{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CIIQ6XOVOIO7ME3NEAMKFD37A4","short_pith_number":"pith:CIIQ6XOV","canonical_record":{"source":{"id":"1502.02099","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-02-07T05:38:34Z","cross_cats_sorted":[],"title_canon_sha256":"54126cc05857a03ee23d956bf4c9f15ea426e75bacfe6bc69b78921c8a1337f9","abstract_canon_sha256":"f1b551b54a54796f19ac2ad0037212218ec34f4f9fd0f0356fde991875108856"},"schema_version":"1.0"},"canonical_sha256":"12110f5dd5721df6136d2018a28f7f07007c09c068f8b7005147504f59fb0a29","source":{"kind":"arxiv","id":"1502.02099","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02099","created_at":"2026-05-18T01:11:21Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02099v3","created_at":"2026-05-18T01:11:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02099","created_at":"2026-05-18T01:11:21Z"},{"alias_kind":"pith_short_12","alias_value":"CIIQ6XOVOIO7","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"CIIQ6XOVOIO7ME3N","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"CIIQ6XOV","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CIIQ6XOVOIO7ME3NEAMKFD37A4","target":"record","payload":{"canonical_record":{"source":{"id":"1502.02099","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-02-07T05:38:34Z","cross_cats_sorted":[],"title_canon_sha256":"54126cc05857a03ee23d956bf4c9f15ea426e75bacfe6bc69b78921c8a1337f9","abstract_canon_sha256":"f1b551b54a54796f19ac2ad0037212218ec34f4f9fd0f0356fde991875108856"},"schema_version":"1.0"},"canonical_sha256":"12110f5dd5721df6136d2018a28f7f07007c09c068f8b7005147504f59fb0a29","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:21.835792Z","signature_b64":"KK8KeKUb2CpHeJR1apZbMF5RP/nP7+wLJz2Q/g/sHN4HjF3AXde9dESUCG+woFFv9ajuNqY/nZZXl2+YrvOgCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12110f5dd5721df6136d2018a28f7f07007c09c068f8b7005147504f59fb0a29","last_reissued_at":"2026-05-18T01:11:21.835303Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:21.835303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.02099","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":"2026-05-18T01:11:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WdFurE9CoGRvFDq2Hhn3fPp/0NJbx84rgKGBZ5WLbkFY7p3yIShfFJiPKLhUwRRf/myOwveOhJSJHJ4q9gVOCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:45:39.000634Z"},"content_sha256":"447944af6df9225f01dd081894915ac4866bb0cc6ed943997bea8176642ffcae","schema_version":"1.0","event_id":"sha256:447944af6df9225f01dd081894915ac4866bb0cc6ed943997bea8176642ffcae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CIIQ6XOVOIO7ME3NEAMKFD37A4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Holes of the Leech lattice and the projective models of K3 surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ichiro Shimada","submitted_at":"2015-02-07T05:38:34Z","abstract_excerpt":"Using the theory of holes of the Leech lattice and Borcherds method for the computation of the automorphism group of a K3 surface, we give an effective bound for the set of isomorphism classes of projective models of fixed degree for certain K3 surfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02099","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":"2026-05-18T01:11:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oXzpBi9ctilcqmZQpcSegdGsvSj/hi7ruIHvq2ghOe/XZ148PGALlYCbDP+qYqgWUkwC4NOQE9CkWcnq3g1IAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:45:39.000981Z"},"content_sha256":"d917e01bbc8d472de96a7e40c599c0e61b5aef57c1f43bb25d92119e7ff3a0f9","schema_version":"1.0","event_id":"sha256:d917e01bbc8d472de96a7e40c599c0e61b5aef57c1f43bb25d92119e7ff3a0f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CIIQ6XOVOIO7ME3NEAMKFD37A4/bundle.json","state_url":"https://pith.science/pith/CIIQ6XOVOIO7ME3NEAMKFD37A4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CIIQ6XOVOIO7ME3NEAMKFD37A4/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":"2026-06-23T16:45:39Z","links":{"resolver":"https://pith.science/pith/CIIQ6XOVOIO7ME3NEAMKFD37A4","bundle":"https://pith.science/pith/CIIQ6XOVOIO7ME3NEAMKFD37A4/bundle.json","state":"https://pith.science/pith/CIIQ6XOVOIO7ME3NEAMKFD37A4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CIIQ6XOVOIO7ME3NEAMKFD37A4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CIIQ6XOVOIO7ME3NEAMKFD37A4","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":"f1b551b54a54796f19ac2ad0037212218ec34f4f9fd0f0356fde991875108856","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-02-07T05:38:34Z","title_canon_sha256":"54126cc05857a03ee23d956bf4c9f15ea426e75bacfe6bc69b78921c8a1337f9"},"schema_version":"1.0","source":{"id":"1502.02099","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02099","created_at":"2026-05-18T01:11:21Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02099v3","created_at":"2026-05-18T01:11:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02099","created_at":"2026-05-18T01:11:21Z"},{"alias_kind":"pith_short_12","alias_value":"CIIQ6XOVOIO7","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"CIIQ6XOVOIO7ME3N","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"CIIQ6XOV","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:d917e01bbc8d472de96a7e40c599c0e61b5aef57c1f43bb25d92119e7ff3a0f9","target":"graph","created_at":"2026-05-18T01:11:21Z","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":"Using the theory of holes of the Leech lattice and Borcherds method for the computation of the automorphism group of a K3 surface, we give an effective bound for the set of isomorphism classes of projective models of fixed degree for certain K3 surfaces.","authors_text":"Ichiro Shimada","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-02-07T05:38:34Z","title":"Holes of the Leech lattice and the projective models of K3 surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02099","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":"sha256:447944af6df9225f01dd081894915ac4866bb0cc6ed943997bea8176642ffcae","target":"record","created_at":"2026-05-18T01:11:21Z","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":"f1b551b54a54796f19ac2ad0037212218ec34f4f9fd0f0356fde991875108856","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-02-07T05:38:34Z","title_canon_sha256":"54126cc05857a03ee23d956bf4c9f15ea426e75bacfe6bc69b78921c8a1337f9"},"schema_version":"1.0","source":{"id":"1502.02099","kind":"arxiv","version":3}},"canonical_sha256":"12110f5dd5721df6136d2018a28f7f07007c09c068f8b7005147504f59fb0a29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12110f5dd5721df6136d2018a28f7f07007c09c068f8b7005147504f59fb0a29","first_computed_at":"2026-05-18T01:11:21.835303Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:21.835303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KK8KeKUb2CpHeJR1apZbMF5RP/nP7+wLJz2Q/g/sHN4HjF3AXde9dESUCG+woFFv9ajuNqY/nZZXl2+YrvOgCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:21.835792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.02099","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:447944af6df9225f01dd081894915ac4866bb0cc6ed943997bea8176642ffcae","sha256:d917e01bbc8d472de96a7e40c599c0e61b5aef57c1f43bb25d92119e7ff3a0f9"],"state_sha256":"0357aec94ac04db3b60665219f5f7d115068211dbcaad4e051caa5d1a44755d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BmZdp28rCPTGX3VCklkw5sFJnmZfvfV1lEtow8VvQttjhf69wtY/bKjp//e5Boa/iWRcELNjeXTdu6fHDYNGCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:45:39.003120Z","bundle_sha256":"16cbf400f62e9151ee65ac7f63e5c87563285a0191c64d09198a5231d3d771b1"}}