{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VUC43R7WFTLOIY5LCOGD2XRJ35","short_pith_number":"pith:VUC43R7W","canonical_record":{"source":{"id":"1703.10797","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-31T08:41:31Z","cross_cats_sorted":["math.OC","math.SP"],"title_canon_sha256":"f4efe9c5f495688ba582402b191a896a0a0f0e8aae6f4ce90cd9720361554ca2","abstract_canon_sha256":"29371e840d9c1e7311c1065eeeba6c53f9326c1b5b5cca894d90f28d915d3d75"},"schema_version":"1.0"},"canonical_sha256":"ad05cdc7f62cd6e463ab138c3d5e29df6e94f452bedbfb8dde463024cccc1772","source":{"kind":"arxiv","id":"1703.10797","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10797","created_at":"2026-05-18T00:47:32Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10797v1","created_at":"2026-05-18T00:47:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10797","created_at":"2026-05-18T00:47:32Z"},{"alias_kind":"pith_short_12","alias_value":"VUC43R7WFTLO","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VUC43R7WFTLOIY5L","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VUC43R7W","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VUC43R7WFTLOIY5LCOGD2XRJ35","target":"record","payload":{"canonical_record":{"source":{"id":"1703.10797","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-31T08:41:31Z","cross_cats_sorted":["math.OC","math.SP"],"title_canon_sha256":"f4efe9c5f495688ba582402b191a896a0a0f0e8aae6f4ce90cd9720361554ca2","abstract_canon_sha256":"29371e840d9c1e7311c1065eeeba6c53f9326c1b5b5cca894d90f28d915d3d75"},"schema_version":"1.0"},"canonical_sha256":"ad05cdc7f62cd6e463ab138c3d5e29df6e94f452bedbfb8dde463024cccc1772","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:32.696428Z","signature_b64":"RO25Uklg231NDB5CRuoth5qs5N/Ii/5h8wnuE9IGW6om/qbIljspKm317eIbYg2NuMBi+MMy2A7t9YjS7qFrDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad05cdc7f62cd6e463ab138c3d5e29df6e94f452bedbfb8dde463024cccc1772","last_reissued_at":"2026-05-18T00:47:32.695841Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:32.695841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.10797","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":"2026-05-18T00:47:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bjswF6Ai74Ei/TPlzE6/hlww/gQ4IBVYk3zlvj66otZJk0ftL7za5wdl9Gm48Q00Qk31I9oTxhqSCJrdgzTvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T00:27:36.587419Z"},"content_sha256":"db29c9702b4b5d40a70ce09a2d86f2d85beaa0bf02eda3c9ee3f0a4f46d78fca","schema_version":"1.0","event_id":"sha256:db29c9702b4b5d40a70ce09a2d86f2d85beaa0bf02eda3c9ee3f0a4f46d78fca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VUC43R7WFTLOIY5LCOGD2XRJ35","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tunneling estimates and approximate controllability for hypoelliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","math.SP"],"primary_cat":"math.AP","authors_text":"Camille Laurent, Matthieu L\\'eautaud","submitted_at":"2017-03-31T08:41:31Z","abstract_excerpt":"This article is concerned with quantitative unique continuation estimates for equations involving a \"sum of squares\" operator $\\mathcal{L}$ on a compact manifold $\\mathcal{M}$ assuming: $(i)$ the Chow-Rashevski-H\\\"ormander condition ensuring the hypoellipticity of $\\mathcal{L}$, and $(ii)$ the analyticity of $\\mathcal{M}$ and the coefficients of $\\mathcal{L}$.\n  The first result is the tunneling estimate $\\|\\varphi\\|_{L^2(\\omega)} \\geq Ce^{- \\lambda^{\\frac{k}{2}}}$ for normalized eigenfunctions $\\varphi$ of $\\mathcal{L}$ from a nonempty open set $\\omega\\subset \\mathcal{M}$, where $k$ is the hy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10797","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":"2026-05-18T00:47:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z0k2sTDKT89OuWOgexLJh/QkOy/Xhl0shW4/JQ9KW3DLXB//xONk65e78NT7B/oOLAGs8zpq+d3R1XSBg1DvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T00:27:36.587770Z"},"content_sha256":"0113aa5bda65bbb07f30b4421884406636bf3773eed9c94246b4c7afff689184","schema_version":"1.0","event_id":"sha256:0113aa5bda65bbb07f30b4421884406636bf3773eed9c94246b4c7afff689184"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VUC43R7WFTLOIY5LCOGD2XRJ35/bundle.json","state_url":"https://pith.science/pith/VUC43R7WFTLOIY5LCOGD2XRJ35/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VUC43R7WFTLOIY5LCOGD2XRJ35/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":"2026-06-27T00:27:36Z","links":{"resolver":"https://pith.science/pith/VUC43R7WFTLOIY5LCOGD2XRJ35","bundle":"https://pith.science/pith/VUC43R7WFTLOIY5LCOGD2XRJ35/bundle.json","state":"https://pith.science/pith/VUC43R7WFTLOIY5LCOGD2XRJ35/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VUC43R7WFTLOIY5LCOGD2XRJ35/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VUC43R7WFTLOIY5LCOGD2XRJ35","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":"29371e840d9c1e7311c1065eeeba6c53f9326c1b5b5cca894d90f28d915d3d75","cross_cats_sorted":["math.OC","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-31T08:41:31Z","title_canon_sha256":"f4efe9c5f495688ba582402b191a896a0a0f0e8aae6f4ce90cd9720361554ca2"},"schema_version":"1.0","source":{"id":"1703.10797","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10797","created_at":"2026-05-18T00:47:32Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10797v1","created_at":"2026-05-18T00:47:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10797","created_at":"2026-05-18T00:47:32Z"},{"alias_kind":"pith_short_12","alias_value":"VUC43R7WFTLO","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VUC43R7WFTLOIY5L","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VUC43R7W","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:0113aa5bda65bbb07f30b4421884406636bf3773eed9c94246b4c7afff689184","target":"graph","created_at":"2026-05-18T00:47:32Z","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":"This article is concerned with quantitative unique continuation estimates for equations involving a \"sum of squares\" operator $\\mathcal{L}$ on a compact manifold $\\mathcal{M}$ assuming: $(i)$ the Chow-Rashevski-H\\\"ormander condition ensuring the hypoellipticity of $\\mathcal{L}$, and $(ii)$ the analyticity of $\\mathcal{M}$ and the coefficients of $\\mathcal{L}$.\n  The first result is the tunneling estimate $\\|\\varphi\\|_{L^2(\\omega)} \\geq Ce^{- \\lambda^{\\frac{k}{2}}}$ for normalized eigenfunctions $\\varphi$ of $\\mathcal{L}$ from a nonempty open set $\\omega\\subset \\mathcal{M}$, where $k$ is the hy","authors_text":"Camille Laurent, Matthieu L\\'eautaud","cross_cats":["math.OC","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-31T08:41:31Z","title":"Tunneling estimates and approximate controllability for hypoelliptic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10797","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:db29c9702b4b5d40a70ce09a2d86f2d85beaa0bf02eda3c9ee3f0a4f46d78fca","target":"record","created_at":"2026-05-18T00:47:32Z","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":"29371e840d9c1e7311c1065eeeba6c53f9326c1b5b5cca894d90f28d915d3d75","cross_cats_sorted":["math.OC","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-31T08:41:31Z","title_canon_sha256":"f4efe9c5f495688ba582402b191a896a0a0f0e8aae6f4ce90cd9720361554ca2"},"schema_version":"1.0","source":{"id":"1703.10797","kind":"arxiv","version":1}},"canonical_sha256":"ad05cdc7f62cd6e463ab138c3d5e29df6e94f452bedbfb8dde463024cccc1772","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad05cdc7f62cd6e463ab138c3d5e29df6e94f452bedbfb8dde463024cccc1772","first_computed_at":"2026-05-18T00:47:32.695841Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:32.695841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RO25Uklg231NDB5CRuoth5qs5N/Ii/5h8wnuE9IGW6om/qbIljspKm317eIbYg2NuMBi+MMy2A7t9YjS7qFrDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:32.696428Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.10797","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db29c9702b4b5d40a70ce09a2d86f2d85beaa0bf02eda3c9ee3f0a4f46d78fca","sha256:0113aa5bda65bbb07f30b4421884406636bf3773eed9c94246b4c7afff689184"],"state_sha256":"55d3182e25b8c80627c5538010399d4649c92ce4b053265648c8810b43334d1d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VvIu2tzPkhRXWOzWLtZSXszuUw8Dez0Yfn91CETYhJzxQbar5xgBAY5Kgk+0IFQ6FA+EbdIjBD+MJc3FBCbSBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T00:27:36.589741Z","bundle_sha256":"7f7aca782d35632a728c6252df69ecb7490e0cfd5da65633988e608a0cfc10e3"}}