{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:ZH46MTMUU3NHCVA26PD74GERI2","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":"e77c50aeadaf3b3c9c51a79f2ebc0921ca4ae7060679c8faa76bf2d19b909b08","cross_cats_sorted":[],"license":"","primary_cat":"math.SG","submitted_at":"2001-01-01T00:00:00Z","title_canon_sha256":"3a327a17c6d8fa802976cfb580002162db91f8ae5e08cd425b67772f52289668"},"schema_version":"1.0","source":{"id":"math/0101266","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0101266","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"arxiv_version","alias_value":"math/0101266v1","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0101266","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"pith_short_12","alias_value":"ZH46MTMUU3NH","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZH46MTMUU3NHCVA2","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZH46MTMU","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:1060b21a6e90728041a7f8f363649701102b1d43e25fc72d6ede01538140ec92","target":"graph","created_at":"2026-05-18T01:38:30Z","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":"Let $M$ be an $n$-dimensional manifold, $V$ the space of a representation $\\rho: GL(n)\\longrightarrow GL(V)$. Locally, let $T(V)$ be the space of sections of the tensor bundle with fiber $V$ over a sufficiently small open set $U\\subset M$, in other words, $T(V)$ is the space of tensor fields of type $V$ on $M$ on which the group $\\Diff (M)$ of diffeomorphisms of $M$ naturally acts. Elsewhere, the author classified the $\\Diff (M)$-invariant differential operators $D: T(V_{1})\\otimes T(V_{2})\\longrightarrow T(V_{3})$ for irreducible fibers with lowest weight. Here the result is generalized to bi","authors_text":"Pavel Grozman","cross_cats":[],"headline":"","license":"","primary_cat":"math.SG","submitted_at":"2001-01-01T00:00:00Z","title":"On bilinear invariant differential operators acting on tensor fields on the symplectic manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0101266","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:d9e3efa44524a12ceff7bb7d15f92b35acff2463f5caa55ab44f201ee909cd4c","target":"record","created_at":"2026-05-18T01:38:30Z","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":"e77c50aeadaf3b3c9c51a79f2ebc0921ca4ae7060679c8faa76bf2d19b909b08","cross_cats_sorted":[],"license":"","primary_cat":"math.SG","submitted_at":"2001-01-01T00:00:00Z","title_canon_sha256":"3a327a17c6d8fa802976cfb580002162db91f8ae5e08cd425b67772f52289668"},"schema_version":"1.0","source":{"id":"math/0101266","kind":"arxiv","version":1}},"canonical_sha256":"c9f9e64d94a6da71541af3c7fe189146bf7fca3242893beecfafdd481ab64e60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9f9e64d94a6da71541af3c7fe189146bf7fca3242893beecfafdd481ab64e60","first_computed_at":"2026-05-18T01:38:30.060556Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:30.060556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JDjjgQ826SSnFm+Ytr5tOxliVFJp2p5sfx+dzPOsh8jrIQY87XwGLrvCFeVKS4joubsMd0kAPU52N9xHAEjSCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:30.061059Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0101266","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9e3efa44524a12ceff7bb7d15f92b35acff2463f5caa55ab44f201ee909cd4c","sha256:1060b21a6e90728041a7f8f363649701102b1d43e25fc72d6ede01538140ec92"],"state_sha256":"887e13d2cf4a8b9ca148e26989a88b5cea8acd4fb23fdf4718f2942051d51613"}