{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3VDN3MGLR5PKFDJF3JC2KKQPMB","short_pith_number":"pith:3VDN3MGL","canonical_record":{"source":{"id":"1511.05059","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-11-16T17:47:17Z","cross_cats_sorted":[],"title_canon_sha256":"ee7490db1d82e96c34a8611b7e70e593adb13b0b4d1bc052864685e79407c2a5","abstract_canon_sha256":"a259e556c6df49b8323618c0d1e0a0577952b5d31b8dde5212c29a4a34099b03"},"schema_version":"1.0"},"canonical_sha256":"dd46ddb0cb8f5ea28d25da45a52a0f60405b2733d62a64cf46730c00783ee0b1","source":{"kind":"arxiv","id":"1511.05059","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05059","created_at":"2026-05-18T01:13:30Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05059v2","created_at":"2026-05-18T01:13:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05059","created_at":"2026-05-18T01:13:30Z"},{"alias_kind":"pith_short_12","alias_value":"3VDN3MGLR5PK","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3VDN3MGLR5PKFDJF","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3VDN3MGL","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3VDN3MGLR5PKFDJF3JC2KKQPMB","target":"record","payload":{"canonical_record":{"source":{"id":"1511.05059","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-11-16T17:47:17Z","cross_cats_sorted":[],"title_canon_sha256":"ee7490db1d82e96c34a8611b7e70e593adb13b0b4d1bc052864685e79407c2a5","abstract_canon_sha256":"a259e556c6df49b8323618c0d1e0a0577952b5d31b8dde5212c29a4a34099b03"},"schema_version":"1.0"},"canonical_sha256":"dd46ddb0cb8f5ea28d25da45a52a0f60405b2733d62a64cf46730c00783ee0b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:30.752873Z","signature_b64":"+Wf3fyVsXc+QbVYAkltj/CItXsX0X+wDjRnj2/03/oDwT1QzKywHWlv+YVyyAWkX13qHJLVCGCCbNs6VSTsKDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd46ddb0cb8f5ea28d25da45a52a0f60405b2733d62a64cf46730c00783ee0b1","last_reissued_at":"2026-05-18T01:13:30.752199Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:30.752199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.05059","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":"2026-05-18T01:13:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H7TsuxWnxMyac1dDAjd57RrMCKgsk/K+0AcW162AEd5Axhz9hpuiF8MeA0t+wts1v/m5vFprgkhnu7C2xxx7AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T01:20:33.634073Z"},"content_sha256":"77555c06a781e5e9f9185bd3347462b483a6cd96f69d80db16651259443abad0","schema_version":"1.0","event_id":"sha256:77555c06a781e5e9f9185bd3347462b483a6cd96f69d80db16651259443abad0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3VDN3MGLR5PKFDJF3JC2KKQPMB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing automorphisms of Mori dream spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Juergen Hausen, Ruediger Wolf, Simon Keicher","submitted_at":"2015-11-16T17:47:17Z","abstract_excerpt":"We present an algorithm to compute the automorphism group of a Mori dream space. As an example calculation, we determine the automorphism groups of singular cubic surfaces with general parameters. The strategy is to study graded automorphisms of affine algebras graded by a finitely generated abelian groups and apply the results to the Cox ring. Besides the application to Mori dream spaces, our results could be used for symmetry based computing, e.g. for Gr\\\"obner bases or tropical varieties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05059","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":"2026-05-18T01:13:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/guOS5OlAUv+E4E6D1pS2heD9nlIuyXPYC3DtlE+M7b41GQn0Hu35STtLh6UqYX9ulNOSPS9Etv/p3RbWTIACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T01:20:33.634441Z"},"content_sha256":"f9a8d910c43969c51bacfd63ee66dadc372555a998cbac69f34bd1defab8dab6","schema_version":"1.0","event_id":"sha256:f9a8d910c43969c51bacfd63ee66dadc372555a998cbac69f34bd1defab8dab6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3VDN3MGLR5PKFDJF3JC2KKQPMB/bundle.json","state_url":"https://pith.science/pith/3VDN3MGLR5PKFDJF3JC2KKQPMB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3VDN3MGLR5PKFDJF3JC2KKQPMB/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":"2026-06-27T01:20:33Z","links":{"resolver":"https://pith.science/pith/3VDN3MGLR5PKFDJF3JC2KKQPMB","bundle":"https://pith.science/pith/3VDN3MGLR5PKFDJF3JC2KKQPMB/bundle.json","state":"https://pith.science/pith/3VDN3MGLR5PKFDJF3JC2KKQPMB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3VDN3MGLR5PKFDJF3JC2KKQPMB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3VDN3MGLR5PKFDJF3JC2KKQPMB","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":"a259e556c6df49b8323618c0d1e0a0577952b5d31b8dde5212c29a4a34099b03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-11-16T17:47:17Z","title_canon_sha256":"ee7490db1d82e96c34a8611b7e70e593adb13b0b4d1bc052864685e79407c2a5"},"schema_version":"1.0","source":{"id":"1511.05059","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05059","created_at":"2026-05-18T01:13:30Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05059v2","created_at":"2026-05-18T01:13:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05059","created_at":"2026-05-18T01:13:30Z"},{"alias_kind":"pith_short_12","alias_value":"3VDN3MGLR5PK","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3VDN3MGLR5PKFDJF","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3VDN3MGL","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:f9a8d910c43969c51bacfd63ee66dadc372555a998cbac69f34bd1defab8dab6","target":"graph","created_at":"2026-05-18T01:13:30Z","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":"We present an algorithm to compute the automorphism group of a Mori dream space. As an example calculation, we determine the automorphism groups of singular cubic surfaces with general parameters. The strategy is to study graded automorphisms of affine algebras graded by a finitely generated abelian groups and apply the results to the Cox ring. Besides the application to Mori dream spaces, our results could be used for symmetry based computing, e.g. for Gr\\\"obner bases or tropical varieties.","authors_text":"Juergen Hausen, Ruediger Wolf, Simon Keicher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-11-16T17:47:17Z","title":"Computing automorphisms of Mori dream spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05059","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":"sha256:77555c06a781e5e9f9185bd3347462b483a6cd96f69d80db16651259443abad0","target":"record","created_at":"2026-05-18T01:13:30Z","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":"a259e556c6df49b8323618c0d1e0a0577952b5d31b8dde5212c29a4a34099b03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-11-16T17:47:17Z","title_canon_sha256":"ee7490db1d82e96c34a8611b7e70e593adb13b0b4d1bc052864685e79407c2a5"},"schema_version":"1.0","source":{"id":"1511.05059","kind":"arxiv","version":2}},"canonical_sha256":"dd46ddb0cb8f5ea28d25da45a52a0f60405b2733d62a64cf46730c00783ee0b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd46ddb0cb8f5ea28d25da45a52a0f60405b2733d62a64cf46730c00783ee0b1","first_computed_at":"2026-05-18T01:13:30.752199Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:30.752199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+Wf3fyVsXc+QbVYAkltj/CItXsX0X+wDjRnj2/03/oDwT1QzKywHWlv+YVyyAWkX13qHJLVCGCCbNs6VSTsKDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:30.752873Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.05059","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77555c06a781e5e9f9185bd3347462b483a6cd96f69d80db16651259443abad0","sha256:f9a8d910c43969c51bacfd63ee66dadc372555a998cbac69f34bd1defab8dab6"],"state_sha256":"e478c4bd46d794d65b1984fafe4fe4fcdd2a7d239cbaa63cd50c405641cca0b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YkRC3bogVAK7xkpqurFIZvSsS74UEezsAIsPoNQACbt4u71f+N1zZNPM1QQJD+FivSCuggRZgG4AgDtt3I2LDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T01:20:33.636294Z","bundle_sha256":"6f640b843d1758d8c9971e13c7fb38b3f5014229230672a5f180f1390f4914b0"}}