{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:U54KBQDVTZU7K5ATCCVMCFKZA5","short_pith_number":"pith:U54KBQDV","canonical_record":{"source":{"id":"0706.3595","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2007-06-25T12:42:09Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"7a3792d59e596e360d8a8889e4312a719435388154e125eb682745490fb5f449","abstract_canon_sha256":"2fdbe41a61551c924bae93a577151b84c32f6a704be05da08eedc6f31ecde9e8"},"schema_version":"1.0"},"canonical_sha256":"a778a0c0759e69f5741310aac11559074a9456c61421ca8fe64484e66f580a0b","source":{"kind":"arxiv","id":"0706.3595","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.3595","created_at":"2026-05-17T23:45:42Z"},{"alias_kind":"arxiv_version","alias_value":"0706.3595v1","created_at":"2026-05-17T23:45:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.3595","created_at":"2026-05-17T23:45:42Z"},{"alias_kind":"pith_short_12","alias_value":"U54KBQDVTZU7","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"U54KBQDVTZU7K5AT","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"U54KBQDV","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:U54KBQDVTZU7K5ATCCVMCFKZA5","target":"record","payload":{"canonical_record":{"source":{"id":"0706.3595","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2007-06-25T12:42:09Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"7a3792d59e596e360d8a8889e4312a719435388154e125eb682745490fb5f449","abstract_canon_sha256":"2fdbe41a61551c924bae93a577151b84c32f6a704be05da08eedc6f31ecde9e8"},"schema_version":"1.0"},"canonical_sha256":"a778a0c0759e69f5741310aac11559074a9456c61421ca8fe64484e66f580a0b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:42.052075Z","signature_b64":"4WS2AVUPIr/p6x+I5xff3rhtoFAiao6U3tsZKMIQJZVMNVkna/Z+nNnwyxl/GEjpLfTBNTxLj91R8clyXCV4Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a778a0c0759e69f5741310aac11559074a9456c61421ca8fe64484e66f580a0b","last_reissued_at":"2026-05-17T23:45:42.051344Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:42.051344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0706.3595","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":"2026-05-17T23:45:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xOZdyvTCqGGSgHrpxH+tEeCQT9X904kq0ktab5A8dX8aTGuePs6exySJgewITWp2f1UE0Chu/kLO1vc389iwAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T01:39:22.480163Z"},"content_sha256":"2bcf6972bf992106e86d8cc315c8d5872fb134e9be7cd7f9a3eeff5cc9ddc64c","schema_version":"1.0","event_id":"sha256:2bcf6972bf992106e86d8cc315c8d5872fb134e9be7cd7f9a3eeff5cc9ddc64c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:U54KBQDVTZU7K5ATCCVMCFKZA5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two-dimensional Schroedinger operators with fast decaying potential and multidimensional $L_2$-kernel","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"I. A. Taimanov, S. P. Tsarev","submitted_at":"2007-06-25T12:42:09Z","abstract_excerpt":"Using Moutard transformations we show how explicit examples of two-dimensional Schroedinger operators with fast decaying potential and multidimensional $L_2$-kernel may be constructed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.3595","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":"2026-05-17T23:45:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fGDdCsbwTj8/tfTGl+63GubMENbyDMx0cwcqxpQKwrwa6wO1DpGtdsyeXxZKB/fajMnSuQcjN+di1LN3W6OrDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T01:39:22.480874Z"},"content_sha256":"4253235b2df7daf4f7cb764e7ec77dc6fe4f06e7f6da28b82aba78cbaaac2017","schema_version":"1.0","event_id":"sha256:4253235b2df7daf4f7cb764e7ec77dc6fe4f06e7f6da28b82aba78cbaaac2017"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U54KBQDVTZU7K5ATCCVMCFKZA5/bundle.json","state_url":"https://pith.science/pith/U54KBQDVTZU7K5ATCCVMCFKZA5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U54KBQDVTZU7K5ATCCVMCFKZA5/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":"2026-06-04T01:39:22Z","links":{"resolver":"https://pith.science/pith/U54KBQDVTZU7K5ATCCVMCFKZA5","bundle":"https://pith.science/pith/U54KBQDVTZU7K5ATCCVMCFKZA5/bundle.json","state":"https://pith.science/pith/U54KBQDVTZU7K5ATCCVMCFKZA5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U54KBQDVTZU7K5ATCCVMCFKZA5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:U54KBQDVTZU7K5ATCCVMCFKZA5","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":"2fdbe41a61551c924bae93a577151b84c32f6a704be05da08eedc6f31ecde9e8","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2007-06-25T12:42:09Z","title_canon_sha256":"7a3792d59e596e360d8a8889e4312a719435388154e125eb682745490fb5f449"},"schema_version":"1.0","source":{"id":"0706.3595","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.3595","created_at":"2026-05-17T23:45:42Z"},{"alias_kind":"arxiv_version","alias_value":"0706.3595v1","created_at":"2026-05-17T23:45:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.3595","created_at":"2026-05-17T23:45:42Z"},{"alias_kind":"pith_short_12","alias_value":"U54KBQDVTZU7","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"U54KBQDVTZU7K5AT","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"U54KBQDV","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:4253235b2df7daf4f7cb764e7ec77dc6fe4f06e7f6da28b82aba78cbaaac2017","target":"graph","created_at":"2026-05-17T23:45:42Z","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":"Using Moutard transformations we show how explicit examples of two-dimensional Schroedinger operators with fast decaying potential and multidimensional $L_2$-kernel may be constructed","authors_text":"I. A. Taimanov, S. P. Tsarev","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2007-06-25T12:42:09Z","title":"Two-dimensional Schroedinger operators with fast decaying potential and multidimensional $L_2$-kernel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.3595","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":"sha256:2bcf6972bf992106e86d8cc315c8d5872fb134e9be7cd7f9a3eeff5cc9ddc64c","target":"record","created_at":"2026-05-17T23:45:42Z","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":"2fdbe41a61551c924bae93a577151b84c32f6a704be05da08eedc6f31ecde9e8","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2007-06-25T12:42:09Z","title_canon_sha256":"7a3792d59e596e360d8a8889e4312a719435388154e125eb682745490fb5f449"},"schema_version":"1.0","source":{"id":"0706.3595","kind":"arxiv","version":1}},"canonical_sha256":"a778a0c0759e69f5741310aac11559074a9456c61421ca8fe64484e66f580a0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a778a0c0759e69f5741310aac11559074a9456c61421ca8fe64484e66f580a0b","first_computed_at":"2026-05-17T23:45:42.051344Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:42.051344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4WS2AVUPIr/p6x+I5xff3rhtoFAiao6U3tsZKMIQJZVMNVkna/Z+nNnwyxl/GEjpLfTBNTxLj91R8clyXCV4Cw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:42.052075Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.3595","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2bcf6972bf992106e86d8cc315c8d5872fb134e9be7cd7f9a3eeff5cc9ddc64c","sha256:4253235b2df7daf4f7cb764e7ec77dc6fe4f06e7f6da28b82aba78cbaaac2017"],"state_sha256":"32081f765d5e481c543dd5578e84e9291072c96165cf852dd7b58fdad8647900"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aNLese7lotcu6PTuRMlSA2rdrLC1rN7b6SSg443bCxLdqIAKyTECSz5cztq/sKYZa/0tSmcfWQ07BTWQnxh6BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T01:39:22.484394Z","bundle_sha256":"0ba9c844ff789b2a3e7718380095b1ff4f25d59770133dc30ae068226757a7c3"}}