{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:7SP244MCSOUDX23Y2YGGKUZ6EP","short_pith_number":"pith:7SP244MC","canonical_record":{"source":{"id":"0912.2898","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-12-15T14:00:05Z","cross_cats_sorted":[],"title_canon_sha256":"0ca77108f147c7d559cc2b62659c4032b8596727292c230c8a4d5ea3ff53d917","abstract_canon_sha256":"faa486b33d46c86d1f6cb85d0b7101f668e456cbbfc3d319c4a75d9c0e52b18f"},"schema_version":"1.0"},"canonical_sha256":"fc9fae718293a83beb78d60c65533e23f9295241c00a1100e944648891792820","source":{"kind":"arxiv","id":"0912.2898","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.2898","created_at":"2026-05-18T04:10:23Z"},{"alias_kind":"arxiv_version","alias_value":"0912.2898v3","created_at":"2026-05-18T04:10:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.2898","created_at":"2026-05-18T04:10:23Z"},{"alias_kind":"pith_short_12","alias_value":"7SP244MCSOUD","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"7SP244MCSOUDX23Y","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"7SP244MC","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:7SP244MCSOUDX23Y2YGGKUZ6EP","target":"record","payload":{"canonical_record":{"source":{"id":"0912.2898","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-12-15T14:00:05Z","cross_cats_sorted":[],"title_canon_sha256":"0ca77108f147c7d559cc2b62659c4032b8596727292c230c8a4d5ea3ff53d917","abstract_canon_sha256":"faa486b33d46c86d1f6cb85d0b7101f668e456cbbfc3d319c4a75d9c0e52b18f"},"schema_version":"1.0"},"canonical_sha256":"fc9fae718293a83beb78d60c65533e23f9295241c00a1100e944648891792820","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:23.858702Z","signature_b64":"SCz05+vQvV2xYbLzLdD7fUwuX2m3lInBZyMm+tU3CmFvMPispW3y8QKOcwhicXdFAAgRb8tzKuB4Xj2Mn9NzDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc9fae718293a83beb78d60c65533e23f9295241c00a1100e944648891792820","last_reissued_at":"2026-05-18T04:10:23.858160Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:23.858160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.2898","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":"2026-05-18T04:10:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nbzkDELzgQqIF+NDvqUt5shvCE9NOG9bRkD9jmZVN/ZzSBuR82pSfhYcvVY1Zo1nGz2HrHNA/yD4snCrOJOkBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T00:30:26.656121Z"},"content_sha256":"661346c4c332e663ddf3375886615b96592a6fe834db7cb97693e6a2e318f981","schema_version":"1.0","event_id":"sha256:661346c4c332e663ddf3375886615b96592a6fe834db7cb97693e6a2e318f981"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:7SP244MCSOUDX23Y2YGGKUZ6EP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On generalisations of Losev-Manin moduli spaces for classical root systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Mark Blume, Victor Batyrev","submitted_at":"2009-12-15T14:00:05Z","abstract_excerpt":"Losev and Manin introduced fine moduli spaces $\\bar{L}_n$ of stable $n$-pointed chains of projective lines. The moduli space $\\bar{L}_{n+1}$ is isomorphic to the toric variety $X(A_n)$ associated with the root system $A_n$, which is part of a general construction to associate with a root system $R$ of rank $n$ an $n$-dimensional smooth projective toric variety $X(R)$. In this paper we investigate generalisations of the Losev-Manin moduli spaces for the other families of classical root systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2898","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":"2026-05-18T04:10:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ahMX9rTbPrumInd0QGR8bKDeqHDuBZXryTl/w4LEvRw+fw5vmeN/14Llsc3CqtBZVfqDeYcg9+A41asN3/BGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T00:30:26.656804Z"},"content_sha256":"2f74d192638132b5221bf65fd1c3cf20479683b140316d803b623c7012518bc2","schema_version":"1.0","event_id":"sha256:2f74d192638132b5221bf65fd1c3cf20479683b140316d803b623c7012518bc2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7SP244MCSOUDX23Y2YGGKUZ6EP/bundle.json","state_url":"https://pith.science/pith/7SP244MCSOUDX23Y2YGGKUZ6EP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7SP244MCSOUDX23Y2YGGKUZ6EP/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":"2026-05-24T00:30:26Z","links":{"resolver":"https://pith.science/pith/7SP244MCSOUDX23Y2YGGKUZ6EP","bundle":"https://pith.science/pith/7SP244MCSOUDX23Y2YGGKUZ6EP/bundle.json","state":"https://pith.science/pith/7SP244MCSOUDX23Y2YGGKUZ6EP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7SP244MCSOUDX23Y2YGGKUZ6EP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:7SP244MCSOUDX23Y2YGGKUZ6EP","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":"faa486b33d46c86d1f6cb85d0b7101f668e456cbbfc3d319c4a75d9c0e52b18f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-12-15T14:00:05Z","title_canon_sha256":"0ca77108f147c7d559cc2b62659c4032b8596727292c230c8a4d5ea3ff53d917"},"schema_version":"1.0","source":{"id":"0912.2898","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.2898","created_at":"2026-05-18T04:10:23Z"},{"alias_kind":"arxiv_version","alias_value":"0912.2898v3","created_at":"2026-05-18T04:10:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.2898","created_at":"2026-05-18T04:10:23Z"},{"alias_kind":"pith_short_12","alias_value":"7SP244MCSOUD","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"7SP244MCSOUDX23Y","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"7SP244MC","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:2f74d192638132b5221bf65fd1c3cf20479683b140316d803b623c7012518bc2","target":"graph","created_at":"2026-05-18T04:10:23Z","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":"Losev and Manin introduced fine moduli spaces $\\bar{L}_n$ of stable $n$-pointed chains of projective lines. The moduli space $\\bar{L}_{n+1}$ is isomorphic to the toric variety $X(A_n)$ associated with the root system $A_n$, which is part of a general construction to associate with a root system $R$ of rank $n$ an $n$-dimensional smooth projective toric variety $X(R)$. In this paper we investigate generalisations of the Losev-Manin moduli spaces for the other families of classical root systems.","authors_text":"Mark Blume, Victor Batyrev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-12-15T14:00:05Z","title":"On generalisations of Losev-Manin moduli spaces for classical root systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2898","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":"sha256:661346c4c332e663ddf3375886615b96592a6fe834db7cb97693e6a2e318f981","target":"record","created_at":"2026-05-18T04:10:23Z","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":"faa486b33d46c86d1f6cb85d0b7101f668e456cbbfc3d319c4a75d9c0e52b18f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-12-15T14:00:05Z","title_canon_sha256":"0ca77108f147c7d559cc2b62659c4032b8596727292c230c8a4d5ea3ff53d917"},"schema_version":"1.0","source":{"id":"0912.2898","kind":"arxiv","version":3}},"canonical_sha256":"fc9fae718293a83beb78d60c65533e23f9295241c00a1100e944648891792820","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc9fae718293a83beb78d60c65533e23f9295241c00a1100e944648891792820","first_computed_at":"2026-05-18T04:10:23.858160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:23.858160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SCz05+vQvV2xYbLzLdD7fUwuX2m3lInBZyMm+tU3CmFvMPispW3y8QKOcwhicXdFAAgRb8tzKuB4Xj2Mn9NzDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:23.858702Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.2898","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:661346c4c332e663ddf3375886615b96592a6fe834db7cb97693e6a2e318f981","sha256:2f74d192638132b5221bf65fd1c3cf20479683b140316d803b623c7012518bc2"],"state_sha256":"73662e366fd50c26fa1aaab92a6951a39cd22ddf3db373845720fd61c0145a98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XHg5ESUMDYDQiyILLWa3sDuoLDbdizMYVm75Lkmle4/vrRG265XlmpXK2bmxvC+X/XBQr/QkHGqWJOgVJ0kiDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T00:30:26.660265Z","bundle_sha256":"40f0c02d5effa2a1e711bc669a6dfeb3afbcd46680cca605e436b9c7953f98d0"}}