{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YRGXUEKUKDS7W53JKGE6U3T4BM","short_pith_number":"pith:YRGXUEKU","canonical_record":{"source":{"id":"1501.01449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-07T11:25:36Z","cross_cats_sorted":[],"title_canon_sha256":"54d650f1855df0846561747ca21d8dcd31a9e36cb704171fe471911f6c63737b","abstract_canon_sha256":"d1230d4e12b48bec932ec6e4cf67d529a876fd0b9ef768ccf23cc42d37b9d743"},"schema_version":"1.0"},"canonical_sha256":"c44d7a115450e5fb77695189ea6e7c0b3091849d0fd31b5eff1ab244953f70c6","source":{"kind":"arxiv","id":"1501.01449","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01449","created_at":"2026-05-17T23:49:28Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01449v1","created_at":"2026-05-17T23:49:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01449","created_at":"2026-05-17T23:49:28Z"},{"alias_kind":"pith_short_12","alias_value":"YRGXUEKUKDS7","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YRGXUEKUKDS7W53J","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YRGXUEKU","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YRGXUEKUKDS7W53JKGE6U3T4BM","target":"record","payload":{"canonical_record":{"source":{"id":"1501.01449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-07T11:25:36Z","cross_cats_sorted":[],"title_canon_sha256":"54d650f1855df0846561747ca21d8dcd31a9e36cb704171fe471911f6c63737b","abstract_canon_sha256":"d1230d4e12b48bec932ec6e4cf67d529a876fd0b9ef768ccf23cc42d37b9d743"},"schema_version":"1.0"},"canonical_sha256":"c44d7a115450e5fb77695189ea6e7c0b3091849d0fd31b5eff1ab244953f70c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:28.824391Z","signature_b64":"LfvHN6sWTsaxU7KloM3ip1Gha7LwFcEL2jO9GcOg0nG1Tv2GMupVDsAmhIfgbyOwtmXWyKrib+LNjepoWG4MDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c44d7a115450e5fb77695189ea6e7c0b3091849d0fd31b5eff1ab244953f70c6","last_reissued_at":"2026-05-17T23:49:28.823704Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:28.823704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.01449","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":"2026-05-17T23:49:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jga4RHkCrLL9Y48yWEVlhtERwfrAIDvEo2OIkJQmKGE3MDqFss0MXW7Arw6aF6StjrmNh8VGnRZOldioQyc0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:46:54.825868Z"},"content_sha256":"e3e281be965a38457f4165217519895086ce5aa46f291e1785029f8d771403bc","schema_version":"1.0","event_id":"sha256:e3e281be965a38457f4165217519895086ce5aa46f291e1785029f8d771403bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YRGXUEKUKDS7W53JKGE6U3T4BM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On local non-zero constraints in PDE with analytic coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giovanni S. Alberti, Yves Capdeboscq","submitted_at":"2015-01-07T11:25:36Z","abstract_excerpt":"We consider the Helmholtz equation with real analytic coefficients on a bounded domain $\\Omega\\subset\\mathbb{R}^{d}$. We take $d+1$ prescribed boundary conditions $f^{i}$ and frequencies $\\omega$ in a fixed interval $[a,b]$. We consider a constraint on the solutions $u_{\\omega}^{i}$ of the form $\\zeta(u_{\\omega}^{1},\\ldots,u_{\\omega}^{d+1},\\nabla u_{\\omega}^{1},\\ldots,\\nabla u_{\\omega}^{d+1})\\neq0$, where $\\zeta$ is analytic, which is satisfied in $\\Omega$ when $\\omega=0$. We show that for any $\\Omega^{\\prime}\\Subset\\Omega$ and almost any $d+1$ frequencies $\\omega_{k}$ in $[a,b]$, there exist "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01449","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":"2026-05-17T23:49:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5s2S94ny2WzyVML92qr+INjW7wKXsd0c2UXpJUFAGghf7YTpheWMsjOUzcdkT1u6D+mD07u4+cJ83SgoavOdBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:46:54.826525Z"},"content_sha256":"8d45eefb21dc6640a8ebc3362ba612fed00791d2b6842087f0b7d5cd48d30b18","schema_version":"1.0","event_id":"sha256:8d45eefb21dc6640a8ebc3362ba612fed00791d2b6842087f0b7d5cd48d30b18"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YRGXUEKUKDS7W53JKGE6U3T4BM/bundle.json","state_url":"https://pith.science/pith/YRGXUEKUKDS7W53JKGE6U3T4BM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YRGXUEKUKDS7W53JKGE6U3T4BM/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":"2026-05-27T14:46:54Z","links":{"resolver":"https://pith.science/pith/YRGXUEKUKDS7W53JKGE6U3T4BM","bundle":"https://pith.science/pith/YRGXUEKUKDS7W53JKGE6U3T4BM/bundle.json","state":"https://pith.science/pith/YRGXUEKUKDS7W53JKGE6U3T4BM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YRGXUEKUKDS7W53JKGE6U3T4BM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YRGXUEKUKDS7W53JKGE6U3T4BM","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":"d1230d4e12b48bec932ec6e4cf67d529a876fd0b9ef768ccf23cc42d37b9d743","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-07T11:25:36Z","title_canon_sha256":"54d650f1855df0846561747ca21d8dcd31a9e36cb704171fe471911f6c63737b"},"schema_version":"1.0","source":{"id":"1501.01449","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01449","created_at":"2026-05-17T23:49:28Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01449v1","created_at":"2026-05-17T23:49:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01449","created_at":"2026-05-17T23:49:28Z"},{"alias_kind":"pith_short_12","alias_value":"YRGXUEKUKDS7","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YRGXUEKUKDS7W53J","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YRGXUEKU","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:8d45eefb21dc6640a8ebc3362ba612fed00791d2b6842087f0b7d5cd48d30b18","target":"graph","created_at":"2026-05-17T23:49:28Z","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 consider the Helmholtz equation with real analytic coefficients on a bounded domain $\\Omega\\subset\\mathbb{R}^{d}$. We take $d+1$ prescribed boundary conditions $f^{i}$ and frequencies $\\omega$ in a fixed interval $[a,b]$. We consider a constraint on the solutions $u_{\\omega}^{i}$ of the form $\\zeta(u_{\\omega}^{1},\\ldots,u_{\\omega}^{d+1},\\nabla u_{\\omega}^{1},\\ldots,\\nabla u_{\\omega}^{d+1})\\neq0$, where $\\zeta$ is analytic, which is satisfied in $\\Omega$ when $\\omega=0$. We show that for any $\\Omega^{\\prime}\\Subset\\Omega$ and almost any $d+1$ frequencies $\\omega_{k}$ in $[a,b]$, there exist ","authors_text":"Giovanni S. Alberti, Yves Capdeboscq","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-07T11:25:36Z","title":"On local non-zero constraints in PDE with analytic coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01449","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:e3e281be965a38457f4165217519895086ce5aa46f291e1785029f8d771403bc","target":"record","created_at":"2026-05-17T23:49:28Z","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":"d1230d4e12b48bec932ec6e4cf67d529a876fd0b9ef768ccf23cc42d37b9d743","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-07T11:25:36Z","title_canon_sha256":"54d650f1855df0846561747ca21d8dcd31a9e36cb704171fe471911f6c63737b"},"schema_version":"1.0","source":{"id":"1501.01449","kind":"arxiv","version":1}},"canonical_sha256":"c44d7a115450e5fb77695189ea6e7c0b3091849d0fd31b5eff1ab244953f70c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c44d7a115450e5fb77695189ea6e7c0b3091849d0fd31b5eff1ab244953f70c6","first_computed_at":"2026-05-17T23:49:28.823704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:28.823704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LfvHN6sWTsaxU7KloM3ip1Gha7LwFcEL2jO9GcOg0nG1Tv2GMupVDsAmhIfgbyOwtmXWyKrib+LNjepoWG4MDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:28.824391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.01449","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3e281be965a38457f4165217519895086ce5aa46f291e1785029f8d771403bc","sha256:8d45eefb21dc6640a8ebc3362ba612fed00791d2b6842087f0b7d5cd48d30b18"],"state_sha256":"4c22c10d8d3e4c047f4b105736300d533a527dfb5d9aeb1cf6995c3d91af0830"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e6iZf+eaRfmG0ht3+48D3NgkelAjRS+LTT4TNm2/A/4dbMr0DMUGzoVZtMYOfI3Jdx2+oDIhrCsnOQOiJ/83Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:46:54.830066Z","bundle_sha256":"df24572f2c43afac7cc80499f203510e14dfb9d46c0fd40b582aed2ff4d30f1c"}}