{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ET4E35QF2VDQHIS25OV6RXMNRE","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":"b887b3041e5b968f0dcc9fb33c84990be44a75bcc62676c3e318fcfcd528d0dd","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"nlin.SI","submitted_at":"2025-01-22T16:55:32Z","title_canon_sha256":"41ce3f5241ff0d22388f633a93c5d3c6ff33abbffeaa33b0fb4829c48ccc086a"},"schema_version":"1.0","source":{"id":"2501.13012","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.13012","created_at":"2026-07-05T11:39:06Z"},{"alias_kind":"arxiv_version","alias_value":"2501.13012v3","created_at":"2026-07-05T11:39:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.13012","created_at":"2026-07-05T11:39:06Z"},{"alias_kind":"pith_short_12","alias_value":"ET4E35QF2VDQ","created_at":"2026-07-05T11:39:06Z"},{"alias_kind":"pith_short_16","alias_value":"ET4E35QF2VDQHIS2","created_at":"2026-07-05T11:39:06Z"},{"alias_kind":"pith_short_8","alias_value":"ET4E35QF","created_at":"2026-07-05T11:39:06Z"}],"graph_snapshots":[{"event_id":"sha256:e31c84632bb2656b3767b5bc25b132bbbfa1de8c85c145207cbc47ede9849dbb","target":"graph","created_at":"2026-07-05T11:39:06Z","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/2501.13012/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Discrete Lagrangian multiform theory is a variational perspective on lattice equations that are integrable in the sense of multidimensional consistency. The Lagrangian multiforms for the equations of the ABS classification formed the start of this theory, but the Lagrangian multiforms that are usually considered in this context produce equations that are slightly weaker than the ABS equations. In this work, we present alternative Lagrangian multiforms that have Euler-Lagrange equations equivalent to the ABS equations. In addition, the treatment of the ABS Lagrangian multiforms in the existing ","authors_text":"Jacob J. Richardson, Mats Vermeeren","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"nlin.SI","submitted_at":"2025-01-22T16:55:32Z","title":"Discrete Lagrangian Multiforms for ABS Equations I: Quad Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.13012","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:d74809763d9974088709f8a2622ee7e456b061c7962d07692d460060a6579033","target":"record","created_at":"2026-07-05T11:39:06Z","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":"b887b3041e5b968f0dcc9fb33c84990be44a75bcc62676c3e318fcfcd528d0dd","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"nlin.SI","submitted_at":"2025-01-22T16:55:32Z","title_canon_sha256":"41ce3f5241ff0d22388f633a93c5d3c6ff33abbffeaa33b0fb4829c48ccc086a"},"schema_version":"1.0","source":{"id":"2501.13012","kind":"arxiv","version":3}},"canonical_sha256":"24f84df605d54703a25aebabe8dd8d89158d684483dac6407e738b4aae06f04f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24f84df605d54703a25aebabe8dd8d89158d684483dac6407e738b4aae06f04f","first_computed_at":"2026-07-05T11:39:06.844463Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:39:06.844463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kjvsGrY9YtAo9k+483cjs5i10+rTfRUtuKJpuXBc8VpFo9DDZy+U5YSDFdHADqOMDfVt8HZ4JsCNXL86r5LcDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:39:06.844896Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.13012","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d74809763d9974088709f8a2622ee7e456b061c7962d07692d460060a6579033","sha256:e31c84632bb2656b3767b5bc25b132bbbfa1de8c85c145207cbc47ede9849dbb"],"state_sha256":"2573d76456372280d7a94b799b6a81327c2ada236ed25ecdaec1a097527dce23"}