{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:FHQL26TIBWFRRIRHBXLLZMCOFX","short_pith_number":"pith:FHQL26TI","canonical_record":{"source":{"id":"2306.11257","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-06-20T03:21:50Z","cross_cats_sorted":["math.DS","math.MP"],"title_canon_sha256":"2a34d0f54bd81b3ff9971f1facdf98f13af6044a1d63595b2d6d803ce3c245be","abstract_canon_sha256":"af2c29359504a301639e8e9f2497a54fef3b46851db1d455606f53ddcaa731d6"},"schema_version":"1.0"},"canonical_sha256":"29e0bd7a680d8b18a2270dd6bcb04e2dc2b2bdb4bc93beea47f85cf3b4ba9809","source":{"kind":"arxiv","id":"2306.11257","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.11257","created_at":"2026-07-05T06:47:23Z"},{"alias_kind":"arxiv_version","alias_value":"2306.11257v2","created_at":"2026-07-05T06:47:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.11257","created_at":"2026-07-05T06:47:23Z"},{"alias_kind":"pith_short_12","alias_value":"FHQL26TIBWFR","created_at":"2026-07-05T06:47:23Z"},{"alias_kind":"pith_short_16","alias_value":"FHQL26TIBWFRRIRH","created_at":"2026-07-05T06:47:23Z"},{"alias_kind":"pith_short_8","alias_value":"FHQL26TI","created_at":"2026-07-05T06:47:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:FHQL26TIBWFRRIRHBXLLZMCOFX","target":"record","payload":{"canonical_record":{"source":{"id":"2306.11257","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-06-20T03:21:50Z","cross_cats_sorted":["math.DS","math.MP"],"title_canon_sha256":"2a34d0f54bd81b3ff9971f1facdf98f13af6044a1d63595b2d6d803ce3c245be","abstract_canon_sha256":"af2c29359504a301639e8e9f2497a54fef3b46851db1d455606f53ddcaa731d6"},"schema_version":"1.0"},"canonical_sha256":"29e0bd7a680d8b18a2270dd6bcb04e2dc2b2bdb4bc93beea47f85cf3b4ba9809","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:47:23.277375Z","signature_b64":"rVxNiVFLuTvuiS4u+nf8lnsImUsp9KT8kdenLssgOpD3tWgW68Kt+JGceb6jrkrWFCoOf3yFxYKGJ/ZskK4tCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29e0bd7a680d8b18a2270dd6bcb04e2dc2b2bdb4bc93beea47f85cf3b4ba9809","last_reissued_at":"2026-07-05T06:47:23.276808Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:47:23.276808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2306.11257","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:47:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KvPjqAb6f2s7YlL+G0HXTxZrYp/SrKS2dywcTy5ugJvXgyX8OyTR43AXo9KW1jJ7fgQU84TsNv4+N0FCd0ICAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T13:38:15.999028Z"},"content_sha256":"80d360b54f1e58c2b53000d7f6702c5edb8aa1c0a3f2e3af2420271e7b31114a","schema_version":"1.0","event_id":"sha256:80d360b54f1e58c2b53000d7f6702c5edb8aa1c0a3f2e3af2420271e7b31114a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:FHQL26TIBWFRRIRHBXLLZMCOFX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometry of quasiperiodic functions on the plane","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS","math.MP"],"primary_cat":"math-ph","authors_text":"A.Ya. Maltsev, I.A. Dynnikov, S.P. Novikov","submitted_at":"2023-06-20T03:21:50Z","abstract_excerpt":"The present article proposes a review of the most recent results obtained in the study of Novikov's problem on the description of the geometry of the level lines of quasi-periodic functions in the plane. Most of the paper is devoted to the results obtained for functions with three quasi-periods, which play a very important role in the theory of transport phenomena in metals. In this part, along with previously known results, a number of new results are presented that significantly refine the general description of the picture that arises in this case. New statements are also presented for the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.11257","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.11257/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:47:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EqyVV8gF7RMXNVqLoGhyeSKvrjWm4x+wPBIMJWMd7quqx5foa7pHGDnuJGOMnYCppDnG15gjvJCZgvmtTzTyBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T13:38:15.999403Z"},"content_sha256":"e92247cb98447d75c0cb189c04a192459c1b76934edeedefc227f491d251966c","schema_version":"1.0","event_id":"sha256:e92247cb98447d75c0cb189c04a192459c1b76934edeedefc227f491d251966c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FHQL26TIBWFRRIRHBXLLZMCOFX/bundle.json","state_url":"https://pith.science/pith/FHQL26TIBWFRRIRHBXLLZMCOFX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FHQL26TIBWFRRIRHBXLLZMCOFX/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":"2026-08-19T13:38:16Z","links":{"resolver":"https://pith.science/pith/FHQL26TIBWFRRIRHBXLLZMCOFX","bundle":"https://pith.science/pith/FHQL26TIBWFRRIRHBXLLZMCOFX/bundle.json","state":"https://pith.science/pith/FHQL26TIBWFRRIRHBXLLZMCOFX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FHQL26TIBWFRRIRHBXLLZMCOFX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:FHQL26TIBWFRRIRHBXLLZMCOFX","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":"af2c29359504a301639e8e9f2497a54fef3b46851db1d455606f53ddcaa731d6","cross_cats_sorted":["math.DS","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-06-20T03:21:50Z","title_canon_sha256":"2a34d0f54bd81b3ff9971f1facdf98f13af6044a1d63595b2d6d803ce3c245be"},"schema_version":"1.0","source":{"id":"2306.11257","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.11257","created_at":"2026-07-05T06:47:23Z"},{"alias_kind":"arxiv_version","alias_value":"2306.11257v2","created_at":"2026-07-05T06:47:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.11257","created_at":"2026-07-05T06:47:23Z"},{"alias_kind":"pith_short_12","alias_value":"FHQL26TIBWFR","created_at":"2026-07-05T06:47:23Z"},{"alias_kind":"pith_short_16","alias_value":"FHQL26TIBWFRRIRH","created_at":"2026-07-05T06:47:23Z"},{"alias_kind":"pith_short_8","alias_value":"FHQL26TI","created_at":"2026-07-05T06:47:23Z"}],"graph_snapshots":[{"event_id":"sha256:e92247cb98447d75c0cb189c04a192459c1b76934edeedefc227f491d251966c","target":"graph","created_at":"2026-07-05T06:47:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2306.11257/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The present article proposes a review of the most recent results obtained in the study of Novikov's problem on the description of the geometry of the level lines of quasi-periodic functions in the plane. Most of the paper is devoted to the results obtained for functions with three quasi-periods, which play a very important role in the theory of transport phenomena in metals. In this part, along with previously known results, a number of new results are presented that significantly refine the general description of the picture that arises in this case. New statements are also presented for the ","authors_text":"A.Ya. Maltsev, I.A. Dynnikov, S.P. Novikov","cross_cats":["math.DS","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-06-20T03:21:50Z","title":"Geometry of quasiperiodic functions on the plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.11257","kind":"arxiv","version":2},"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":"sha256:80d360b54f1e58c2b53000d7f6702c5edb8aa1c0a3f2e3af2420271e7b31114a","target":"record","created_at":"2026-07-05T06:47:23Z","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":"af2c29359504a301639e8e9f2497a54fef3b46851db1d455606f53ddcaa731d6","cross_cats_sorted":["math.DS","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-06-20T03:21:50Z","title_canon_sha256":"2a34d0f54bd81b3ff9971f1facdf98f13af6044a1d63595b2d6d803ce3c245be"},"schema_version":"1.0","source":{"id":"2306.11257","kind":"arxiv","version":2}},"canonical_sha256":"29e0bd7a680d8b18a2270dd6bcb04e2dc2b2bdb4bc93beea47f85cf3b4ba9809","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29e0bd7a680d8b18a2270dd6bcb04e2dc2b2bdb4bc93beea47f85cf3b4ba9809","first_computed_at":"2026-07-05T06:47:23.276808Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:47:23.276808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rVxNiVFLuTvuiS4u+nf8lnsImUsp9KT8kdenLssgOpD3tWgW68Kt+JGceb6jrkrWFCoOf3yFxYKGJ/ZskK4tCg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:47:23.277375Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.11257","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80d360b54f1e58c2b53000d7f6702c5edb8aa1c0a3f2e3af2420271e7b31114a","sha256:e92247cb98447d75c0cb189c04a192459c1b76934edeedefc227f491d251966c"],"state_sha256":"6396b14dbe05143ce14da18a20802693e2723ebfa0a4b242419adfd6a0672dd1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3NYQfehO5a7pF8eO6+mgXOrSFXVz7MjtPT66vlXxKZeyuZw6YbZrs8hrROmLabPiH29EBbHncs/7MT9IXdFBCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T13:38:16.001938Z","bundle_sha256":"6e7a0f155e48b44f3c559744656fb9a939cb23c536da7a2133e2189a12ed92a5"}}