{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:BM6X43FWIAPANWSAKIQV3Z3D4X","short_pith_number":"pith:BM6X43FW","canonical_record":{"source":{"id":"0709.1768","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"2007-09-12T07:48:33Z","cross_cats_sorted":[],"title_canon_sha256":"2b589ef9880b67120a55c5f4f118530ab6f47104812a6806841aa88115eda0af","abstract_canon_sha256":"e0dbdd0119799f4ab02381ddea2834ed22a977b122d2f416a5dba5a2124f7281"},"schema_version":"1.0"},"canonical_sha256":"0b3d7e6cb6401e06da4052215de763e5e4b779606fab73ada7eb6d24c3721073","source":{"kind":"arxiv","id":"0709.1768","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0709.1768","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"arxiv_version","alias_value":"0709.1768v1","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.1768","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"pith_short_12","alias_value":"BM6X43FWIAPA","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"BM6X43FWIAPANWSA","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"BM6X43FW","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:BM6X43FWIAPANWSAKIQV3Z3D4X","target":"record","payload":{"canonical_record":{"source":{"id":"0709.1768","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"2007-09-12T07:48:33Z","cross_cats_sorted":[],"title_canon_sha256":"2b589ef9880b67120a55c5f4f118530ab6f47104812a6806841aa88115eda0af","abstract_canon_sha256":"e0dbdd0119799f4ab02381ddea2834ed22a977b122d2f416a5dba5a2124f7281"},"schema_version":"1.0"},"canonical_sha256":"0b3d7e6cb6401e06da4052215de763e5e4b779606fab73ada7eb6d24c3721073","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:22:06.653881Z","signature_b64":"2UW9rtCvUjpZGWE2z/j0IIe11a/7RGJ0TyzOOfsB+PX3cZ6xfzaNtBl+TIsB7GnimhHxA/nbdkCXaanTQL3ADQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b3d7e6cb6401e06da4052215de763e5e4b779606fab73ada7eb6d24c3721073","last_reissued_at":"2026-05-18T03:22:06.653036Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:22:06.653036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0709.1768","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:22:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bW6d2qpki5RJTKU6HYajVGY2Fu0pQ54XVFDeRQQPxtRzEiXh8Vv3qHf2CywJWG9QEre3L04xRN/3JC+SAG7MBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:50:50.406126Z"},"content_sha256":"5296c5202dba19083f5a0523fbafa2e1d5a44af3c6426b237ab62d265b2f44a3","schema_version":"1.0","event_id":"sha256:5296c5202dba19083f5a0523fbafa2e1d5a44af3c6426b237ab62d265b2f44a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:BM6X43FWIAPANWSAKIQV3Z3D4X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cohomology of $\\mathfrak {osp}(1|2)$ acting on linear differential operators on the supercircle $S^{1|1}","license":"","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Imed Basdouri, Mabrouk Ben Ammar","submitted_at":"2007-09-12T07:48:33Z","abstract_excerpt":"We compute the first cohomology spaces $H^1(\\mathfrak{osp}(1|2);\\mathfrak{D}_{\\lambda,\\mu})$ ($\\lambda, \\mu\\in\\mathbb{R}$) of the Lie superalgebra $\\mathfrak{osp}(1|2)$ with coefficients in the superspace $\\mathfrak{D}_{\\lambda,\\mu}$ of linear differential operators acting on weighted densities on the supercircle $S^{1|1}$. The structure of these spaces was conjectured in \\cite{gmo}. In fact, we prove here that the situation is a little bit more complicated. (To appear in LMP.)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.1768","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:22:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Imqx4C+qU6Vg0k0QhkiP6Yv7KCAeSNNiv2v6dEhNBcNLyehO4ggdFadHpLsSR960iPUNSbTA8eQOXF8jWQLBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:50:50.406497Z"},"content_sha256":"7cb4491eb2219304893051ea499f22ee1120dd30e0f00ba6eb022013210b1cc8","schema_version":"1.0","event_id":"sha256:7cb4491eb2219304893051ea499f22ee1120dd30e0f00ba6eb022013210b1cc8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BM6X43FWIAPANWSAKIQV3Z3D4X/bundle.json","state_url":"https://pith.science/pith/BM6X43FWIAPANWSAKIQV3Z3D4X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BM6X43FWIAPANWSAKIQV3Z3D4X/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-21T20:50:50Z","links":{"resolver":"https://pith.science/pith/BM6X43FWIAPANWSAKIQV3Z3D4X","bundle":"https://pith.science/pith/BM6X43FWIAPANWSAKIQV3Z3D4X/bundle.json","state":"https://pith.science/pith/BM6X43FWIAPANWSAKIQV3Z3D4X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BM6X43FWIAPANWSAKIQV3Z3D4X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:BM6X43FWIAPANWSAKIQV3Z3D4X","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":"e0dbdd0119799f4ab02381ddea2834ed22a977b122d2f416a5dba5a2124f7281","cross_cats_sorted":[],"license":"","primary_cat":"math.RT","submitted_at":"2007-09-12T07:48:33Z","title_canon_sha256":"2b589ef9880b67120a55c5f4f118530ab6f47104812a6806841aa88115eda0af"},"schema_version":"1.0","source":{"id":"0709.1768","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0709.1768","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"arxiv_version","alias_value":"0709.1768v1","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.1768","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"pith_short_12","alias_value":"BM6X43FWIAPA","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"BM6X43FWIAPANWSA","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"BM6X43FW","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:7cb4491eb2219304893051ea499f22ee1120dd30e0f00ba6eb022013210b1cc8","target":"graph","created_at":"2026-05-18T03:22:06Z","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"},"paper":{"abstract_excerpt":"We compute the first cohomology spaces $H^1(\\mathfrak{osp}(1|2);\\mathfrak{D}_{\\lambda,\\mu})$ ($\\lambda, \\mu\\in\\mathbb{R}$) of the Lie superalgebra $\\mathfrak{osp}(1|2)$ with coefficients in the superspace $\\mathfrak{D}_{\\lambda,\\mu}$ of linear differential operators acting on weighted densities on the supercircle $S^{1|1}$. The structure of these spaces was conjectured in \\cite{gmo}. In fact, we prove here that the situation is a little bit more complicated. (To appear in LMP.)","authors_text":"Imed Basdouri, Mabrouk Ben Ammar","cross_cats":[],"headline":"","license":"","primary_cat":"math.RT","submitted_at":"2007-09-12T07:48:33Z","title":"Cohomology of $\\mathfrak {osp}(1|2)$ acting on linear differential operators on the supercircle $S^{1|1}"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.1768","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":"sha256:5296c5202dba19083f5a0523fbafa2e1d5a44af3c6426b237ab62d265b2f44a3","target":"record","created_at":"2026-05-18T03:22:06Z","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":"e0dbdd0119799f4ab02381ddea2834ed22a977b122d2f416a5dba5a2124f7281","cross_cats_sorted":[],"license":"","primary_cat":"math.RT","submitted_at":"2007-09-12T07:48:33Z","title_canon_sha256":"2b589ef9880b67120a55c5f4f118530ab6f47104812a6806841aa88115eda0af"},"schema_version":"1.0","source":{"id":"0709.1768","kind":"arxiv","version":1}},"canonical_sha256":"0b3d7e6cb6401e06da4052215de763e5e4b779606fab73ada7eb6d24c3721073","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b3d7e6cb6401e06da4052215de763e5e4b779606fab73ada7eb6d24c3721073","first_computed_at":"2026-05-18T03:22:06.653036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:22:06.653036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2UW9rtCvUjpZGWE2z/j0IIe11a/7RGJ0TyzOOfsB+PX3cZ6xfzaNtBl+TIsB7GnimhHxA/nbdkCXaanTQL3ADQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:22:06.653881Z","signed_message":"canonical_sha256_bytes"},"source_id":"0709.1768","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5296c5202dba19083f5a0523fbafa2e1d5a44af3c6426b237ab62d265b2f44a3","sha256:7cb4491eb2219304893051ea499f22ee1120dd30e0f00ba6eb022013210b1cc8"],"state_sha256":"ccfd571982c6810e1870c41f7bcbf490d28b0279307efb7e2c89ab67fe7d0df6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XPM2dQ1OSz0JmUNGKVGJINHUR+PRBqWmDyAoMt1LuUTZOvd0/kgzRR6MG5ksv955lIibl6/eIlKbEick7i8uAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T20:50:50.408516Z","bundle_sha256":"1a3611ea1563c1c717a9199d2b2857b77e3b2a62579358f73ded5aee901c9b56"}}