{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:MEHTB3VZ4SZ7I23HCBACURC4X6","short_pith_number":"pith:MEHTB3VZ","canonical_record":{"source":{"id":"1109.4990","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2011-09-23T02:50:05Z","cross_cats_sorted":[],"title_canon_sha256":"74953f7e5265b7d367717dc72e091e29db95f9f1bfcc84bdb4071a6a3f380d97","abstract_canon_sha256":"9fbb1fc1dc36f60f0105c39fa924baf043264a156dbbf01d88a01d0a38aeb45b"},"schema_version":"1.0"},"canonical_sha256":"610f30eeb9e4b3f46b6710402a445cbf96ef0f3d9db2504205c191efa9817dce","source":{"kind":"arxiv","id":"1109.4990","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4990","created_at":"2026-05-18T04:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4990v3","created_at":"2026-05-18T04:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4990","created_at":"2026-05-18T04:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"MEHTB3VZ4SZ7","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MEHTB3VZ4SZ7I23H","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MEHTB3VZ","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:MEHTB3VZ4SZ7I23HCBACURC4X6","target":"record","payload":{"canonical_record":{"source":{"id":"1109.4990","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2011-09-23T02:50:05Z","cross_cats_sorted":[],"title_canon_sha256":"74953f7e5265b7d367717dc72e091e29db95f9f1bfcc84bdb4071a6a3f380d97","abstract_canon_sha256":"9fbb1fc1dc36f60f0105c39fa924baf043264a156dbbf01d88a01d0a38aeb45b"},"schema_version":"1.0"},"canonical_sha256":"610f30eeb9e4b3f46b6710402a445cbf96ef0f3d9db2504205c191efa9817dce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:46.842804Z","signature_b64":"mVjkAmKZd+bWMuoos3SICbXX0MoElJSiPUwSCAGR9cZ7uL26xxDrK2eMP43Vja8Ajc9xTKeMsXUvt5CLOdjNCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"610f30eeb9e4b3f46b6710402a445cbf96ef0f3d9db2504205c191efa9817dce","last_reissued_at":"2026-05-18T04:05:46.842423Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:46.842423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.4990","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":"2026-05-18T04:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aFKy6EZiNfxVY6XGiKOM/uIlhf/Xh958xkUNYyiTowerx4VXn54CRYSeSCxw7XbeJROO3NVDrjArw6uOz1m1Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:00:29.829541Z"},"content_sha256":"47f051010761c6db23dab805d7593ef6a6d4ee4cc6c9101ded3529a5d2c7ac47","schema_version":"1.0","event_id":"sha256:47f051010761c6db23dab805d7593ef6a6d4ee4cc6c9101ded3529a5d2c7ac47"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:MEHTB3VZ4SZ7I23HCBACURC4X6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spin waves in a skyrmion crystal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mes-hall","authors_text":"Oleg Tchernyshyov, Olga Petrova","submitted_at":"2011-09-23T02:50:05Z","abstract_excerpt":"We derive the spectrum of low-frequency spin waves in skyrmion crystals observed recently in noncentrosymmetric ferromagnets. We treat the skyrmion crystal as a superposition of three helices whose wavevectors form an equilateral triangle. The low-frequency spin waves are Goldstone modes associated with displacements of skyrmions. Their dispersion is determined by the elastic properties of the skyrmion crystal and by the kinetic terms of the effective Lagrangian, which include both kinetic energy and a Berry-phase term reflecting a nontrivial topology of magnetization. The Berry-phase term act"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4990","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":"2026-05-18T04:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V9B1+yGAucdwXUfOh4D44Mx5v4A6mBGjxGPRn1m3wT6NIiD3bV+i5xPl6YNbilMKdfbdxpbN9paXj5M5a/oCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:00:29.829888Z"},"content_sha256":"fb9e26906d57c4899af746639a98d4717b0f4beeaa0823b20da197767339d152","schema_version":"1.0","event_id":"sha256:fb9e26906d57c4899af746639a98d4717b0f4beeaa0823b20da197767339d152"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MEHTB3VZ4SZ7I23HCBACURC4X6/bundle.json","state_url":"https://pith.science/pith/MEHTB3VZ4SZ7I23HCBACURC4X6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MEHTB3VZ4SZ7I23HCBACURC4X6/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":"2026-06-05T15:00:29Z","links":{"resolver":"https://pith.science/pith/MEHTB3VZ4SZ7I23HCBACURC4X6","bundle":"https://pith.science/pith/MEHTB3VZ4SZ7I23HCBACURC4X6/bundle.json","state":"https://pith.science/pith/MEHTB3VZ4SZ7I23HCBACURC4X6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MEHTB3VZ4SZ7I23HCBACURC4X6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MEHTB3VZ4SZ7I23HCBACURC4X6","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":"9fbb1fc1dc36f60f0105c39fa924baf043264a156dbbf01d88a01d0a38aeb45b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2011-09-23T02:50:05Z","title_canon_sha256":"74953f7e5265b7d367717dc72e091e29db95f9f1bfcc84bdb4071a6a3f380d97"},"schema_version":"1.0","source":{"id":"1109.4990","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4990","created_at":"2026-05-18T04:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4990v3","created_at":"2026-05-18T04:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4990","created_at":"2026-05-18T04:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"MEHTB3VZ4SZ7","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MEHTB3VZ4SZ7I23H","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MEHTB3VZ","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:fb9e26906d57c4899af746639a98d4717b0f4beeaa0823b20da197767339d152","target":"graph","created_at":"2026-05-18T04:05:46Z","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 derive the spectrum of low-frequency spin waves in skyrmion crystals observed recently in noncentrosymmetric ferromagnets. We treat the skyrmion crystal as a superposition of three helices whose wavevectors form an equilateral triangle. The low-frequency spin waves are Goldstone modes associated with displacements of skyrmions. Their dispersion is determined by the elastic properties of the skyrmion crystal and by the kinetic terms of the effective Lagrangian, which include both kinetic energy and a Berry-phase term reflecting a nontrivial topology of magnetization. The Berry-phase term act","authors_text":"Oleg Tchernyshyov, Olga Petrova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2011-09-23T02:50:05Z","title":"Spin waves in a skyrmion crystal"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4990","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":"sha256:47f051010761c6db23dab805d7593ef6a6d4ee4cc6c9101ded3529a5d2c7ac47","target":"record","created_at":"2026-05-18T04:05:46Z","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":"9fbb1fc1dc36f60f0105c39fa924baf043264a156dbbf01d88a01d0a38aeb45b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2011-09-23T02:50:05Z","title_canon_sha256":"74953f7e5265b7d367717dc72e091e29db95f9f1bfcc84bdb4071a6a3f380d97"},"schema_version":"1.0","source":{"id":"1109.4990","kind":"arxiv","version":3}},"canonical_sha256":"610f30eeb9e4b3f46b6710402a445cbf96ef0f3d9db2504205c191efa9817dce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"610f30eeb9e4b3f46b6710402a445cbf96ef0f3d9db2504205c191efa9817dce","first_computed_at":"2026-05-18T04:05:46.842423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:46.842423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mVjkAmKZd+bWMuoos3SICbXX0MoElJSiPUwSCAGR9cZ7uL26xxDrK2eMP43Vja8Ajc9xTKeMsXUvt5CLOdjNCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:46.842804Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4990","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47f051010761c6db23dab805d7593ef6a6d4ee4cc6c9101ded3529a5d2c7ac47","sha256:fb9e26906d57c4899af746639a98d4717b0f4beeaa0823b20da197767339d152"],"state_sha256":"e48c144f3750aec0fb31ff9019224736b9824ef78414c5ddbba169a3176ce761"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PHCzkZPZe5+UdEe0QS60+3ORLuVQB2ruBkxLTy8MunrNB5A4v4ADkJltnaMbdLgTa6gbO0X3x31sQ/j497UlDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T15:00:29.831845Z","bundle_sha256":"63603e0a24d38a29473045a6c057086a0c047fbbc7045211b2425317b5e8fb3f"}}