{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:5LO7SXHAPNMY6D67INCVOOPCJD","short_pith_number":"pith:5LO7SXHA","canonical_record":{"source":{"id":"1103.1892","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-09T21:24:03Z","cross_cats_sorted":[],"title_canon_sha256":"13bf54415dd9e44badb6e1d0b449279b8de12b3fbe74f7b3c222be950e818808","abstract_canon_sha256":"e2a9ab46fdb6681c55eeae34cc9e75b2f7303712d72d63392cbf0da616655bd4"},"schema_version":"1.0"},"canonical_sha256":"eaddf95ce07b598f0fdf43455739e248d16b4f7cbeb6ac4295c65f1d941b83e5","source":{"kind":"arxiv","id":"1103.1892","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1892","created_at":"2026-05-18T04:20:52Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1892v2","created_at":"2026-05-18T04:20:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1892","created_at":"2026-05-18T04:20:52Z"},{"alias_kind":"pith_short_12","alias_value":"5LO7SXHAPNMY","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5LO7SXHAPNMY6D67","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5LO7SXHA","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:5LO7SXHAPNMY6D67INCVOOPCJD","target":"record","payload":{"canonical_record":{"source":{"id":"1103.1892","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-09T21:24:03Z","cross_cats_sorted":[],"title_canon_sha256":"13bf54415dd9e44badb6e1d0b449279b8de12b3fbe74f7b3c222be950e818808","abstract_canon_sha256":"e2a9ab46fdb6681c55eeae34cc9e75b2f7303712d72d63392cbf0da616655bd4"},"schema_version":"1.0"},"canonical_sha256":"eaddf95ce07b598f0fdf43455739e248d16b4f7cbeb6ac4295c65f1d941b83e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:52.433861Z","signature_b64":"uSmxIHSFy69EcWOJr7INEKmvhGIRjWPQiqjT/314k/Eo7OzG0wBf20D/yvmdWeap4m3jfd0GG/oYuAGvEnPECQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eaddf95ce07b598f0fdf43455739e248d16b4f7cbeb6ac4295c65f1d941b83e5","last_reissued_at":"2026-05-18T04:20:52.433287Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:52.433287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.1892","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":"2026-05-18T04:20:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AJznj1DlNQJkmbHZIi+VQho/TQ26ABCckEoWLwN3FGPWMy2KWpCjMMzveukywKch02WCIokXPJP6b539LUE4Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:55:24.024565Z"},"content_sha256":"9cd2698d18946904a66b761bffe019abb6088333af09b1da6a07c49781915e0b","schema_version":"1.0","event_id":"sha256:9cd2698d18946904a66b761bffe019abb6088333af09b1da6a07c49781915e0b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:5LO7SXHAPNMY6D67INCVOOPCJD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a family of K3 surfaces with $\\mathcal{S}_4$ symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dagan Karp, Daniel Moore, Dmitri Skjorshammer, Jacob Lewis, Ursula Whitcher","submitted_at":"2011-03-09T21:24:03Z","abstract_excerpt":"The largest group which occurs as the rotational symmetries of a three-dimensional reflexive polytope is the symmetric group on four elements. There are three pairs of three-dimensional reflexive polytopes with this symmetry group, up to isomorphism. We identify a natural one-parameter family of K3 surfaces corresponding to each of these pairs, show that the symmetric group on four elements acts symplectically on members of these families, and show that a general K3 surface in each family has Picard rank 19. The properties of two of these families have been analyzed in the literature using oth"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1892","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":"2026-05-18T04:20:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lm2VRElGwQBF4VDmkRMCWo3X8kBFW/+kJ9uqPvCzori7eHBu54vMS/ibIFYSNiMvRU7IioowO7GrOayahlgLDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:55:24.025161Z"},"content_sha256":"a65777a31c9516f0d51ff994a6cdfe953c0ba8a513a6850d6b98ecd8b54ffeab","schema_version":"1.0","event_id":"sha256:a65777a31c9516f0d51ff994a6cdfe953c0ba8a513a6850d6b98ecd8b54ffeab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5LO7SXHAPNMY6D67INCVOOPCJD/bundle.json","state_url":"https://pith.science/pith/5LO7SXHAPNMY6D67INCVOOPCJD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5LO7SXHAPNMY6D67INCVOOPCJD/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":"2026-05-28T01:55:24Z","links":{"resolver":"https://pith.science/pith/5LO7SXHAPNMY6D67INCVOOPCJD","bundle":"https://pith.science/pith/5LO7SXHAPNMY6D67INCVOOPCJD/bundle.json","state":"https://pith.science/pith/5LO7SXHAPNMY6D67INCVOOPCJD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5LO7SXHAPNMY6D67INCVOOPCJD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5LO7SXHAPNMY6D67INCVOOPCJD","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":"e2a9ab46fdb6681c55eeae34cc9e75b2f7303712d72d63392cbf0da616655bd4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-09T21:24:03Z","title_canon_sha256":"13bf54415dd9e44badb6e1d0b449279b8de12b3fbe74f7b3c222be950e818808"},"schema_version":"1.0","source":{"id":"1103.1892","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1892","created_at":"2026-05-18T04:20:52Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1892v2","created_at":"2026-05-18T04:20:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1892","created_at":"2026-05-18T04:20:52Z"},{"alias_kind":"pith_short_12","alias_value":"5LO7SXHAPNMY","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5LO7SXHAPNMY6D67","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5LO7SXHA","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:a65777a31c9516f0d51ff994a6cdfe953c0ba8a513a6850d6b98ecd8b54ffeab","target":"graph","created_at":"2026-05-18T04:20:52Z","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":"The largest group which occurs as the rotational symmetries of a three-dimensional reflexive polytope is the symmetric group on four elements. There are three pairs of three-dimensional reflexive polytopes with this symmetry group, up to isomorphism. We identify a natural one-parameter family of K3 surfaces corresponding to each of these pairs, show that the symmetric group on four elements acts symplectically on members of these families, and show that a general K3 surface in each family has Picard rank 19. The properties of two of these families have been analyzed in the literature using oth","authors_text":"Dagan Karp, Daniel Moore, Dmitri Skjorshammer, Jacob Lewis, Ursula Whitcher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-09T21:24:03Z","title":"On a family of K3 surfaces with $\\mathcal{S}_4$ symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1892","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":"sha256:9cd2698d18946904a66b761bffe019abb6088333af09b1da6a07c49781915e0b","target":"record","created_at":"2026-05-18T04:20:52Z","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":"e2a9ab46fdb6681c55eeae34cc9e75b2f7303712d72d63392cbf0da616655bd4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-09T21:24:03Z","title_canon_sha256":"13bf54415dd9e44badb6e1d0b449279b8de12b3fbe74f7b3c222be950e818808"},"schema_version":"1.0","source":{"id":"1103.1892","kind":"arxiv","version":2}},"canonical_sha256":"eaddf95ce07b598f0fdf43455739e248d16b4f7cbeb6ac4295c65f1d941b83e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eaddf95ce07b598f0fdf43455739e248d16b4f7cbeb6ac4295c65f1d941b83e5","first_computed_at":"2026-05-18T04:20:52.433287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:52.433287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uSmxIHSFy69EcWOJr7INEKmvhGIRjWPQiqjT/314k/Eo7OzG0wBf20D/yvmdWeap4m3jfd0GG/oYuAGvEnPECQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:52.433861Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.1892","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9cd2698d18946904a66b761bffe019abb6088333af09b1da6a07c49781915e0b","sha256:a65777a31c9516f0d51ff994a6cdfe953c0ba8a513a6850d6b98ecd8b54ffeab"],"state_sha256":"557c232f8717243ac45692e05a95048875b67f23b1db26b2b927c85fe9c69140"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VHi19gHJKq7QGUcSPiqJivWNqa6PsSLhh0Vu+nt2OXRZ7Qyskw0bI+vUmMK+P6l2/beLVis2kiBXcjEeWsOiCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T01:55:24.027962Z","bundle_sha256":"3d1e9c00af5abdbe3c29c4ea2035df720920bd40f841898103d92d2c504a82fe"}}