{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HROJW7UJ2EW73MHXSW22J6ILBZ","short_pith_number":"pith:HROJW7UJ","canonical_record":{"source":{"id":"1606.04857","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-15T16:47:22Z","cross_cats_sorted":[],"title_canon_sha256":"99c3986b3f3e84665ce8b193cc9c5c6ab5feccf9b129761ab82c0c7724cf2e50","abstract_canon_sha256":"c04ac1b11c8590b44c496080aa837bff891d0963e9f5fe79dceb6727ca963271"},"schema_version":"1.0"},"canonical_sha256":"3c5c9b7e89d12dfdb0f795b5a4f90b0e4187f220905eaefee7e3bc91425dc565","source":{"kind":"arxiv","id":"1606.04857","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.04857","created_at":"2026-05-18T01:12:23Z"},{"alias_kind":"arxiv_version","alias_value":"1606.04857v1","created_at":"2026-05-18T01:12:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.04857","created_at":"2026-05-18T01:12:23Z"},{"alias_kind":"pith_short_12","alias_value":"HROJW7UJ2EW7","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HROJW7UJ2EW73MHX","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HROJW7UJ","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HROJW7UJ2EW73MHXSW22J6ILBZ","target":"record","payload":{"canonical_record":{"source":{"id":"1606.04857","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-15T16:47:22Z","cross_cats_sorted":[],"title_canon_sha256":"99c3986b3f3e84665ce8b193cc9c5c6ab5feccf9b129761ab82c0c7724cf2e50","abstract_canon_sha256":"c04ac1b11c8590b44c496080aa837bff891d0963e9f5fe79dceb6727ca963271"},"schema_version":"1.0"},"canonical_sha256":"3c5c9b7e89d12dfdb0f795b5a4f90b0e4187f220905eaefee7e3bc91425dc565","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:23.253275Z","signature_b64":"CCGFyfdkHbgii1OLfxBh0n/Ns5fEreRJvYbSIj9rB3o8yJ982e0WvOq1wMjRoTf953U26cG5hBTkITZMf7S1Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c5c9b7e89d12dfdb0f795b5a4f90b0e4187f220905eaefee7e3bc91425dc565","last_reissued_at":"2026-05-18T01:12:23.252944Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:23.252944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.04857","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":"2026-05-18T01:12:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SYewsPWv2tjATW9OeXcUN7OMqwYuYEne5kncMqAweUNT4FCWknX6qyBebux0nn411a7rZByDbAUP0AEIbDhIBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:25:37.237797Z"},"content_sha256":"7f71a5212c08dbf9b39cbb5a33069b6cdbc47ede67f7061c29c4fd05c5082887","schema_version":"1.0","event_id":"sha256:7f71a5212c08dbf9b39cbb5a33069b6cdbc47ede67f7061c29c4fd05c5082887"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HROJW7UJ2EW73MHXSW22J6ILBZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A combinatorial construction of an M_{12}-invariant code","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fernanda Pambianco, Juergen Bierbrauer, Stefano Marcugini","submitted_at":"2016-06-15T16:47:22Z","abstract_excerpt":"In this work we summarized some recent results to be included in a forthcoming paper. A ternary [66,10,36]_3-code admitting the Mathieu group M_{12} as a group of automorphisms has recently been constructed by N. Pace. We give a construction of the Pace code in terms of $M_{12}$ as well as a combinatorial description in terms of the small Witt design, the Steiner system S(5,6,12). We also present a proof that the Pace code does indeed have minimum distance 36."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04857","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":"2026-05-18T01:12:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+jBf8PivWXowxJnzH8W0kyVTRwVPfGl3bohhxsgTlf8S5cnri1cgJcNpVKudfx6sobYOtTQd0Hbt+NqGlFpXDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:25:37.238180Z"},"content_sha256":"d2f73383aa0d43155c809c33fb0fbc5ff6dde7f5f4a8cac51974c3c274af5b81","schema_version":"1.0","event_id":"sha256:d2f73383aa0d43155c809c33fb0fbc5ff6dde7f5f4a8cac51974c3c274af5b81"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HROJW7UJ2EW73MHXSW22J6ILBZ/bundle.json","state_url":"https://pith.science/pith/HROJW7UJ2EW73MHXSW22J6ILBZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HROJW7UJ2EW73MHXSW22J6ILBZ/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":"2026-05-30T09:25:37Z","links":{"resolver":"https://pith.science/pith/HROJW7UJ2EW73MHXSW22J6ILBZ","bundle":"https://pith.science/pith/HROJW7UJ2EW73MHXSW22J6ILBZ/bundle.json","state":"https://pith.science/pith/HROJW7UJ2EW73MHXSW22J6ILBZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HROJW7UJ2EW73MHXSW22J6ILBZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HROJW7UJ2EW73MHXSW22J6ILBZ","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":"c04ac1b11c8590b44c496080aa837bff891d0963e9f5fe79dceb6727ca963271","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-15T16:47:22Z","title_canon_sha256":"99c3986b3f3e84665ce8b193cc9c5c6ab5feccf9b129761ab82c0c7724cf2e50"},"schema_version":"1.0","source":{"id":"1606.04857","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.04857","created_at":"2026-05-18T01:12:23Z"},{"alias_kind":"arxiv_version","alias_value":"1606.04857v1","created_at":"2026-05-18T01:12:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.04857","created_at":"2026-05-18T01:12:23Z"},{"alias_kind":"pith_short_12","alias_value":"HROJW7UJ2EW7","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HROJW7UJ2EW73MHX","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HROJW7UJ","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:d2f73383aa0d43155c809c33fb0fbc5ff6dde7f5f4a8cac51974c3c274af5b81","target":"graph","created_at":"2026-05-18T01:12:23Z","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":"In this work we summarized some recent results to be included in a forthcoming paper. A ternary [66,10,36]_3-code admitting the Mathieu group M_{12} as a group of automorphisms has recently been constructed by N. Pace. We give a construction of the Pace code in terms of $M_{12}$ as well as a combinatorial description in terms of the small Witt design, the Steiner system S(5,6,12). We also present a proof that the Pace code does indeed have minimum distance 36.","authors_text":"Fernanda Pambianco, Juergen Bierbrauer, Stefano Marcugini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-15T16:47:22Z","title":"A combinatorial construction of an M_{12}-invariant code"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04857","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":"sha256:7f71a5212c08dbf9b39cbb5a33069b6cdbc47ede67f7061c29c4fd05c5082887","target":"record","created_at":"2026-05-18T01:12:23Z","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":"c04ac1b11c8590b44c496080aa837bff891d0963e9f5fe79dceb6727ca963271","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-15T16:47:22Z","title_canon_sha256":"99c3986b3f3e84665ce8b193cc9c5c6ab5feccf9b129761ab82c0c7724cf2e50"},"schema_version":"1.0","source":{"id":"1606.04857","kind":"arxiv","version":1}},"canonical_sha256":"3c5c9b7e89d12dfdb0f795b5a4f90b0e4187f220905eaefee7e3bc91425dc565","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c5c9b7e89d12dfdb0f795b5a4f90b0e4187f220905eaefee7e3bc91425dc565","first_computed_at":"2026-05-18T01:12:23.252944Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:23.252944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CCGFyfdkHbgii1OLfxBh0n/Ns5fEreRJvYbSIj9rB3o8yJ982e0WvOq1wMjRoTf953U26cG5hBTkITZMf7S1Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:23.253275Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.04857","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f71a5212c08dbf9b39cbb5a33069b6cdbc47ede67f7061c29c4fd05c5082887","sha256:d2f73383aa0d43155c809c33fb0fbc5ff6dde7f5f4a8cac51974c3c274af5b81"],"state_sha256":"de35dc05d18c6f32bf6d3fe4cae7bbb96754216b7849b7dbca7d5e0d983ceb56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3YAjzZGwCI3Jlbl7Z0QMdKlGCrKdiEyH+Pszd+NJGZBFPKZUMn8vmveP6lKfLiiY1N0V2gywanhjfEu4Sp2yBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T09:25:37.241629Z","bundle_sha256":"19e95ac29e19969c31fc7fa2e324154f4795e4fee2a868aa41e57778624b19fe"}}