{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BDQ3JK2NTB7MXLO754GBB4RKE5","short_pith_number":"pith:BDQ3JK2N","canonical_record":{"source":{"id":"1208.1031","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-05T16:05:38Z","cross_cats_sorted":["math.DG","math.MP"],"title_canon_sha256":"27da77c2913fb196c5c060e9979ab15e3eec848ec9d439d361d61d421bf94cde","abstract_canon_sha256":"28d5965016badb1aa7ea3a41a2bedc8ae042710a34f99bcb5bd0b57020dfbb60"},"schema_version":"1.0"},"canonical_sha256":"08e1b4ab4d987ecbaddfef0c10f22a2761fc805853e202600628021948ada1a0","source":{"kind":"arxiv","id":"1208.1031","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1031","created_at":"2026-05-18T03:29:37Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1031v1","created_at":"2026-05-18T03:29:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1031","created_at":"2026-05-18T03:29:37Z"},{"alias_kind":"pith_short_12","alias_value":"BDQ3JK2NTB7M","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BDQ3JK2NTB7MXLO7","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BDQ3JK2N","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BDQ3JK2NTB7MXLO754GBB4RKE5","target":"record","payload":{"canonical_record":{"source":{"id":"1208.1031","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-05T16:05:38Z","cross_cats_sorted":["math.DG","math.MP"],"title_canon_sha256":"27da77c2913fb196c5c060e9979ab15e3eec848ec9d439d361d61d421bf94cde","abstract_canon_sha256":"28d5965016badb1aa7ea3a41a2bedc8ae042710a34f99bcb5bd0b57020dfbb60"},"schema_version":"1.0"},"canonical_sha256":"08e1b4ab4d987ecbaddfef0c10f22a2761fc805853e202600628021948ada1a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:37.623626Z","signature_b64":"9dtyDu9Vn8EEiJLr/8ASjoQ/pPHOnYEgr2FLTS2Q26srnrC4aueZnb7QdtU49GQ6FUC0k/VpDXqqaHZTKv1TDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08e1b4ab4d987ecbaddfef0c10f22a2761fc805853e202600628021948ada1a0","last_reissued_at":"2026-05-18T03:29:37.622791Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:37.622791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.1031","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":"2026-05-18T03:29:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zu3x0KnAxlqoqHwU7CJ5gaGx8jQALPpqZ5FZeQXCiFnNMqdilaN+pcqrjdwDOvcPduM8L6xIm2KsuBJHODVPBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:51:24.189494Z"},"content_sha256":"ac5006242845c9a0f735864f8c6a37229c4f85dba2819348e516e2930a02eb10","schema_version":"1.0","event_id":"sha256:ac5006242845c9a0f735864f8c6a37229c4f85dba2819348e516e2930a02eb10"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BDQ3JK2NTB7MXLO754GBB4RKE5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Jet theoretical Yang-Mills energy in the geometric dynamics of 2D-monolayer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"H.V. Grushevskaya, M. Neagu, N.G. Krylova","submitted_at":"2012-08-05T16:05:38Z","abstract_excerpt":"Langmuir-Blodgett films (LB-films) consist from few LB-monolayers which are high structured nanomaterials that are very promising materials for applications. We use a geometrical approach to describe structurization into LB-monolayers. Consequently, we develop on the 1-jet space J^1([0,\\infty),R^2) the single-time Lagrange geometry (in the sense of distinguished (d-) connection, d-torsions and an abstract anisotropic electromagnetic-like d-field) for the Lagrangian governing the 2D-motion of a particle of monolayer. One assumed that an expansion near singular points for the constructed geometr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1031","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":"2026-05-18T03:29:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PnxojhOWN4ZyNLfmf32D5bjdbasL3aIVnyMJb3Az/EFoB3SPsLZ6P/FeoW8I8K2btxx0PcBefZ17RlCD4SdIBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:51:24.189885Z"},"content_sha256":"2888b7d0d8a5a64b61b5f8bc78084894e39da92d6a9a7357420968c64bdfbef8","schema_version":"1.0","event_id":"sha256:2888b7d0d8a5a64b61b5f8bc78084894e39da92d6a9a7357420968c64bdfbef8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BDQ3JK2NTB7MXLO754GBB4RKE5/bundle.json","state_url":"https://pith.science/pith/BDQ3JK2NTB7MXLO754GBB4RKE5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BDQ3JK2NTB7MXLO754GBB4RKE5/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":"2026-06-08T23:51:24Z","links":{"resolver":"https://pith.science/pith/BDQ3JK2NTB7MXLO754GBB4RKE5","bundle":"https://pith.science/pith/BDQ3JK2NTB7MXLO754GBB4RKE5/bundle.json","state":"https://pith.science/pith/BDQ3JK2NTB7MXLO754GBB4RKE5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BDQ3JK2NTB7MXLO754GBB4RKE5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BDQ3JK2NTB7MXLO754GBB4RKE5","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":"28d5965016badb1aa7ea3a41a2bedc8ae042710a34f99bcb5bd0b57020dfbb60","cross_cats_sorted":["math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-05T16:05:38Z","title_canon_sha256":"27da77c2913fb196c5c060e9979ab15e3eec848ec9d439d361d61d421bf94cde"},"schema_version":"1.0","source":{"id":"1208.1031","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1031","created_at":"2026-05-18T03:29:37Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1031v1","created_at":"2026-05-18T03:29:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1031","created_at":"2026-05-18T03:29:37Z"},{"alias_kind":"pith_short_12","alias_value":"BDQ3JK2NTB7M","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BDQ3JK2NTB7MXLO7","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BDQ3JK2N","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:2888b7d0d8a5a64b61b5f8bc78084894e39da92d6a9a7357420968c64bdfbef8","target":"graph","created_at":"2026-05-18T03:29:37Z","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":"Langmuir-Blodgett films (LB-films) consist from few LB-monolayers which are high structured nanomaterials that are very promising materials for applications. We use a geometrical approach to describe structurization into LB-monolayers. Consequently, we develop on the 1-jet space J^1([0,\\infty),R^2) the single-time Lagrange geometry (in the sense of distinguished (d-) connection, d-torsions and an abstract anisotropic electromagnetic-like d-field) for the Lagrangian governing the 2D-motion of a particle of monolayer. One assumed that an expansion near singular points for the constructed geometr","authors_text":"H.V. Grushevskaya, M. Neagu, N.G. Krylova","cross_cats":["math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-05T16:05:38Z","title":"Jet theoretical Yang-Mills energy in the geometric dynamics of 2D-monolayer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1031","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:ac5006242845c9a0f735864f8c6a37229c4f85dba2819348e516e2930a02eb10","target":"record","created_at":"2026-05-18T03:29:37Z","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":"28d5965016badb1aa7ea3a41a2bedc8ae042710a34f99bcb5bd0b57020dfbb60","cross_cats_sorted":["math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-05T16:05:38Z","title_canon_sha256":"27da77c2913fb196c5c060e9979ab15e3eec848ec9d439d361d61d421bf94cde"},"schema_version":"1.0","source":{"id":"1208.1031","kind":"arxiv","version":1}},"canonical_sha256":"08e1b4ab4d987ecbaddfef0c10f22a2761fc805853e202600628021948ada1a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08e1b4ab4d987ecbaddfef0c10f22a2761fc805853e202600628021948ada1a0","first_computed_at":"2026-05-18T03:29:37.622791Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:37.622791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9dtyDu9Vn8EEiJLr/8ASjoQ/pPHOnYEgr2FLTS2Q26srnrC4aueZnb7QdtU49GQ6FUC0k/VpDXqqaHZTKv1TDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:37.623626Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1031","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac5006242845c9a0f735864f8c6a37229c4f85dba2819348e516e2930a02eb10","sha256:2888b7d0d8a5a64b61b5f8bc78084894e39da92d6a9a7357420968c64bdfbef8"],"state_sha256":"371b4ef7d7fa396ea948bb37a08decc0d285a17f93ac5a8b4456910f06a13ce8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1cgCpkRqx4xcWmOla6/N0arNHv4g5atlceb/VDdZx6S65AxTNKAlne7ooSnDnmFrhjYkMERtcxxWgtcWNReeCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T23:51:24.191965Z","bundle_sha256":"e9209b622ba723764208eace1f1f11b5646dbc188fe2f0787c314be3af75b78b"}}