{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:RBVSGQRNK7OTR65PSA3S6SKPIY","short_pith_number":"pith:RBVSGQRN","canonical_record":{"source":{"id":"1008.0954","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-08-05T11:46:24Z","cross_cats_sorted":["math.AG","math.GR"],"title_canon_sha256":"3ee6ead95351c9e228108e18658f2bcab2f6bc1c21529ca6918de2d06922eefb","abstract_canon_sha256":"bd00f931a35e3749577191510ec0dfcd10b38fa697e341505697d2e5115f658e"},"schema_version":"1.0"},"canonical_sha256":"886b23422d57dd38fbaf90372f494f46332282dc0be70b4b8c127083e0a4164f","source":{"kind":"arxiv","id":"1008.0954","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.0954","created_at":"2026-05-18T04:17:15Z"},{"alias_kind":"arxiv_version","alias_value":"1008.0954v3","created_at":"2026-05-18T04:17:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0954","created_at":"2026-05-18T04:17:15Z"},{"alias_kind":"pith_short_12","alias_value":"RBVSGQRNK7OT","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RBVSGQRNK7OTR65P","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RBVSGQRN","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:RBVSGQRNK7OTR65PSA3S6SKPIY","target":"record","payload":{"canonical_record":{"source":{"id":"1008.0954","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-08-05T11:46:24Z","cross_cats_sorted":["math.AG","math.GR"],"title_canon_sha256":"3ee6ead95351c9e228108e18658f2bcab2f6bc1c21529ca6918de2d06922eefb","abstract_canon_sha256":"bd00f931a35e3749577191510ec0dfcd10b38fa697e341505697d2e5115f658e"},"schema_version":"1.0"},"canonical_sha256":"886b23422d57dd38fbaf90372f494f46332282dc0be70b4b8c127083e0a4164f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:17:15.354598Z","signature_b64":"6F+ywNEfU9d3QFWzRqoFiqezRFcPpbo0I9NduJil4wEeOP9GRxGGRA0WBCNKCId6tp35OO4h9mj7+9SXSyoyCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"886b23422d57dd38fbaf90372f494f46332282dc0be70b4b8c127083e0a4164f","last_reissued_at":"2026-05-18T04:17:15.353890Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:17:15.353890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.0954","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":"2026-05-18T04:17:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l+oapFzzxgStfZ8w0vRoDHwaV1Oxm8/WGGEykrEFzAQyCf+oYZRgeB9nu9X1petpnA/YZ1iF1JEkwHmepcC2AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:26:46.817814Z"},"content_sha256":"b4fde8a8328d15caec71cadd7486c8380a05e90484187b33cc4fe8779c7f6af5","schema_version":"1.0","event_id":"sha256:b4fde8a8328d15caec71cadd7486c8380a05e90484187b33cc4fe8779c7f6af5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:RBVSGQRNK7OTR65PSA3S6SKPIY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The symmetries of the tetrahedral Kummer surface in the Mathieu group M_24","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GR"],"primary_cat":"hep-th","authors_text":"Anne Taormina, Katrin Wendland","submitted_at":"2010-08-05T11:46:24Z","abstract_excerpt":"We provide a method, based on Nikulin's lattice gluing techniques, which identifies the symplectic automorphisms of Kummer surfaces as permutation groups on 24 elements preserving the Golay code. In other words, we explicitly realise these symplectic automorphism groups as subgroups of the Mathieu group M_24. The example of the tetrahedral Kummer surface is treated in detail, confirming the existence proofs of Mukai and Kondo, that its group of symplectic automorphisms is a subgroup of one of eleven subgroups of the sporadic group known as Mathieu group M_23. Kondo's lattice construction, whic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0954","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":"2026-05-18T04:17:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NLzM4eqW0NaAUjnGyRKuSDdgzGfK3igjKR+oNMOgp9GnUmmvUF+FcVQbK6Aof7DOEYgoW8hynYfdHqoo72GlAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:26:46.818517Z"},"content_sha256":"7ac4e92ab26c908bca961c61293ffaa9892d601b515ccbcb6a56ab46c357fd26","schema_version":"1.0","event_id":"sha256:7ac4e92ab26c908bca961c61293ffaa9892d601b515ccbcb6a56ab46c357fd26"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RBVSGQRNK7OTR65PSA3S6SKPIY/bundle.json","state_url":"https://pith.science/pith/RBVSGQRNK7OTR65PSA3S6SKPIY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RBVSGQRNK7OTR65PSA3S6SKPIY/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":"2026-05-25T18:26:46Z","links":{"resolver":"https://pith.science/pith/RBVSGQRNK7OTR65PSA3S6SKPIY","bundle":"https://pith.science/pith/RBVSGQRNK7OTR65PSA3S6SKPIY/bundle.json","state":"https://pith.science/pith/RBVSGQRNK7OTR65PSA3S6SKPIY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RBVSGQRNK7OTR65PSA3S6SKPIY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:RBVSGQRNK7OTR65PSA3S6SKPIY","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":"bd00f931a35e3749577191510ec0dfcd10b38fa697e341505697d2e5115f658e","cross_cats_sorted":["math.AG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-08-05T11:46:24Z","title_canon_sha256":"3ee6ead95351c9e228108e18658f2bcab2f6bc1c21529ca6918de2d06922eefb"},"schema_version":"1.0","source":{"id":"1008.0954","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.0954","created_at":"2026-05-18T04:17:15Z"},{"alias_kind":"arxiv_version","alias_value":"1008.0954v3","created_at":"2026-05-18T04:17:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0954","created_at":"2026-05-18T04:17:15Z"},{"alias_kind":"pith_short_12","alias_value":"RBVSGQRNK7OT","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RBVSGQRNK7OTR65P","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RBVSGQRN","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:7ac4e92ab26c908bca961c61293ffaa9892d601b515ccbcb6a56ab46c357fd26","target":"graph","created_at":"2026-05-18T04:17:15Z","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 provide a method, based on Nikulin's lattice gluing techniques, which identifies the symplectic automorphisms of Kummer surfaces as permutation groups on 24 elements preserving the Golay code. In other words, we explicitly realise these symplectic automorphism groups as subgroups of the Mathieu group M_24. The example of the tetrahedral Kummer surface is treated in detail, confirming the existence proofs of Mukai and Kondo, that its group of symplectic automorphisms is a subgroup of one of eleven subgroups of the sporadic group known as Mathieu group M_23. Kondo's lattice construction, whic","authors_text":"Anne Taormina, Katrin Wendland","cross_cats":["math.AG","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-08-05T11:46:24Z","title":"The symmetries of the tetrahedral Kummer surface in the Mathieu group M_24"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0954","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:b4fde8a8328d15caec71cadd7486c8380a05e90484187b33cc4fe8779c7f6af5","target":"record","created_at":"2026-05-18T04:17:15Z","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":"bd00f931a35e3749577191510ec0dfcd10b38fa697e341505697d2e5115f658e","cross_cats_sorted":["math.AG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-08-05T11:46:24Z","title_canon_sha256":"3ee6ead95351c9e228108e18658f2bcab2f6bc1c21529ca6918de2d06922eefb"},"schema_version":"1.0","source":{"id":"1008.0954","kind":"arxiv","version":3}},"canonical_sha256":"886b23422d57dd38fbaf90372f494f46332282dc0be70b4b8c127083e0a4164f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"886b23422d57dd38fbaf90372f494f46332282dc0be70b4b8c127083e0a4164f","first_computed_at":"2026-05-18T04:17:15.353890Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:15.353890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6F+ywNEfU9d3QFWzRqoFiqezRFcPpbo0I9NduJil4wEeOP9GRxGGRA0WBCNKCId6tp35OO4h9mj7+9SXSyoyCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:15.354598Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.0954","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4fde8a8328d15caec71cadd7486c8380a05e90484187b33cc4fe8779c7f6af5","sha256:7ac4e92ab26c908bca961c61293ffaa9892d601b515ccbcb6a56ab46c357fd26"],"state_sha256":"3838394e438271bbb8a335fde1a73ef895bc707361dcebac4ce138d1effdfa25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X6TgE4hHQ+9pCd2w9Q8dh4UjmNd5ZoBr1f/aIejqAQbmXDnaGDvGeniFcfjYkJaKGEDGTqARRL6+dYZUmollAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T18:26:46.822471Z","bundle_sha256":"cce3d042bb9189ab533fe4e4794aa3120da50d2b06786cf86633a152db302fb8"}}