{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:BIFGR5TZQH567RNU33R5FHXAYD","short_pith_number":"pith:BIFGR5TZ","canonical_record":{"source":{"id":"1410.0232","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-01T14:12:47Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"f404eb863b56899aaebb29520238dbcbfb44a7b24c3bf5a31d26b6aec23f28ee","abstract_canon_sha256":"faa033e5f1a7fa98c295c5c21ea38a5db9751e865f4f8bacc91ace34689f5f37"},"schema_version":"1.0"},"canonical_sha256":"0a0a68f67981fbefc5b4dee3d29ee0c0d29858bbce1119536dd86a7b21f07e12","source":{"kind":"arxiv","id":"1410.0232","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0232","created_at":"2026-05-18T01:08:27Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0232v4","created_at":"2026-05-18T01:08:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0232","created_at":"2026-05-18T01:08:27Z"},{"alias_kind":"pith_short_12","alias_value":"BIFGR5TZQH56","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BIFGR5TZQH567RNU","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BIFGR5TZ","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:BIFGR5TZQH567RNU33R5FHXAYD","target":"record","payload":{"canonical_record":{"source":{"id":"1410.0232","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-01T14:12:47Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"f404eb863b56899aaebb29520238dbcbfb44a7b24c3bf5a31d26b6aec23f28ee","abstract_canon_sha256":"faa033e5f1a7fa98c295c5c21ea38a5db9751e865f4f8bacc91ace34689f5f37"},"schema_version":"1.0"},"canonical_sha256":"0a0a68f67981fbefc5b4dee3d29ee0c0d29858bbce1119536dd86a7b21f07e12","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:27.487182Z","signature_b64":"Qi49GVG0nd0w94B5WJIFj7+Z8gqHMjGG9dXYo+n/j7JO09ZBMLx5quxhevf75D+4YUwMR52kPyfd+8ZuQ8F4BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a0a68f67981fbefc5b4dee3d29ee0c0d29858bbce1119536dd86a7b21f07e12","last_reissued_at":"2026-05-18T01:08:27.486726Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:27.486726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.0232","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bRTvVNx+a52zCBWPNgQ5DoDVICQrrOy3tyWeWew3hk1z1TamiCBOB7NuNxvxzuc6jxBKnoBJ515sWDjOiNsLCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T02:00:26.286875Z"},"content_sha256":"2f7170ac67925fea3e5fd5442499fe618cec54b1a6fea20fe4f00ef1b46e0e8d","schema_version":"1.0","event_id":"sha256:2f7170ac67925fea3e5fd5442499fe618cec54b1a6fea20fe4f00ef1b46e0e8d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:BIFGR5TZQH567RNU33R5FHXAYD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The One-Sided Isometric Extension Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Micha Wasem, Norbert Hungerb\\\"uhler","submitted_at":"2014-10-01T14:12:47Z","abstract_excerpt":"Let $\\Sigma$ be a codimension one submanifold of an $n$-dimensional Riemannian manifold $M$, $n\\geqslant 2$. We give a necessary condition for an isometric immersion of $\\Sigma$ into $\\mathbb R^q$ equipped with the standard Euclidean metric, $q\\geqslant n+1$, to be locally isometrically $C^1$-extendable to $M$. Even if this condition is not met, \"one-sided\" isometric $C^1$-extensions may exist and turn out to satisfy a $C^0$-dense parametric $h$-principle in the sense of Gromov."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0232","kind":"arxiv","version":4},"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":"2026-05-18T01:08:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2A/Wn2k68OSx/0RYNVGyw08ftoMP9ujlATzqxtxEBUfo2OnOcOLKFYferY0rMMizL7VBhEXouCqEFM19nJdqAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T02:00:26.287612Z"},"content_sha256":"a22010e0b77e7bedc99aa490c3b0ffee6d7d5b7d367797a683d19197788c26eb","schema_version":"1.0","event_id":"sha256:a22010e0b77e7bedc99aa490c3b0ffee6d7d5b7d367797a683d19197788c26eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BIFGR5TZQH567RNU33R5FHXAYD/bundle.json","state_url":"https://pith.science/pith/BIFGR5TZQH567RNU33R5FHXAYD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BIFGR5TZQH567RNU33R5FHXAYD/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":"2026-06-12T02:00:26Z","links":{"resolver":"https://pith.science/pith/BIFGR5TZQH567RNU33R5FHXAYD","bundle":"https://pith.science/pith/BIFGR5TZQH567RNU33R5FHXAYD/bundle.json","state":"https://pith.science/pith/BIFGR5TZQH567RNU33R5FHXAYD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BIFGR5TZQH567RNU33R5FHXAYD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BIFGR5TZQH567RNU33R5FHXAYD","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":"faa033e5f1a7fa98c295c5c21ea38a5db9751e865f4f8bacc91ace34689f5f37","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-01T14:12:47Z","title_canon_sha256":"f404eb863b56899aaebb29520238dbcbfb44a7b24c3bf5a31d26b6aec23f28ee"},"schema_version":"1.0","source":{"id":"1410.0232","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0232","created_at":"2026-05-18T01:08:27Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0232v4","created_at":"2026-05-18T01:08:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0232","created_at":"2026-05-18T01:08:27Z"},{"alias_kind":"pith_short_12","alias_value":"BIFGR5TZQH56","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BIFGR5TZQH567RNU","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BIFGR5TZ","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:a22010e0b77e7bedc99aa490c3b0ffee6d7d5b7d367797a683d19197788c26eb","target":"graph","created_at":"2026-05-18T01:08:27Z","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":"Let $\\Sigma$ be a codimension one submanifold of an $n$-dimensional Riemannian manifold $M$, $n\\geqslant 2$. We give a necessary condition for an isometric immersion of $\\Sigma$ into $\\mathbb R^q$ equipped with the standard Euclidean metric, $q\\geqslant n+1$, to be locally isometrically $C^1$-extendable to $M$. Even if this condition is not met, \"one-sided\" isometric $C^1$-extensions may exist and turn out to satisfy a $C^0$-dense parametric $h$-principle in the sense of Gromov.","authors_text":"Micha Wasem, Norbert Hungerb\\\"uhler","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-01T14:12:47Z","title":"The One-Sided Isometric Extension Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0232","kind":"arxiv","version":4},"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":"sha256:2f7170ac67925fea3e5fd5442499fe618cec54b1a6fea20fe4f00ef1b46e0e8d","target":"record","created_at":"2026-05-18T01:08:27Z","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":"faa033e5f1a7fa98c295c5c21ea38a5db9751e865f4f8bacc91ace34689f5f37","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-01T14:12:47Z","title_canon_sha256":"f404eb863b56899aaebb29520238dbcbfb44a7b24c3bf5a31d26b6aec23f28ee"},"schema_version":"1.0","source":{"id":"1410.0232","kind":"arxiv","version":4}},"canonical_sha256":"0a0a68f67981fbefc5b4dee3d29ee0c0d29858bbce1119536dd86a7b21f07e12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a0a68f67981fbefc5b4dee3d29ee0c0d29858bbce1119536dd86a7b21f07e12","first_computed_at":"2026-05-18T01:08:27.486726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:27.486726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qi49GVG0nd0w94B5WJIFj7+Z8gqHMjGG9dXYo+n/j7JO09ZBMLx5quxhevf75D+4YUwMR52kPyfd+8ZuQ8F4BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:27.487182Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.0232","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f7170ac67925fea3e5fd5442499fe618cec54b1a6fea20fe4f00ef1b46e0e8d","sha256:a22010e0b77e7bedc99aa490c3b0ffee6d7d5b7d367797a683d19197788c26eb"],"state_sha256":"b52c57937c9441ce06be8633cbc2e2ac3189ae05261ed034320f0596165372e6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fGcV5M1s1FFlY6uVoZ9/omhksmUb6I8OyZZcQtPrePxR0WcSO09yE2U4SWvaB8xGBlfqNP0DTyGZ0oyJPFFLCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T02:00:26.290622Z","bundle_sha256":"0f45f16a4bffa5dbfaaf160f627c386aca180688e8f40e3b2e7638230cc59d2e"}}