{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KH5K6GFPT7BTCSN55KGL7VKCL5","short_pith_number":"pith:KH5K6GFP","canonical_record":{"source":{"id":"1606.08606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-28T08:32:20Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"acac690ee38fc8fb0a14b41af6254eecd3a017a87273b37ad0a2467f254e1b07","abstract_canon_sha256":"6109a767a8c9ca5f300040cd0ba86af78c7f6d37b4a20bf5ed3432f5c8a01e33"},"schema_version":"1.0"},"canonical_sha256":"51faaf18af9fc33149bdea8cbfd5425f6f837e944df8c34ad0186048589c990e","source":{"kind":"arxiv","id":"1606.08606","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.08606","created_at":"2026-05-18T01:11:47Z"},{"alias_kind":"arxiv_version","alias_value":"1606.08606v1","created_at":"2026-05-18T01:11:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08606","created_at":"2026-05-18T01:11:47Z"},{"alias_kind":"pith_short_12","alias_value":"KH5K6GFPT7BT","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KH5K6GFPT7BTCSN5","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KH5K6GFP","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KH5K6GFPT7BTCSN55KGL7VKCL5","target":"record","payload":{"canonical_record":{"source":{"id":"1606.08606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-28T08:32:20Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"acac690ee38fc8fb0a14b41af6254eecd3a017a87273b37ad0a2467f254e1b07","abstract_canon_sha256":"6109a767a8c9ca5f300040cd0ba86af78c7f6d37b4a20bf5ed3432f5c8a01e33"},"schema_version":"1.0"},"canonical_sha256":"51faaf18af9fc33149bdea8cbfd5425f6f837e944df8c34ad0186048589c990e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:47.387831Z","signature_b64":"tQud6s5tD9PAygGQlR2Bk9EUIPI1OxYDdX1MK5l/YfX/HSQZxRJbjx0Ajff4P7Gjq98O1sMWANjgWVoujZq1Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51faaf18af9fc33149bdea8cbfd5425f6f837e944df8c34ad0186048589c990e","last_reissued_at":"2026-05-18T01:11:47.387484Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:47.387484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.08606","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":"2026-05-18T01:11:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ofp7P1VNnScLZY/3KLg6pm7+j869fnCpUiUjzcaBInZiAi/i7crMjimP+BSzj5B6xx3nnXBWMfVk3MhdVX1hCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:16:36.057870Z"},"content_sha256":"fa91866b5d2d193b2221a0935a8db8123d6d772395500c9bcdd4e3c4de30f646","schema_version":"1.0","event_id":"sha256:fa91866b5d2d193b2221a0935a8db8123d6d772395500c9bcdd4e3c4de30f646"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KH5K6GFPT7BTCSN55KGL7VKCL5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mityagin's Extension Problem. Progress Report","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Alexander Goncharov, Zeliha Ural","submitted_at":"2016-06-28T08:32:20Z","abstract_excerpt":"Given a compact set $K\\subset {\\Bbb R}^d,$ let ${\\mathcal E}(K)$ denote the space of Whitney jets on $K$. The compact set $K$ is said to have the extension property if there exists a continuous linear extension operator $W:{\\mathcal E}(K) \\longrightarrow C^{\\infty}({\\Bbb R}^d)$. In 1961 B. S. Mityagin posed a problem to give a characterization of the extension property in geometric terms. We show that there is no such complete description in terms of densities of Hausdorff contents or related characteristics. Also the extension property cannot be characterized in terms of growth of Markov's fa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08606","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":"2026-05-18T01:11:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DuHhRYYY6JxOEL306zPdd8TUUreUfr6+C5IVCh4CnQvNaG5OAMxD7HrEZxcDshjTIxxLavODtEBC5HwSvBZnCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:16:36.058497Z"},"content_sha256":"f2a0f0db47d10564eefe776e6a30dffa0482e23c2cdc95e79eda5f0dae982dab","schema_version":"1.0","event_id":"sha256:f2a0f0db47d10564eefe776e6a30dffa0482e23c2cdc95e79eda5f0dae982dab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KH5K6GFPT7BTCSN55KGL7VKCL5/bundle.json","state_url":"https://pith.science/pith/KH5K6GFPT7BTCSN55KGL7VKCL5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KH5K6GFPT7BTCSN55KGL7VKCL5/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":"2026-05-30T01:16:36Z","links":{"resolver":"https://pith.science/pith/KH5K6GFPT7BTCSN55KGL7VKCL5","bundle":"https://pith.science/pith/KH5K6GFPT7BTCSN55KGL7VKCL5/bundle.json","state":"https://pith.science/pith/KH5K6GFPT7BTCSN55KGL7VKCL5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KH5K6GFPT7BTCSN55KGL7VKCL5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KH5K6GFPT7BTCSN55KGL7VKCL5","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":"6109a767a8c9ca5f300040cd0ba86af78c7f6d37b4a20bf5ed3432f5c8a01e33","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-28T08:32:20Z","title_canon_sha256":"acac690ee38fc8fb0a14b41af6254eecd3a017a87273b37ad0a2467f254e1b07"},"schema_version":"1.0","source":{"id":"1606.08606","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.08606","created_at":"2026-05-18T01:11:47Z"},{"alias_kind":"arxiv_version","alias_value":"1606.08606v1","created_at":"2026-05-18T01:11:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08606","created_at":"2026-05-18T01:11:47Z"},{"alias_kind":"pith_short_12","alias_value":"KH5K6GFPT7BT","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KH5K6GFPT7BTCSN5","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KH5K6GFP","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:f2a0f0db47d10564eefe776e6a30dffa0482e23c2cdc95e79eda5f0dae982dab","target":"graph","created_at":"2026-05-18T01:11:47Z","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":"Given a compact set $K\\subset {\\Bbb R}^d,$ let ${\\mathcal E}(K)$ denote the space of Whitney jets on $K$. The compact set $K$ is said to have the extension property if there exists a continuous linear extension operator $W:{\\mathcal E}(K) \\longrightarrow C^{\\infty}({\\Bbb R}^d)$. In 1961 B. S. Mityagin posed a problem to give a characterization of the extension property in geometric terms. We show that there is no such complete description in terms of densities of Hausdorff contents or related characteristics. Also the extension property cannot be characterized in terms of growth of Markov's fa","authors_text":"Alexander Goncharov, Zeliha Ural","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-28T08:32:20Z","title":"Mityagin's Extension Problem. Progress Report"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08606","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:fa91866b5d2d193b2221a0935a8db8123d6d772395500c9bcdd4e3c4de30f646","target":"record","created_at":"2026-05-18T01:11:47Z","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":"6109a767a8c9ca5f300040cd0ba86af78c7f6d37b4a20bf5ed3432f5c8a01e33","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-28T08:32:20Z","title_canon_sha256":"acac690ee38fc8fb0a14b41af6254eecd3a017a87273b37ad0a2467f254e1b07"},"schema_version":"1.0","source":{"id":"1606.08606","kind":"arxiv","version":1}},"canonical_sha256":"51faaf18af9fc33149bdea8cbfd5425f6f837e944df8c34ad0186048589c990e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51faaf18af9fc33149bdea8cbfd5425f6f837e944df8c34ad0186048589c990e","first_computed_at":"2026-05-18T01:11:47.387484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:47.387484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tQud6s5tD9PAygGQlR2Bk9EUIPI1OxYDdX1MK5l/YfX/HSQZxRJbjx0Ajff4P7Gjq98O1sMWANjgWVoujZq1Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:47.387831Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.08606","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa91866b5d2d193b2221a0935a8db8123d6d772395500c9bcdd4e3c4de30f646","sha256:f2a0f0db47d10564eefe776e6a30dffa0482e23c2cdc95e79eda5f0dae982dab"],"state_sha256":"819db36d5bd5dfa305ad4145d0f68a8d6de10e111aa296d4ddbaa0c5fe9aed08"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HY+CyygcX6nE/okxZUjFnEyUJeRaldZVXyCd+7jLmfnYbtXTsxPi9w4LVkNcNiaq6PnvfIkn37v/+5AgnfaPDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T01:16:36.062089Z","bundle_sha256":"24ebb931a0716498421ec6a507d04161ee8aac62f11b6da257bc58f230d194a6"}}