2","last_reissued_at":"2026-05-18T03:12:20.691413Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:20.691413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.6555","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":"2026-05-18T03:12:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D0WOiVOgtjJkW72wpju6mnVtyLkI8DtzBKo6+IK79LcEqAZ1alTygChOnbui05NGelR9f+uiA8jkBVKRjt2WDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:10:00.725875Z"},"content_sha256":"9888da35c9e80da22bd3c9cc566d2256c5f8306e5d9c6e408833e7d6c7a60ce3","schema_version":"1.0","event_id":"sha256:9888da35c9e80da22bd3c9cc566d2256c5f8306e5d9c6e408833e7d6c7a60ce3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:NSQ2MRQSF5JTABMUQS4KCIBHTL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On dependence between the norm of a function and norms of its derivatives of orders k, r - 2 and r, 0 < k < r - 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Oleg Kovalenko, Vladyslav Babenko","submitted_at":"2013-09-25T16:09:51Z","abstract_excerpt":"Necessary and sufficient conditions on the system of positive numbers $ M_{k_1}, M_{k_2}, M_{k_3}, M_{k_4}$, $0= k_1<k_2<k_3=r-2$, $k_4 = r$, which guarantee the existence of a function $x\\in L_{\\infty,\\infty}^r(R)$, such that $\\|x^{(k_i)}\\|_{\\infty}=M_{k_i},\\; i=1,2,3,4, $ are found."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6555","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":"2026-05-18T03:12:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O3phFEhF5a53jwpnWaENichB75MZd5n7UbPUEojnFP6xH3fwzmX6lGgbnBujzR1caMjE6nI92i17AuhRTPcOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:10:00.726219Z"},"content_sha256":"8a048d9f7e91c39e6da5af2ed772f8686e86574af5e7bde1b07322b2f8cbabe5","schema_version":"1.0","event_id":"sha256:8a048d9f7e91c39e6da5af2ed772f8686e86574af5e7bde1b07322b2f8cbabe5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NSQ2MRQSF5JTABMUQS4KCIBHTL/bundle.json","state_url":"https://pith.science/pith/NSQ2MRQSF5JTABMUQS4KCIBHTL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NSQ2MRQSF5JTABMUQS4KCIBHTL/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":"2026-05-31T06:10:00Z","links":{"resolver":"https://pith.science/pith/NSQ2MRQSF5JTABMUQS4KCIBHTL","bundle":"https://pith.science/pith/NSQ2MRQSF5JTABMUQS4KCIBHTL/bundle.json","state":"https://pith.science/pith/NSQ2MRQSF5JTABMUQS4KCIBHTL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NSQ2MRQSF5JTABMUQS4KCIBHTL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NSQ2MRQSF5JTABMUQS4KCIBHTL","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":"81f4c52c557f853a07dbbffcbbc0d1169091cb8f33b600070c6aaeb2482ca7a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-25T16:09:51Z","title_canon_sha256":"b1aa887117a7a53b0801b9562d9b58aea1483c2bd51b2d662c2a41bb56c9d721"},"schema_version":"1.0","source":{"id":"1309.6555","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6555","created_at":"2026-05-18T03:12:20Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6555v1","created_at":"2026-05-18T03:12:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6555","created_at":"2026-05-18T03:12:20Z"},{"alias_kind":"pith_short_12","alias_value":"NSQ2MRQSF5JT","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NSQ2MRQSF5JTABMU","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NSQ2MRQS","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:8a048d9f7e91c39e6da5af2ed772f8686e86574af5e7bde1b07322b2f8cbabe5","target":"graph","created_at":"2026-05-18T03:12:20Z","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":"Necessary and sufficient conditions on the system of positive numbers $ M_{k_1}, M_{k_2}, M_{k_3}, M_{k_4}$, $0= k_1<k_2<k_3=r-2$, $k_4 = r$, which guarantee the existence of a function $x\\in L_{\\infty,\\infty}^r(R)$, such that $\\|x^{(k_i)}\\|_{\\infty}=M_{k_i},\\; i=1,2,3,4, $ are found.","authors_text":"Oleg Kovalenko, Vladyslav Babenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-25T16:09:51Z","title":"On dependence between the norm of a function and norms of its derivatives of orders k, r - 2 and r, 0 < k < r - 2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6555","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":"sha256:9888da35c9e80da22bd3c9cc566d2256c5f8306e5d9c6e408833e7d6c7a60ce3","target":"record","created_at":"2026-05-18T03:12:20Z","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":"81f4c52c557f853a07dbbffcbbc0d1169091cb8f33b600070c6aaeb2482ca7a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-25T16:09:51Z","title_canon_sha256":"b1aa887117a7a53b0801b9562d9b58aea1483c2bd51b2d662c2a41bb56c9d721"},"schema_version":"1.0","source":{"id":"1309.6555","kind":"arxiv","version":1}},"canonical_sha256":"6ca1a646122f5330059484b8a120279ad89cb49699887503bdef0e0d5f878fe2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ca1a646122f5330059484b8a120279ad89cb49699887503bdef0e0d5f878fe2","first_computed_at":"2026-05-18T03:12:20.691413Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:20.691413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pW7xlFJHfXY6hMrnAlqvYPBGEAnzBb3Idec+jEr4/dje1S9d6pg8pzGLtg6AWk0GpUivQICCOqBosTsXf7BwCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:20.692305Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.6555","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9888da35c9e80da22bd3c9cc566d2256c5f8306e5d9c6e408833e7d6c7a60ce3","sha256:8a048d9f7e91c39e6da5af2ed772f8686e86574af5e7bde1b07322b2f8cbabe5"],"state_sha256":"ca27327aa2bfebe96051d730995b93b3ff99639ad95f13066836745406939a5d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0DTXMTF9KnWl3PV9jS9JyUfPo0W9YMj2E1TCpMoh6X5gupl2N75TmPrGbJhvba1Z032ddZliTmaWgNZqIxiEDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:10:00.728183Z","bundle_sha256":"881b988e93ece1da5c5261c3a91f4b78f430883814f4b16c0f0bb10f57634e08"}}