{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RLFIWA726BO56DVU7NU6KT6YPA","short_pith_number":"pith:RLFIWA72","canonical_record":{"source":{"id":"1308.2604","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-12T15:58:22Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"6676e5b28a30d4d3bd19174580fcf6ffc10bdf3bc0323c9d02d96636fb3684a0","abstract_canon_sha256":"cbd5eb916189f540d26fb69acca6f7cbdd14284364db3372d3220a69d09bfa78"},"schema_version":"1.0"},"canonical_sha256":"8aca8b03faf05ddf0eb4fb69e54fd8781a95a9f66a7d239d3e8f7fab9d1beb15","source":{"kind":"arxiv","id":"1308.2604","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2604","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2604v2","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2604","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"pith_short_12","alias_value":"RLFIWA726BO5","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RLFIWA726BO56DVU","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RLFIWA72","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RLFIWA726BO56DVU7NU6KT6YPA","target":"record","payload":{"canonical_record":{"source":{"id":"1308.2604","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-12T15:58:22Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"6676e5b28a30d4d3bd19174580fcf6ffc10bdf3bc0323c9d02d96636fb3684a0","abstract_canon_sha256":"cbd5eb916189f540d26fb69acca6f7cbdd14284364db3372d3220a69d09bfa78"},"schema_version":"1.0"},"canonical_sha256":"8aca8b03faf05ddf0eb4fb69e54fd8781a95a9f66a7d239d3e8f7fab9d1beb15","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:19.969579Z","signature_b64":"Tl9n16/pBlSsXcfcF0zmK8W6afE02DGQwnx/6Z24VsyV5+F0rermY9y++mYSAV8t8NN98HsFYHNDxRt/fFwbAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8aca8b03faf05ddf0eb4fb69e54fd8781a95a9f66a7d239d3e8f7fab9d1beb15","last_reissued_at":"2026-05-18T02:25:19.969186Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:19.969186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.2604","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:25:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GmROctwRy0XHdAcQMGxT5Qqkq4z0KVvIKVRZP3o8w44BJ+YlYRD/KQCZxOfBi9xHzMrCzMAedVoWRL4dAizWCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T01:45:03.415943Z"},"content_sha256":"39977e11c882fda04ab11cb909d33a7acd7128ae239bba26ebdd43a618c013c1","schema_version":"1.0","event_id":"sha256:39977e11c882fda04ab11cb909d33a7acd7128ae239bba26ebdd43a618c013c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RLFIWA726BO56DVU7NU6KT6YPA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On algebraic spaces with an action of G_m","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Vladimir Drinfeld","submitted_at":"2013-08-12T15:58:22Z","abstract_excerpt":"Let Z be an algebraic space of finite type over a field, equipped with an action of the multiplicative group $G_m$. In this situation we define and study a certain algebraic space equipped with an unramified morphism to $A^1\\times Z\\times Z$, where $A^1$ is the affine line. (If Z is affine and smooth this is just the closure of the graph of the action map $G_m\\times Z\\to Z$.)\n  In articles joint with D.Gaitsgory we use this set-up to prove a new result in the geometric theory of automorphic forms and to give a new proof of a very important theorem of T. Braden."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2604","kind":"arxiv","version":2},"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":"2026-05-18T02:25:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oO1idLkdqCwU4XxgeVZbwwrQBQrcwhSIkkz0vDXK2CqP+j/XVyXO8lDBJRzR6VjsATmwMwpdIYqF9khGPLusDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T01:45:03.416714Z"},"content_sha256":"60cf803093d719ebf954e2902ca4df5b5b4c550b202034649c991364e12410ca","schema_version":"1.0","event_id":"sha256:60cf803093d719ebf954e2902ca4df5b5b4c550b202034649c991364e12410ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RLFIWA726BO56DVU7NU6KT6YPA/bundle.json","state_url":"https://pith.science/pith/RLFIWA726BO56DVU7NU6KT6YPA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RLFIWA726BO56DVU7NU6KT6YPA/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":"2026-05-24T01:45:03Z","links":{"resolver":"https://pith.science/pith/RLFIWA726BO56DVU7NU6KT6YPA","bundle":"https://pith.science/pith/RLFIWA726BO56DVU7NU6KT6YPA/bundle.json","state":"https://pith.science/pith/RLFIWA726BO56DVU7NU6KT6YPA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RLFIWA726BO56DVU7NU6KT6YPA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RLFIWA726BO56DVU7NU6KT6YPA","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":"cbd5eb916189f540d26fb69acca6f7cbdd14284364db3372d3220a69d09bfa78","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-12T15:58:22Z","title_canon_sha256":"6676e5b28a30d4d3bd19174580fcf6ffc10bdf3bc0323c9d02d96636fb3684a0"},"schema_version":"1.0","source":{"id":"1308.2604","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2604","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2604v2","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2604","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"pith_short_12","alias_value":"RLFIWA726BO5","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RLFIWA726BO56DVU","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RLFIWA72","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:60cf803093d719ebf954e2902ca4df5b5b4c550b202034649c991364e12410ca","target":"graph","created_at":"2026-05-18T02:25:19Z","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 Z be an algebraic space of finite type over a field, equipped with an action of the multiplicative group $G_m$. In this situation we define and study a certain algebraic space equipped with an unramified morphism to $A^1\\times Z\\times Z$, where $A^1$ is the affine line. (If Z is affine and smooth this is just the closure of the graph of the action map $G_m\\times Z\\to Z$.)\n  In articles joint with D.Gaitsgory we use this set-up to prove a new result in the geometric theory of automorphic forms and to give a new proof of a very important theorem of T. Braden.","authors_text":"Vladimir Drinfeld","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-12T15:58:22Z","title":"On algebraic spaces with an action of G_m"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2604","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":"sha256:39977e11c882fda04ab11cb909d33a7acd7128ae239bba26ebdd43a618c013c1","target":"record","created_at":"2026-05-18T02:25:19Z","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":"cbd5eb916189f540d26fb69acca6f7cbdd14284364db3372d3220a69d09bfa78","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-12T15:58:22Z","title_canon_sha256":"6676e5b28a30d4d3bd19174580fcf6ffc10bdf3bc0323c9d02d96636fb3684a0"},"schema_version":"1.0","source":{"id":"1308.2604","kind":"arxiv","version":2}},"canonical_sha256":"8aca8b03faf05ddf0eb4fb69e54fd8781a95a9f66a7d239d3e8f7fab9d1beb15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8aca8b03faf05ddf0eb4fb69e54fd8781a95a9f66a7d239d3e8f7fab9d1beb15","first_computed_at":"2026-05-18T02:25:19.969186Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:19.969186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tl9n16/pBlSsXcfcF0zmK8W6afE02DGQwnx/6Z24VsyV5+F0rermY9y++mYSAV8t8NN98HsFYHNDxRt/fFwbAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:19.969579Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.2604","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39977e11c882fda04ab11cb909d33a7acd7128ae239bba26ebdd43a618c013c1","sha256:60cf803093d719ebf954e2902ca4df5b5b4c550b202034649c991364e12410ca"],"state_sha256":"9a60321ad88ef736702ebcf3cc20f4555996bbc1ccf3fee8554715f013dfbf06"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dbMSL+0SDD9aO0TnBxhXr+UVLfcIaYePyJRFLNYuHN0pTPyRw3sDz2IlQDyVHsVNs7WUC2b/cW+R6vl8QId/Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T01:45:03.420790Z","bundle_sha256":"df3e7eea7e8cc202251cd88ce681e76d7bb04f0871a4b90d44bc0bb390f1076e"}}