{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:UFZCM57NCXR6OPWFPH4GLEZEYH","short_pith_number":"pith:UFZCM57N","canonical_record":{"source":{"id":"1403.1522","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-06T18:29:05Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0006571a9280c2086f7355a2896cb3489e351486949c834a996ad4c98c05f481","abstract_canon_sha256":"af2392b3150991b228775360c4bf50d77fc8c561e63989a48611e14e19488104"},"schema_version":"1.0"},"canonical_sha256":"a1722677ed15e3e73ec579f8659324c1ce40d53625407c653dc224e6fc33a268","source":{"kind":"arxiv","id":"1403.1522","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.1522","created_at":"2026-05-18T02:48:33Z"},{"alias_kind":"arxiv_version","alias_value":"1403.1522v3","created_at":"2026-05-18T02:48:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1522","created_at":"2026-05-18T02:48:33Z"},{"alias_kind":"pith_short_12","alias_value":"UFZCM57NCXR6","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UFZCM57NCXR6OPWF","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UFZCM57N","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:UFZCM57NCXR6OPWFPH4GLEZEYH","target":"record","payload":{"canonical_record":{"source":{"id":"1403.1522","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-06T18:29:05Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0006571a9280c2086f7355a2896cb3489e351486949c834a996ad4c98c05f481","abstract_canon_sha256":"af2392b3150991b228775360c4bf50d77fc8c561e63989a48611e14e19488104"},"schema_version":"1.0"},"canonical_sha256":"a1722677ed15e3e73ec579f8659324c1ce40d53625407c653dc224e6fc33a268","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:33.984740Z","signature_b64":"7Q96O9h++Qpd+CuuGxO/z0Yhbij07zqnqcuZf9OL5Qx1HFNsjILxQJIki5Wjbnp1xG6gIqG+MczC8/RiiEXuBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1722677ed15e3e73ec579f8659324c1ce40d53625407c653dc224e6fc33a268","last_reissued_at":"2026-05-18T02:48:33.984050Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:33.984050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.1522","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:48:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jPeUJ8Khjm+JuQLiEKXfNmUPjGnVRIgF0MCnko8F3Pa0vH4drvZRiQ8TP7G4GxxKRsse3Ge0YXHWwieNJVtRDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T07:58:34.883568Z"},"content_sha256":"8441b0e07a6bea5a837379bd6749899db4683471cc15ee8c01db9ea3b1596343","schema_version":"1.0","event_id":"sha256:8441b0e07a6bea5a837379bd6749899db4683471cc15ee8c01db9ea3b1596343"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:UFZCM57NCXR6OPWFPH4GLEZEYH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sets of unique continuation for heat equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Nadezda Varkentina, Nikolai Nadirashvili","submitted_at":"2014-03-06T18:29:05Z","abstract_excerpt":"We study nodal lines of solutions to the heat equations. We are interested in the global geometry of nodal sets, in the whole domain of definition of the solution. The local structure of nodal sets is a well understander subject, while the global geometry of nodal lines is much less clear. We give a detailed analysis of a simple component of a nodal set of a solution of the heat equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1522","kind":"arxiv","version":3},"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":"2026-05-18T02:48:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wa0TJHCYqFcGAXypmLYYiin9QGRowAbONeQTpUeTCEmdLH7+c7VqPxsxCkl7EOVhStoIofLmYyTq08a52w7oDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T07:58:34.883913Z"},"content_sha256":"02bcc2fb5f706f0d83097aaa88b729fe22f763a40e69ea921dfbcd7e39e4d07d","schema_version":"1.0","event_id":"sha256:02bcc2fb5f706f0d83097aaa88b729fe22f763a40e69ea921dfbcd7e39e4d07d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UFZCM57NCXR6OPWFPH4GLEZEYH/bundle.json","state_url":"https://pith.science/pith/UFZCM57NCXR6OPWFPH4GLEZEYH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UFZCM57NCXR6OPWFPH4GLEZEYH/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":"2026-06-12T07:58:34Z","links":{"resolver":"https://pith.science/pith/UFZCM57NCXR6OPWFPH4GLEZEYH","bundle":"https://pith.science/pith/UFZCM57NCXR6OPWFPH4GLEZEYH/bundle.json","state":"https://pith.science/pith/UFZCM57NCXR6OPWFPH4GLEZEYH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UFZCM57NCXR6OPWFPH4GLEZEYH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UFZCM57NCXR6OPWFPH4GLEZEYH","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":"af2392b3150991b228775360c4bf50d77fc8c561e63989a48611e14e19488104","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-06T18:29:05Z","title_canon_sha256":"0006571a9280c2086f7355a2896cb3489e351486949c834a996ad4c98c05f481"},"schema_version":"1.0","source":{"id":"1403.1522","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.1522","created_at":"2026-05-18T02:48:33Z"},{"alias_kind":"arxiv_version","alias_value":"1403.1522v3","created_at":"2026-05-18T02:48:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1522","created_at":"2026-05-18T02:48:33Z"},{"alias_kind":"pith_short_12","alias_value":"UFZCM57NCXR6","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UFZCM57NCXR6OPWF","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UFZCM57N","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:02bcc2fb5f706f0d83097aaa88b729fe22f763a40e69ea921dfbcd7e39e4d07d","target":"graph","created_at":"2026-05-18T02:48:33Z","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 study nodal lines of solutions to the heat equations. We are interested in the global geometry of nodal sets, in the whole domain of definition of the solution. The local structure of nodal sets is a well understander subject, while the global geometry of nodal lines is much less clear. We give a detailed analysis of a simple component of a nodal set of a solution of the heat equation.","authors_text":"Nadezda Varkentina, Nikolai Nadirashvili","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-06T18:29:05Z","title":"Sets of unique continuation for heat equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1522","kind":"arxiv","version":3},"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":"sha256:8441b0e07a6bea5a837379bd6749899db4683471cc15ee8c01db9ea3b1596343","target":"record","created_at":"2026-05-18T02:48:33Z","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":"af2392b3150991b228775360c4bf50d77fc8c561e63989a48611e14e19488104","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-06T18:29:05Z","title_canon_sha256":"0006571a9280c2086f7355a2896cb3489e351486949c834a996ad4c98c05f481"},"schema_version":"1.0","source":{"id":"1403.1522","kind":"arxiv","version":3}},"canonical_sha256":"a1722677ed15e3e73ec579f8659324c1ce40d53625407c653dc224e6fc33a268","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1722677ed15e3e73ec579f8659324c1ce40d53625407c653dc224e6fc33a268","first_computed_at":"2026-05-18T02:48:33.984050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:33.984050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Q96O9h++Qpd+CuuGxO/z0Yhbij07zqnqcuZf9OL5Qx1HFNsjILxQJIki5Wjbnp1xG6gIqG+MczC8/RiiEXuBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:33.984740Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.1522","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8441b0e07a6bea5a837379bd6749899db4683471cc15ee8c01db9ea3b1596343","sha256:02bcc2fb5f706f0d83097aaa88b729fe22f763a40e69ea921dfbcd7e39e4d07d"],"state_sha256":"16681f8dfd085d3378693a7ba66f1f1f6d173780dce9c40dc6a0fa84e8c5af76"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"seoIulgU1hY8dpnqlmKPQ4t2ismBJxdb3htG2MFHX/iMWzrw0PLXG7tsoKYhwgvKcWHzCmIjfRc4BJq7uQH8AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T07:58:34.885902Z","bundle_sha256":"83f5f0a8e476430938a94bf8252caf895bbafc7b7dce4dc926c0c687badf49d7"}}