{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:AAV3SRZPR7U4TFA72SN6DSTHPM","short_pith_number":"pith:AAV3SRZP","canonical_record":{"source":{"id":"1706.01721","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-06T12:03:40Z","cross_cats_sorted":[],"title_canon_sha256":"da4c2db8cbb7d83537e4d5b824d057c063c2ec00d3aa754e04a8f6f80836f8a3","abstract_canon_sha256":"dc140ac1be163896b013575aa1612446cbde5e52c08d8e1a37b1fdacbadb1fcd"},"schema_version":"1.0"},"canonical_sha256":"002bb9472f8fe9c9941fd49be1ca677b0c8b24f3e53908b89cdcea732409d632","source":{"kind":"arxiv","id":"1706.01721","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.01721","created_at":"2026-05-18T00:23:08Z"},{"alias_kind":"arxiv_version","alias_value":"1706.01721v2","created_at":"2026-05-18T00:23:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.01721","created_at":"2026-05-18T00:23:08Z"},{"alias_kind":"pith_short_12","alias_value":"AAV3SRZPR7U4","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AAV3SRZPR7U4TFA7","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AAV3SRZP","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:AAV3SRZPR7U4TFA72SN6DSTHPM","target":"record","payload":{"canonical_record":{"source":{"id":"1706.01721","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-06T12:03:40Z","cross_cats_sorted":[],"title_canon_sha256":"da4c2db8cbb7d83537e4d5b824d057c063c2ec00d3aa754e04a8f6f80836f8a3","abstract_canon_sha256":"dc140ac1be163896b013575aa1612446cbde5e52c08d8e1a37b1fdacbadb1fcd"},"schema_version":"1.0"},"canonical_sha256":"002bb9472f8fe9c9941fd49be1ca677b0c8b24f3e53908b89cdcea732409d632","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:08.834204Z","signature_b64":"mHu4faeBoMa+rHwvNcAucBkq2bnZ/0E4eJ0A/N8ysvN2LwXSM5qu0YW3gqBA3qGM6rICuBE0BmoLKWOQprrWCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"002bb9472f8fe9c9941fd49be1ca677b0c8b24f3e53908b89cdcea732409d632","last_reissued_at":"2026-05-18T00:23:08.833700Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:08.833700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.01721","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Dr3JzQ7oEtVKVvcrMclQ0WsRpB1XCe+0l6Bp9qRBPLw8XGU8Lbq6IBP0qS1Nmi5eq6JN4mI9hoZx8u3bEhSBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T03:53:13.577873Z"},"content_sha256":"2fab3970b15bb9f8b4fd956147753fac1e0d3aee3a96f9ab59e9c8d6eb16cea4","schema_version":"1.0","event_id":"sha256:2fab3970b15bb9f8b4fd956147753fac1e0d3aee3a96f9ab59e9c8d6eb16cea4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:AAV3SRZPR7U4TFA72SN6DSTHPM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Explicit formulas for $C^{1,1}$ Glaeser-Whitney extensions of 1-fields in Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Aris Daniilidis, Erwan Le Gruyer (IRMAR), Mounir Haddou (IRMAR), Olivier Ley (IRMAR)","submitted_at":"2017-06-06T12:03:40Z","abstract_excerpt":"We give a simple alternative proof for the $C^{1,1}$--convex extension problem which has been introduced and studied by D. Azagra and C. Mudarra [2]. As an application, we obtain an easy constructive proof for the Glaeser-Whitney problem of $C^{1,1}$ extensions on a Hilbert space. In both cases we provide explicit formulae for the extensions. For the Gleaser-Whitney problem the obtained extension is almost minimal, that is, minimal up to a factor $\\frac{1+\\sqrt{3}}{2}$ in the sense of Le Gruyer [15]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01721","kind":"arxiv","version":2},"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":"2026-05-18T00:23:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lgs68wyn/dfMcn9mGiPl8/KOkdxNK2gCD70RuZSC40BSVUaGSY7IZb55Q9aEWptjgc/L7DutMCEDQiM55UngDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T03:53:13.578257Z"},"content_sha256":"6ce427c549e601464914dea5c4a12c81983b7ff46cc3dfc2ecd9473e343a5b2b","schema_version":"1.0","event_id":"sha256:6ce427c549e601464914dea5c4a12c81983b7ff46cc3dfc2ecd9473e343a5b2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AAV3SRZPR7U4TFA72SN6DSTHPM/bundle.json","state_url":"https://pith.science/pith/AAV3SRZPR7U4TFA72SN6DSTHPM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AAV3SRZPR7U4TFA72SN6DSTHPM/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":"2026-05-30T03:53:13Z","links":{"resolver":"https://pith.science/pith/AAV3SRZPR7U4TFA72SN6DSTHPM","bundle":"https://pith.science/pith/AAV3SRZPR7U4TFA72SN6DSTHPM/bundle.json","state":"https://pith.science/pith/AAV3SRZPR7U4TFA72SN6DSTHPM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AAV3SRZPR7U4TFA72SN6DSTHPM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AAV3SRZPR7U4TFA72SN6DSTHPM","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":"dc140ac1be163896b013575aa1612446cbde5e52c08d8e1a37b1fdacbadb1fcd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-06T12:03:40Z","title_canon_sha256":"da4c2db8cbb7d83537e4d5b824d057c063c2ec00d3aa754e04a8f6f80836f8a3"},"schema_version":"1.0","source":{"id":"1706.01721","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.01721","created_at":"2026-05-18T00:23:08Z"},{"alias_kind":"arxiv_version","alias_value":"1706.01721v2","created_at":"2026-05-18T00:23:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.01721","created_at":"2026-05-18T00:23:08Z"},{"alias_kind":"pith_short_12","alias_value":"AAV3SRZPR7U4","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AAV3SRZPR7U4TFA7","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AAV3SRZP","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:6ce427c549e601464914dea5c4a12c81983b7ff46cc3dfc2ecd9473e343a5b2b","target":"graph","created_at":"2026-05-18T00:23:08Z","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 give a simple alternative proof for the $C^{1,1}$--convex extension problem which has been introduced and studied by D. Azagra and C. Mudarra [2]. As an application, we obtain an easy constructive proof for the Glaeser-Whitney problem of $C^{1,1}$ extensions on a Hilbert space. In both cases we provide explicit formulae for the extensions. For the Gleaser-Whitney problem the obtained extension is almost minimal, that is, minimal up to a factor $\\frac{1+\\sqrt{3}}{2}$ in the sense of Le Gruyer [15].","authors_text":"Aris Daniilidis, Erwan Le Gruyer (IRMAR), Mounir Haddou (IRMAR), Olivier Ley (IRMAR)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-06T12:03:40Z","title":"Explicit formulas for $C^{1,1}$ Glaeser-Whitney extensions of 1-fields in Hilbert spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01721","kind":"arxiv","version":2},"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":"sha256:2fab3970b15bb9f8b4fd956147753fac1e0d3aee3a96f9ab59e9c8d6eb16cea4","target":"record","created_at":"2026-05-18T00:23:08Z","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":"dc140ac1be163896b013575aa1612446cbde5e52c08d8e1a37b1fdacbadb1fcd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-06T12:03:40Z","title_canon_sha256":"da4c2db8cbb7d83537e4d5b824d057c063c2ec00d3aa754e04a8f6f80836f8a3"},"schema_version":"1.0","source":{"id":"1706.01721","kind":"arxiv","version":2}},"canonical_sha256":"002bb9472f8fe9c9941fd49be1ca677b0c8b24f3e53908b89cdcea732409d632","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"002bb9472f8fe9c9941fd49be1ca677b0c8b24f3e53908b89cdcea732409d632","first_computed_at":"2026-05-18T00:23:08.833700Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:08.833700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mHu4faeBoMa+rHwvNcAucBkq2bnZ/0E4eJ0A/N8ysvN2LwXSM5qu0YW3gqBA3qGM6rICuBE0BmoLKWOQprrWCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:08.834204Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.01721","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fab3970b15bb9f8b4fd956147753fac1e0d3aee3a96f9ab59e9c8d6eb16cea4","sha256:6ce427c549e601464914dea5c4a12c81983b7ff46cc3dfc2ecd9473e343a5b2b"],"state_sha256":"d24cb668d46001093870297c3913a27848275ad3200c8c28c02b91325092d459"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UoUZXIIzNQdqHasPVBLBIpuIwzH0emfgbY9jk6XCV8amARTySG6rO5GIcCNFQX0n2XzjamqyuAZn7K04xlQICA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T03:53:13.580444Z","bundle_sha256":"0fe4374b5e28e17fa07b8fda1684d63cabdec7752302df8cb387535a5ec8f4c1"}}