{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PWULMET7TGTGS6G4Y5QM7QXRSM","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":"30d1d61d4c424b6f1dbfd20899ccb6d0e1f3ac51db7d818f85e8ea8ed60be788","cross_cats_sorted":["hep-th","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-01T21:09:43Z","title_canon_sha256":"438ce2d7d3ea926a4ff3b77bf45c15c744f6fd4346b7108943e2c7752f2f10ed"},"schema_version":"1.0","source":{"id":"1602.00708","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.00708","created_at":"2026-05-18T00:47:59Z"},{"alias_kind":"arxiv_version","alias_value":"1602.00708v2","created_at":"2026-05-18T00:47:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00708","created_at":"2026-05-18T00:47:59Z"},{"alias_kind":"pith_short_12","alias_value":"PWULMET7TGTG","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PWULMET7TGTGS6G4","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PWULMET7","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:5a805bae6e9fc8948644f77634031e6dc7a853534df6b7f636118ee0be3bb54c","target":"graph","created_at":"2026-05-18T00:47:59Z","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 develop an approach to construct Poisson algebras for non-linear scalar field theories that is based on the Cahiers topos model for synthetic differential geometry. In this framework the solution space of the field equation carries a natural smooth structure and, following Zuckerman's ideas, we can endow it with a presymplectic current. We formulate the Hamiltonian vector field equation in this setting and show that it selects a family of observables which forms a Poisson algebra. Our approach provides a clean splitting between geometric and algebraic aspects of the construction of a Poisso","authors_text":"Alexander Schenkel, Marco Benini","cross_cats":["hep-th","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-01T21:09:43Z","title":"Poisson algebras for non-linear field theories in the Cahiers topos"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00708","kind":"arxiv","version":2},"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":"sha256:12fbcd9afead97e8b845234c5e493f99e8a6b4bdffe90af477c32bb38543eef8","target":"record","created_at":"2026-05-18T00:47:59Z","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":"30d1d61d4c424b6f1dbfd20899ccb6d0e1f3ac51db7d818f85e8ea8ed60be788","cross_cats_sorted":["hep-th","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-01T21:09:43Z","title_canon_sha256":"438ce2d7d3ea926a4ff3b77bf45c15c744f6fd4346b7108943e2c7752f2f10ed"},"schema_version":"1.0","source":{"id":"1602.00708","kind":"arxiv","version":2}},"canonical_sha256":"7da8b6127f99a66978dcc760cfc2f1930fb43a639dbb3180c6e19375da13c48e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7da8b6127f99a66978dcc760cfc2f1930fb43a639dbb3180c6e19375da13c48e","first_computed_at":"2026-05-18T00:47:59.194062Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:59.194062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z+r0gtZ16vRZrHTa0DaMh87sWZBxeag0wsiFREufd4NNMsVfkM6EIsgVYz5MTQvIa21l3+FQ58T25MiV3wxLAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:59.194719Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.00708","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12fbcd9afead97e8b845234c5e493f99e8a6b4bdffe90af477c32bb38543eef8","sha256:5a805bae6e9fc8948644f77634031e6dc7a853534df6b7f636118ee0be3bb54c"],"state_sha256":"b8c105dada7122ecd38f2612d6b2b77a8de0b41cdad5b11cb35984efbfc0e75b"}