{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:HIPWGV2IDWBIBE4K37GGG2FFME","short_pith_number":"pith:HIPWGV2I","canonical_record":{"source":{"id":"1703.07245","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-21T14:40:21Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"688fcf19de9f087df1eaeecf8559587eb8e405bed9b7886796d6a12f478b15ea","abstract_canon_sha256":"839c3fb1e894450e38f9c24896dda62033766af769b8288f074dc136e3a3a747"},"schema_version":"1.0"},"canonical_sha256":"3a1f6357481d8280938adfcc6368a5610b0a10d78d615c540e0cbcd3bb7830d1","source":{"kind":"arxiv","id":"1703.07245","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07245","created_at":"2026-05-17T23:59:33Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07245v3","created_at":"2026-05-17T23:59:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07245","created_at":"2026-05-17T23:59:33Z"},{"alias_kind":"pith_short_12","alias_value":"HIPWGV2IDWBI","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HIPWGV2IDWBIBE4K","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HIPWGV2I","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:HIPWGV2IDWBIBE4K37GGG2FFME","target":"record","payload":{"canonical_record":{"source":{"id":"1703.07245","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-21T14:40:21Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"688fcf19de9f087df1eaeecf8559587eb8e405bed9b7886796d6a12f478b15ea","abstract_canon_sha256":"839c3fb1e894450e38f9c24896dda62033766af769b8288f074dc136e3a3a747"},"schema_version":"1.0"},"canonical_sha256":"3a1f6357481d8280938adfcc6368a5610b0a10d78d615c540e0cbcd3bb7830d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:33.367461Z","signature_b64":"m9DJxBLeTjua6Cp4EaZYnyWIJ8xW1tO/ZqmAyP/Ruwvf1ayYoRk8NQLOSBxAoCvj3lLXqpepacyUEnI/+Nj3BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a1f6357481d8280938adfcc6368a5610b0a10d78d615c540e0cbcd3bb7830d1","last_reissued_at":"2026-05-17T23:59:33.366825Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:33.366825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.07245","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":"2026-05-17T23:59:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oXZCXkqpBiTrslJiS8AOFkO8FwdmHB8YwAEo+lT7L6GXT334kU+eSVy0svAhLtOjXKDcaBNFH8DfG5DNh6TKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T21:52:52.346194Z"},"content_sha256":"b25c43b8c98e4f6470f2a96e6a94c7557a6958449c89e8c44be435e17d16d165","schema_version":"1.0","event_id":"sha256:b25c43b8c98e4f6470f2a96e6a94c7557a6958449c89e8c44be435e17d16d165"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:HIPWGV2IDWBIBE4K37GGG2FFME","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear Stark-Wannier equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Andrea Sacchetti","submitted_at":"2017-03-21T14:40:21Z","abstract_excerpt":"In this paper we consider stationary solutions to the nonlinear one-dimensional Schroedinger equation with a periodic potential and a Stark-type perturbation. In the limit of large periodic potential the Stark-Wannier ladders of the linear equation become a dense energy spectrum because a cascade of bifurcations of stationary solutions occurs when the ratio between the effective nonlinearity strength and the tilt of the external field increases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07245","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":"2026-05-17T23:59:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5/GdaZxINtIaJu7n0TqigQf19dknyw5hJ41IBx9XxSqrrp25MI3E34V3ckGt1jr44a0YDZeoE4H/DaUit+LlBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T21:52:52.346566Z"},"content_sha256":"95f3ccfaca88f730acecddd4f1e2d56a31ae51d6e43d980aa7e8e0b7a5ae1724","schema_version":"1.0","event_id":"sha256:95f3ccfaca88f730acecddd4f1e2d56a31ae51d6e43d980aa7e8e0b7a5ae1724"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HIPWGV2IDWBIBE4K37GGG2FFME/bundle.json","state_url":"https://pith.science/pith/HIPWGV2IDWBIBE4K37GGG2FFME/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HIPWGV2IDWBIBE4K37GGG2FFME/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":"2026-07-03T21:52:52Z","links":{"resolver":"https://pith.science/pith/HIPWGV2IDWBIBE4K37GGG2FFME","bundle":"https://pith.science/pith/HIPWGV2IDWBIBE4K37GGG2FFME/bundle.json","state":"https://pith.science/pith/HIPWGV2IDWBIBE4K37GGG2FFME/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HIPWGV2IDWBIBE4K37GGG2FFME/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HIPWGV2IDWBIBE4K37GGG2FFME","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":"839c3fb1e894450e38f9c24896dda62033766af769b8288f074dc136e3a3a747","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-21T14:40:21Z","title_canon_sha256":"688fcf19de9f087df1eaeecf8559587eb8e405bed9b7886796d6a12f478b15ea"},"schema_version":"1.0","source":{"id":"1703.07245","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07245","created_at":"2026-05-17T23:59:33Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07245v3","created_at":"2026-05-17T23:59:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07245","created_at":"2026-05-17T23:59:33Z"},{"alias_kind":"pith_short_12","alias_value":"HIPWGV2IDWBI","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HIPWGV2IDWBIBE4K","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HIPWGV2I","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:95f3ccfaca88f730acecddd4f1e2d56a31ae51d6e43d980aa7e8e0b7a5ae1724","target":"graph","created_at":"2026-05-17T23:59:33Z","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":"In this paper we consider stationary solutions to the nonlinear one-dimensional Schroedinger equation with a periodic potential and a Stark-type perturbation. In the limit of large periodic potential the Stark-Wannier ladders of the linear equation become a dense energy spectrum because a cascade of bifurcations of stationary solutions occurs when the ratio between the effective nonlinearity strength and the tilt of the external field increases.","authors_text":"Andrea Sacchetti","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-21T14:40:21Z","title":"Nonlinear Stark-Wannier equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07245","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:b25c43b8c98e4f6470f2a96e6a94c7557a6958449c89e8c44be435e17d16d165","target":"record","created_at":"2026-05-17T23:59:33Z","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":"839c3fb1e894450e38f9c24896dda62033766af769b8288f074dc136e3a3a747","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-21T14:40:21Z","title_canon_sha256":"688fcf19de9f087df1eaeecf8559587eb8e405bed9b7886796d6a12f478b15ea"},"schema_version":"1.0","source":{"id":"1703.07245","kind":"arxiv","version":3}},"canonical_sha256":"3a1f6357481d8280938adfcc6368a5610b0a10d78d615c540e0cbcd3bb7830d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a1f6357481d8280938adfcc6368a5610b0a10d78d615c540e0cbcd3bb7830d1","first_computed_at":"2026-05-17T23:59:33.366825Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:33.366825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m9DJxBLeTjua6Cp4EaZYnyWIJ8xW1tO/ZqmAyP/Ruwvf1ayYoRk8NQLOSBxAoCvj3lLXqpepacyUEnI/+Nj3BA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:33.367461Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.07245","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b25c43b8c98e4f6470f2a96e6a94c7557a6958449c89e8c44be435e17d16d165","sha256:95f3ccfaca88f730acecddd4f1e2d56a31ae51d6e43d980aa7e8e0b7a5ae1724"],"state_sha256":"8dfbee55d047b56616f32db56670a245912580f6b47912f9f79fd87e40f724dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CvGExHrZEcpGPVQEP8p9GZkhNWy5uWT5Im+kagpM82v1HRwlziR56yCMjC14y08p5MpvolMni5vnQyXrbWc5Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T21:52:52.348644Z","bundle_sha256":"b9df98052cf09974e1a12efb328c545042a2529cef1998aa0a55f0afa547075d"}}