{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:XCCAXZ477JW35H5TPPN2XWEDDP","short_pith_number":"pith:XCCAXZ47","canonical_record":{"source":{"id":"1302.0033","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-01-31T23:02:36Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"39c0c8ed3370d52b220021af2ac4d4a7280c6ce819e1624447798a960eebff02","abstract_canon_sha256":"ac6c642e6539432b8ea24e4b8602d8bb381d4c55ef5b50ecab51370606883718"},"schema_version":"1.0"},"canonical_sha256":"b8840be79ffa6dbe9fb37bdbabd8831be126213b723119a6b884bde23f47036b","source":{"kind":"arxiv","id":"1302.0033","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0033","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0033v1","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0033","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"pith_short_12","alias_value":"XCCAXZ477JW3","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XCCAXZ477JW35H5T","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XCCAXZ47","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:XCCAXZ477JW35H5TPPN2XWEDDP","target":"record","payload":{"canonical_record":{"source":{"id":"1302.0033","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-01-31T23:02:36Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"39c0c8ed3370d52b220021af2ac4d4a7280c6ce819e1624447798a960eebff02","abstract_canon_sha256":"ac6c642e6539432b8ea24e4b8602d8bb381d4c55ef5b50ecab51370606883718"},"schema_version":"1.0"},"canonical_sha256":"b8840be79ffa6dbe9fb37bdbabd8831be126213b723119a6b884bde23f47036b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:47.698916Z","signature_b64":"QzcHJVR8ACMd586CvURkq2FEHMWlTYdrdJgMpa5y5oWMBkChDz7GQYKPbhheD1HPCBWbqRuR86UB1tQVJl1JBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8840be79ffa6dbe9fb37bdbabd8831be126213b723119a6b884bde23f47036b","last_reissued_at":"2026-05-18T03:34:47.698123Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:47.698123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.0033","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:34:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HLFg8KpYgABkA8DzrvyedJoqflIqZUthKyVFAXxOnj5lIOus5Y6bu0FvUBv1Epj2ZCSWwxI+iNLMaxk+xSocAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:51:22.672550Z"},"content_sha256":"6a3929a3fd004f38a180eeba647b130071610c06d9f711311c6509a2e20ba158","schema_version":"1.0","event_id":"sha256:6a3929a3fd004f38a180eeba647b130071610c06d9f711311c6509a2e20ba158"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:XCCAXZ477JW35H5TPPN2XWEDDP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On extremal self-dual codes of length 120","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"J. de la Cruz","submitted_at":"2013-01-31T23:02:36Z","abstract_excerpt":"We prove that the only primes which may divide the order of the automorphism group of a putative binary self-dual doubly-even [120, 60, 24] code are 2, 3, 5, 7, 19, 23 and 29. Furthermore we prove that automorphisms of prime order $p \\geq 5$ have a unique cycle structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0033","kind":"arxiv","version":1},"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":"2026-05-18T03:34:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uc5laRdcjZY5pos+ZAkrwYrSXTkwsYR/QgW4EQBQmPFzapunEGYWMcj42SHgi8Q5N4FK/B4amHpunA+Eg7PnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:51:22.673297Z"},"content_sha256":"b1d75491c2c36856d91ed42162260d3e26cae9f00f2ded3cf57821de236611c8","schema_version":"1.0","event_id":"sha256:b1d75491c2c36856d91ed42162260d3e26cae9f00f2ded3cf57821de236611c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XCCAXZ477JW35H5TPPN2XWEDDP/bundle.json","state_url":"https://pith.science/pith/XCCAXZ477JW35H5TPPN2XWEDDP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XCCAXZ477JW35H5TPPN2XWEDDP/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":"2026-06-09T08:51:22Z","links":{"resolver":"https://pith.science/pith/XCCAXZ477JW35H5TPPN2XWEDDP","bundle":"https://pith.science/pith/XCCAXZ477JW35H5TPPN2XWEDDP/bundle.json","state":"https://pith.science/pith/XCCAXZ477JW35H5TPPN2XWEDDP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XCCAXZ477JW35H5TPPN2XWEDDP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XCCAXZ477JW35H5TPPN2XWEDDP","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":"ac6c642e6539432b8ea24e4b8602d8bb381d4c55ef5b50ecab51370606883718","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-01-31T23:02:36Z","title_canon_sha256":"39c0c8ed3370d52b220021af2ac4d4a7280c6ce819e1624447798a960eebff02"},"schema_version":"1.0","source":{"id":"1302.0033","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0033","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0033v1","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0033","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"pith_short_12","alias_value":"XCCAXZ477JW3","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XCCAXZ477JW35H5T","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XCCAXZ47","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:b1d75491c2c36856d91ed42162260d3e26cae9f00f2ded3cf57821de236611c8","target":"graph","created_at":"2026-05-18T03:34:47Z","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 prove that the only primes which may divide the order of the automorphism group of a putative binary self-dual doubly-even [120, 60, 24] code are 2, 3, 5, 7, 19, 23 and 29. Furthermore we prove that automorphisms of prime order $p \\geq 5$ have a unique cycle structure.","authors_text":"J. de la Cruz","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-01-31T23:02:36Z","title":"On extremal self-dual codes of length 120"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0033","kind":"arxiv","version":1},"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":"sha256:6a3929a3fd004f38a180eeba647b130071610c06d9f711311c6509a2e20ba158","target":"record","created_at":"2026-05-18T03:34:47Z","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":"ac6c642e6539432b8ea24e4b8602d8bb381d4c55ef5b50ecab51370606883718","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-01-31T23:02:36Z","title_canon_sha256":"39c0c8ed3370d52b220021af2ac4d4a7280c6ce819e1624447798a960eebff02"},"schema_version":"1.0","source":{"id":"1302.0033","kind":"arxiv","version":1}},"canonical_sha256":"b8840be79ffa6dbe9fb37bdbabd8831be126213b723119a6b884bde23f47036b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8840be79ffa6dbe9fb37bdbabd8831be126213b723119a6b884bde23f47036b","first_computed_at":"2026-05-18T03:34:47.698123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:47.698123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QzcHJVR8ACMd586CvURkq2FEHMWlTYdrdJgMpa5y5oWMBkChDz7GQYKPbhheD1HPCBWbqRuR86UB1tQVJl1JBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:47.698916Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.0033","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a3929a3fd004f38a180eeba647b130071610c06d9f711311c6509a2e20ba158","sha256:b1d75491c2c36856d91ed42162260d3e26cae9f00f2ded3cf57821de236611c8"],"state_sha256":"e91c78800fa386c947506d6d610008de5d3dcf3b8fdc00788f1ae07f47333f3d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C136Rcw6aGCohEVNvvbHd4ExPvnI6NqNxsvk9YBiYMfD1aW6eHHEdX2tTvg7aEgmJhy4BrpzZGx40U+D0H0eDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T08:51:22.677132Z","bundle_sha256":"8075b1095da5800e76a5dd523f22ae22a80afe1b839e0d4ea1eb0f54e7462540"}}