{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WMT43VUK26G4UP63C7TWSLSUBK","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":"c11a7fabd92410de62c2508514ec70874cf98d28e304b6258ad5681e3c5cbe79","cross_cats_sorted":["math.DG","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-07-31T19:42:13Z","title_canon_sha256":"2e754da8611a7b1b692e7410cefd86549f2b0fc8bad9cfa56ea80b525d7b67ea"},"schema_version":"1.0","source":{"id":"2508.00133","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.00133","created_at":"2026-07-21T02:21:20Z"},{"alias_kind":"arxiv_version","alias_value":"2508.00133v3","created_at":"2026-07-21T02:21:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.00133","created_at":"2026-07-21T02:21:20Z"},{"alias_kind":"pith_short_12","alias_value":"WMT43VUK26G4","created_at":"2026-07-21T02:21:20Z"},{"alias_kind":"pith_short_16","alias_value":"WMT43VUK26G4UP63","created_at":"2026-07-21T02:21:20Z"},{"alias_kind":"pith_short_8","alias_value":"WMT43VUK","created_at":"2026-07-21T02:21:20Z"}],"graph_snapshots":[{"event_id":"sha256:44391a36d35237b50a53c036e07a932ea9d80ad1497842b4487a0d396eac8b18","target":"graph","created_at":"2026-07-21T02:21:20Z","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/2508.00133/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Consider the variational bicomplex for $\\mathcal{E}$ the space of sections of a graded, affine bundle. Local functionals $\\mathcal{F}$ are defined as an equivalence class of density-valued functionals, which represent Lagrangian densities. A choice of a $k$-symplectic local form $\\omega$ on $\\mathcal{E}$ induces a Lie$[k]$ algebra structure on (Hamiltonian) local functionals $(\\mathcal{F}_{\\mathrm{ham}},\\{\\cdot,\\cdot\\}_{\\mathrm{ham}})$. For any $\\omega$ and any choice of a cohomological vector field $Q$ compatible with $\\omega$, we build three explicit $L_\\infty$ algebras on a resolution of $\\","authors_text":"Jonas Schnitzer, Michele Schiavina","cross_cats":["math.DG","math.MP","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-07-31T19:42:13Z","title":"Homotopies for Lagrangian field theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.00133","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:f8bcecf3cd1131a6e58c5a155a4610ca656f4f71d2ba826eb5c82c819afbfe72","target":"record","created_at":"2026-07-21T02:21:20Z","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":"c11a7fabd92410de62c2508514ec70874cf98d28e304b6258ad5681e3c5cbe79","cross_cats_sorted":["math.DG","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-07-31T19:42:13Z","title_canon_sha256":"2e754da8611a7b1b692e7410cefd86549f2b0fc8bad9cfa56ea80b525d7b67ea"},"schema_version":"1.0","source":{"id":"2508.00133","kind":"arxiv","version":3}},"canonical_sha256":"b327cdd68ad78dca3fdb17e7692e540a88693fe19ece7ccad262d97a7717047c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b327cdd68ad78dca3fdb17e7692e540a88693fe19ece7ccad262d97a7717047c","first_computed_at":"2026-07-21T02:21:20.350227Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-21T02:21:20.350227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mn4joubnvEQmZp3jdEbFZYaNtJrQ9yAbSJ7mAC5WM4OO1+ABbHxf8ZXOKFf6YFfXl2DijgSjcalCPJkJpKnCDA==","signature_status":"signed_v1","signed_at":"2026-07-21T02:21:20.351118Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.00133","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8bcecf3cd1131a6e58c5a155a4610ca656f4f71d2ba826eb5c82c819afbfe72","sha256:44391a36d35237b50a53c036e07a932ea9d80ad1497842b4487a0d396eac8b18"],"state_sha256":"57cd4f69db0ff057f3bc2e5c61461d6adc7187774e4ead5497458e2fff3b44aa"}