{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:A7AS4HPDDRV7CFKITXWBT3V5QC","short_pith_number":"pith:A7AS4HPD","canonical_record":{"source":{"id":"1601.05296","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-01-20T15:17:06Z","cross_cats_sorted":["math.MP","math.SG","nlin.SI"],"title_canon_sha256":"6f8f9b27210cc7f16b732c37845f0e2e93d303113c6f4987da53986007e82247","abstract_canon_sha256":"de8639b856eb941acf27e48f4139375bb3d3f6eb35e46dab0b80f1f06a98796a"},"schema_version":"1.0"},"canonical_sha256":"07c12e1de31c6bf115489dec19eebd809cdbf7b94ccaedd925f3d6ab3d9731fe","source":{"kind":"arxiv","id":"1601.05296","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05296","created_at":"2026-05-18T01:22:15Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05296v1","created_at":"2026-05-18T01:22:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05296","created_at":"2026-05-18T01:22:15Z"},{"alias_kind":"pith_short_12","alias_value":"A7AS4HPDDRV7","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A7AS4HPDDRV7CFKI","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A7AS4HPD","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:A7AS4HPDDRV7CFKITXWBT3V5QC","target":"record","payload":{"canonical_record":{"source":{"id":"1601.05296","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-01-20T15:17:06Z","cross_cats_sorted":["math.MP","math.SG","nlin.SI"],"title_canon_sha256":"6f8f9b27210cc7f16b732c37845f0e2e93d303113c6f4987da53986007e82247","abstract_canon_sha256":"de8639b856eb941acf27e48f4139375bb3d3f6eb35e46dab0b80f1f06a98796a"},"schema_version":"1.0"},"canonical_sha256":"07c12e1de31c6bf115489dec19eebd809cdbf7b94ccaedd925f3d6ab3d9731fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:15.521640Z","signature_b64":"Sud50R+g7/HUWiggloGP6jsOSLg/WvR70+M06wBS8p3uj88EpxEP7hp80hvBS8Neia2KydEOWGtmVytmkgUWDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07c12e1de31c6bf115489dec19eebd809cdbf7b94ccaedd925f3d6ab3d9731fe","last_reissued_at":"2026-05-18T01:22:15.520930Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:15.520930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.05296","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":"2026-05-18T01:22:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t54yIUF2Vw5CThYNx2w8viv2kTMDUOuvlP2JsDQot6faG39ZnBT8IKIr05r0w4nStHdEWCLBTxUrDneA7VbyAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:22:44.934122Z"},"content_sha256":"c5677ac9c22c08faaed5a708135e114b58a0248438f7076deab6fe39cac02f61","schema_version":"1.0","event_id":"sha256:c5677ac9c22c08faaed5a708135e114b58a0248438f7076deab6fe39cac02f61"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:A7AS4HPDDRV7CFKITXWBT3V5QC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two-dimensional variational systems on the root lattice $Q(A_{N})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SG","nlin.SI"],"primary_cat":"math-ph","authors_text":"Raphael Boll","submitted_at":"2016-01-20T15:17:06Z","abstract_excerpt":"We study certain two-dimensional variational systems, namely pluri-Lagrangian systems on the root lattice $Q(A_{N})$. Here, we follow the scheme which was already used to define two-dimensional pluri-Lagrangian systems on the lattice $\\mathbb{Z}^{N}$ and three-dimensional pluri-Lagrangian systems on the lattice $\\mathbb{Z}^{N}$ as well as on $Q(A_{N})$. We will show that the two-dimensional pluri-Lagragian systems on $Q(A_{N})$ are more general than the ones on $\\mathbb{Z}^{N}$, in the sense that they can encode several different pluri-Lagrangian systems on $\\mathbb{Z}^{N}$. This also means th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05296","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":"2026-05-18T01:22:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GlnPcDpfNe3wBa+ELnq3i5rlpM0aU9NUuJUQuZ2zSu3UnQZQ8hF2I8f/jeaISxg0ch9DwW9G6oXU0wlwK0/xDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:22:44.934498Z"},"content_sha256":"d915236c30665c36ac1a09a8bb60e255de12d52c6939f47efc1864b01f6c047f","schema_version":"1.0","event_id":"sha256:d915236c30665c36ac1a09a8bb60e255de12d52c6939f47efc1864b01f6c047f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A7AS4HPDDRV7CFKITXWBT3V5QC/bundle.json","state_url":"https://pith.science/pith/A7AS4HPDDRV7CFKITXWBT3V5QC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A7AS4HPDDRV7CFKITXWBT3V5QC/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":"2026-05-31T21:22:44Z","links":{"resolver":"https://pith.science/pith/A7AS4HPDDRV7CFKITXWBT3V5QC","bundle":"https://pith.science/pith/A7AS4HPDDRV7CFKITXWBT3V5QC/bundle.json","state":"https://pith.science/pith/A7AS4HPDDRV7CFKITXWBT3V5QC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A7AS4HPDDRV7CFKITXWBT3V5QC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:A7AS4HPDDRV7CFKITXWBT3V5QC","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":"de8639b856eb941acf27e48f4139375bb3d3f6eb35e46dab0b80f1f06a98796a","cross_cats_sorted":["math.MP","math.SG","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-01-20T15:17:06Z","title_canon_sha256":"6f8f9b27210cc7f16b732c37845f0e2e93d303113c6f4987da53986007e82247"},"schema_version":"1.0","source":{"id":"1601.05296","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05296","created_at":"2026-05-18T01:22:15Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05296v1","created_at":"2026-05-18T01:22:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05296","created_at":"2026-05-18T01:22:15Z"},{"alias_kind":"pith_short_12","alias_value":"A7AS4HPDDRV7","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A7AS4HPDDRV7CFKI","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A7AS4HPD","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:d915236c30665c36ac1a09a8bb60e255de12d52c6939f47efc1864b01f6c047f","target":"graph","created_at":"2026-05-18T01:22:15Z","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 study certain two-dimensional variational systems, namely pluri-Lagrangian systems on the root lattice $Q(A_{N})$. Here, we follow the scheme which was already used to define two-dimensional pluri-Lagrangian systems on the lattice $\\mathbb{Z}^{N}$ and three-dimensional pluri-Lagrangian systems on the lattice $\\mathbb{Z}^{N}$ as well as on $Q(A_{N})$. We will show that the two-dimensional pluri-Lagragian systems on $Q(A_{N})$ are more general than the ones on $\\mathbb{Z}^{N}$, in the sense that they can encode several different pluri-Lagrangian systems on $\\mathbb{Z}^{N}$. This also means th","authors_text":"Raphael Boll","cross_cats":["math.MP","math.SG","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-01-20T15:17:06Z","title":"Two-dimensional variational systems on the root lattice $Q(A_{N})$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05296","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:c5677ac9c22c08faaed5a708135e114b58a0248438f7076deab6fe39cac02f61","target":"record","created_at":"2026-05-18T01:22:15Z","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":"de8639b856eb941acf27e48f4139375bb3d3f6eb35e46dab0b80f1f06a98796a","cross_cats_sorted":["math.MP","math.SG","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-01-20T15:17:06Z","title_canon_sha256":"6f8f9b27210cc7f16b732c37845f0e2e93d303113c6f4987da53986007e82247"},"schema_version":"1.0","source":{"id":"1601.05296","kind":"arxiv","version":1}},"canonical_sha256":"07c12e1de31c6bf115489dec19eebd809cdbf7b94ccaedd925f3d6ab3d9731fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07c12e1de31c6bf115489dec19eebd809cdbf7b94ccaedd925f3d6ab3d9731fe","first_computed_at":"2026-05-18T01:22:15.520930Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:15.520930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sud50R+g7/HUWiggloGP6jsOSLg/WvR70+M06wBS8p3uj88EpxEP7hp80hvBS8Neia2KydEOWGtmVytmkgUWDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:15.521640Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05296","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5677ac9c22c08faaed5a708135e114b58a0248438f7076deab6fe39cac02f61","sha256:d915236c30665c36ac1a09a8bb60e255de12d52c6939f47efc1864b01f6c047f"],"state_sha256":"8b8384feb1f36b44cc2222b45b6ed96b6fee3d78d62fe759ad089aa0806d9712"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qU+lsWJA1rjyMUNU9RhytcK43b51haqOs75tycXNdqlwGzVZ8H3+KVNl64twR3Vd6yzNry3NkFldgzlbYRv/Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T21:22:44.936684Z","bundle_sha256":"784d56e922f31be0beabf8c344a76beaac7fe097378e0895373322b4fde0201f"}}