{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:VYSOFQYVH7OMWXTHB3FCEQTMI7","short_pith_number":"pith:VYSOFQYV","canonical_record":{"source":{"id":"1105.4830","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-24T16:53:25Z","cross_cats_sorted":["math-ph","math.MP","math.SG"],"title_canon_sha256":"5ab9efd513ddaa97e4f25c60a5a1f3e3ce8422d96e000512119c94e55f769d30","abstract_canon_sha256":"b9b3463b9e893babae0d15a1add3bd194fc7bb3e44f83be9bba331a859c52fc9"},"schema_version":"1.0"},"canonical_sha256":"ae24e2c3153fdccb5e670eca22426c47dce15d1d4cccf3e5812356072375b5d4","source":{"kind":"arxiv","id":"1105.4830","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4830","created_at":"2026-05-18T01:21:23Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4830v3","created_at":"2026-05-18T01:21:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4830","created_at":"2026-05-18T01:21:23Z"},{"alias_kind":"pith_short_12","alias_value":"VYSOFQYVH7OM","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VYSOFQYVH7OMWXTH","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VYSOFQYV","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:VYSOFQYVH7OMWXTHB3FCEQTMI7","target":"record","payload":{"canonical_record":{"source":{"id":"1105.4830","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-24T16:53:25Z","cross_cats_sorted":["math-ph","math.MP","math.SG"],"title_canon_sha256":"5ab9efd513ddaa97e4f25c60a5a1f3e3ce8422d96e000512119c94e55f769d30","abstract_canon_sha256":"b9b3463b9e893babae0d15a1add3bd194fc7bb3e44f83be9bba331a859c52fc9"},"schema_version":"1.0"},"canonical_sha256":"ae24e2c3153fdccb5e670eca22426c47dce15d1d4cccf3e5812356072375b5d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:23.389598Z","signature_b64":"nX5zOo6o9ZA5staa2B+2NDl399Ajr9b1/Zy3KwXnXJ7AsdeFnj12FIrbfSBx6jN7giSx9CWikf307f4QWmqBCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae24e2c3153fdccb5e670eca22426c47dce15d1d4cccf3e5812356072375b5d4","last_reissued_at":"2026-05-18T01:21:23.389056Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:23.389056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.4830","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:21:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P78jrPniD+jWbP9BQQtAPr6FPwLgdn7cg2CvMtTIfpcyFwsTbvfpF9zUcIQHIIvhI8IZEQuSJKzocYl28JqmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:27:06.610490Z"},"content_sha256":"aa9ebdbf439258c17325437e07aac5bd4c0716f79cfd26ade7b527165167b41f","schema_version":"1.0","event_id":"sha256:aa9ebdbf439258c17325437e07aac5bd4c0716f79cfd26ade7b527165167b41f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:VYSOFQYVH7OMWXTHB3FCEQTMI7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compactifications of reductive groups as moduli stacks of bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SG"],"primary_cat":"math.AG","authors_text":"Johan Martens, Michael Thaddeus","submitted_at":"2011-05-24T16:53:25Z","abstract_excerpt":"Let G be a split reductive group. We introduce the moduli problem of \"bundle chains\" parametrizing framed principal G-bundles on chains of lines. Any fan supported in a Weyl chamber determines a stability condition on bundle chains. Its moduli stack provides an equivariant toroidal compactification of G. All toric orbifolds may be thus obtained. Moreover, we get a canonical compactification of any semisimple G, which agrees with the wonderful compactification in the adjoint case, but which in other cases is an orbifold. Finally, we describe the connections with Losev-Manin's spaces of weighted"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4830","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":""},"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":"2026-05-18T01:21:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0oOFSaede1aP9XfSnMF8p5HTJYL8AGa6hFt7NgliGJgw7tBKAz0OwUOypdGcLqP8Kr5a2xpk34aiFlURqueJAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:27:06.611173Z"},"content_sha256":"3ea8b16435193ec6a31e487f505dfa78163e0942b57e6e3a84fe3aba127847b6","schema_version":"1.0","event_id":"sha256:3ea8b16435193ec6a31e487f505dfa78163e0942b57e6e3a84fe3aba127847b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VYSOFQYVH7OMWXTHB3FCEQTMI7/bundle.json","state_url":"https://pith.science/pith/VYSOFQYVH7OMWXTHB3FCEQTMI7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VYSOFQYVH7OMWXTHB3FCEQTMI7/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":"2026-05-27T04:27:06Z","links":{"resolver":"https://pith.science/pith/VYSOFQYVH7OMWXTHB3FCEQTMI7","bundle":"https://pith.science/pith/VYSOFQYVH7OMWXTHB3FCEQTMI7/bundle.json","state":"https://pith.science/pith/VYSOFQYVH7OMWXTHB3FCEQTMI7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VYSOFQYVH7OMWXTHB3FCEQTMI7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VYSOFQYVH7OMWXTHB3FCEQTMI7","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":"b9b3463b9e893babae0d15a1add3bd194fc7bb3e44f83be9bba331a859c52fc9","cross_cats_sorted":["math-ph","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-24T16:53:25Z","title_canon_sha256":"5ab9efd513ddaa97e4f25c60a5a1f3e3ce8422d96e000512119c94e55f769d30"},"schema_version":"1.0","source":{"id":"1105.4830","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4830","created_at":"2026-05-18T01:21:23Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4830v3","created_at":"2026-05-18T01:21:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4830","created_at":"2026-05-18T01:21:23Z"},{"alias_kind":"pith_short_12","alias_value":"VYSOFQYVH7OM","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VYSOFQYVH7OMWXTH","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VYSOFQYV","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:3ea8b16435193ec6a31e487f505dfa78163e0942b57e6e3a84fe3aba127847b6","target":"graph","created_at":"2026-05-18T01:21:23Z","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 G be a split reductive group. We introduce the moduli problem of \"bundle chains\" parametrizing framed principal G-bundles on chains of lines. Any fan supported in a Weyl chamber determines a stability condition on bundle chains. Its moduli stack provides an equivariant toroidal compactification of G. All toric orbifolds may be thus obtained. Moreover, we get a canonical compactification of any semisimple G, which agrees with the wonderful compactification in the adjoint case, but which in other cases is an orbifold. Finally, we describe the connections with Losev-Manin's spaces of weighted","authors_text":"Johan Martens, Michael Thaddeus","cross_cats":["math-ph","math.MP","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-24T16:53:25Z","title":"Compactifications of reductive groups as moduli stacks of bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4830","kind":"arxiv","version":3},"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:aa9ebdbf439258c17325437e07aac5bd4c0716f79cfd26ade7b527165167b41f","target":"record","created_at":"2026-05-18T01:21:23Z","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":"b9b3463b9e893babae0d15a1add3bd194fc7bb3e44f83be9bba331a859c52fc9","cross_cats_sorted":["math-ph","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-24T16:53:25Z","title_canon_sha256":"5ab9efd513ddaa97e4f25c60a5a1f3e3ce8422d96e000512119c94e55f769d30"},"schema_version":"1.0","source":{"id":"1105.4830","kind":"arxiv","version":3}},"canonical_sha256":"ae24e2c3153fdccb5e670eca22426c47dce15d1d4cccf3e5812356072375b5d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae24e2c3153fdccb5e670eca22426c47dce15d1d4cccf3e5812356072375b5d4","first_computed_at":"2026-05-18T01:21:23.389056Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:23.389056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nX5zOo6o9ZA5staa2B+2NDl399Ajr9b1/Zy3KwXnXJ7AsdeFnj12FIrbfSBx6jN7giSx9CWikf307f4QWmqBCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:23.389598Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4830","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa9ebdbf439258c17325437e07aac5bd4c0716f79cfd26ade7b527165167b41f","sha256:3ea8b16435193ec6a31e487f505dfa78163e0942b57e6e3a84fe3aba127847b6"],"state_sha256":"ef63a4dedc04ec1d0df9615ea8843c1ddb14942b3894ed16ca1dc6c83b0ac55e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t0GGg3BAy3XsVAFwOuUdeWyw15uwjHtvxsAQKS85rIFDmh6lgkagyyB+TZt6xk8561Obeg+N3JugVlK8S1tjDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T04:27:06.614580Z","bundle_sha256":"3e9320d663be2dc6af83cd7b804861f4e65dd4da88429d62862970676a74b22f"}}