{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:WMT43VUK26G4UP63C7TWSLSUBK","short_pith_number":"pith:WMT43VUK","schema_version":"1.0","canonical_sha256":"b327cdd68ad78dca3fdb17e7692e540a88693fe19ece7ccad262d97a7717047c","source":{"kind":"arxiv","id":"2508.00133","version":3},"attestation_state":"computed","paper":{"title":"Homotopies for Lagrangian field theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MP","math.SG"],"primary_cat":"math-ph","authors_text":"Jonas Schnitzer, Michele Schiavina","submitted_at":"2025-07-31T19:42:13Z","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 $\\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2508.00133","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-07-31T19:42:13Z","cross_cats_sorted":["math.DG","math.MP","math.SG"],"title_canon_sha256":"2e754da8611a7b1b692e7410cefd86549f2b0fc8bad9cfa56ea80b525d7b67ea","abstract_canon_sha256":"c11a7fabd92410de62c2508514ec70874cf98d28e304b6258ad5681e3c5cbe79"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-21T02:21:20.351118Z","signature_b64":"Mn4joubnvEQmZp3jdEbFZYaNtJrQ9yAbSJ7mAC5WM4OO1+ABbHxf8ZXOKFf6YFfXl2DijgSjcalCPJkJpKnCDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b327cdd68ad78dca3fdb17e7692e540a88693fe19ece7ccad262d97a7717047c","last_reissued_at":"2026-07-21T02:21:20.350227Z","signature_status":"signed_v1","first_computed_at":"2026-07-21T02:21:20.350227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homotopies for Lagrangian field theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MP","math.SG"],"primary_cat":"math-ph","authors_text":"Jonas Schnitzer, Michele Schiavina","submitted_at":"2025-07-31T19:42:13Z","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 $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.00133","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.00133/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2508.00133","created_at":"2026-07-21T02:21:20.350649+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.00133v3","created_at":"2026-07-21T02:21:20.350649+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.00133","created_at":"2026-07-21T02:21:20.350649+00:00"},{"alias_kind":"pith_short_12","alias_value":"WMT43VUK26G4","created_at":"2026-07-21T02:21:20.350649+00:00"},{"alias_kind":"pith_short_16","alias_value":"WMT43VUK26G4UP63","created_at":"2026-07-21T02:21:20.350649+00:00"},{"alias_kind":"pith_short_8","alias_value":"WMT43VUK","created_at":"2026-07-21T02:21:20.350649+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WMT43VUK26G4UP63C7TWSLSUBK","json":"https://pith.science/pith/WMT43VUK26G4UP63C7TWSLSUBK.json","graph_json":"https://pith.science/api/pith-number/WMT43VUK26G4UP63C7TWSLSUBK/graph.json","events_json":"https://pith.science/api/pith-number/WMT43VUK26G4UP63C7TWSLSUBK/events.json","paper":"https://pith.science/paper/WMT43VUK"},"agent_actions":{"view_html":"https://pith.science/pith/WMT43VUK26G4UP63C7TWSLSUBK","download_json":"https://pith.science/pith/WMT43VUK26G4UP63C7TWSLSUBK.json","view_paper":"https://pith.science/paper/WMT43VUK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.00133&json=true","fetch_graph":"https://pith.science/api/pith-number/WMT43VUK26G4UP63C7TWSLSUBK/graph.json","fetch_events":"https://pith.science/api/pith-number/WMT43VUK26G4UP63C7TWSLSUBK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WMT43VUK26G4UP63C7TWSLSUBK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WMT43VUK26G4UP63C7TWSLSUBK/action/storage_attestation","attest_author":"https://pith.science/pith/WMT43VUK26G4UP63C7TWSLSUBK/action/author_attestation","sign_citation":"https://pith.science/pith/WMT43VUK26G4UP63C7TWSLSUBK/action/citation_signature","submit_replication":"https://pith.science/pith/WMT43VUK26G4UP63C7TWSLSUBK/action/replication_record"}},"created_at":"2026-07-21T02:21:20.350649+00:00","updated_at":"2026-07-21T02:21:20.350649+00:00"}