{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:5K2Q5CLXUMBPQX5SV24VCJVQ72","short_pith_number":"pith:5K2Q5CLX","canonical_record":{"source":{"id":"1206.6006","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-06-26T14:38:40Z","cross_cats_sorted":["cs.DM","math.CO","math.IT"],"title_canon_sha256":"5cc0fb6fa03214759ccfd47e7d47f4ea8e60afdfd5b393cbf78d082a428daba6","abstract_canon_sha256":"2e5568ccdfa3690a847e2a3adb08b49ade8e251d3a42fb44eaa6aee8e44a7c20"},"schema_version":"1.0"},"canonical_sha256":"eab50e8977a302f85fb2aeb95126b0feb2f4cd3b1281f89ea20efd5f4e7fa330","source":{"kind":"arxiv","id":"1206.6006","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.6006","created_at":"2026-05-18T00:57:56Z"},{"alias_kind":"arxiv_version","alias_value":"1206.6006v2","created_at":"2026-05-18T00:57:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.6006","created_at":"2026-05-18T00:57:56Z"},{"alias_kind":"pith_short_12","alias_value":"5K2Q5CLXUMBP","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5K2Q5CLXUMBPQX5S","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5K2Q5CLX","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:5K2Q5CLXUMBPQX5SV24VCJVQ72","target":"record","payload":{"canonical_record":{"source":{"id":"1206.6006","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-06-26T14:38:40Z","cross_cats_sorted":["cs.DM","math.CO","math.IT"],"title_canon_sha256":"5cc0fb6fa03214759ccfd47e7d47f4ea8e60afdfd5b393cbf78d082a428daba6","abstract_canon_sha256":"2e5568ccdfa3690a847e2a3adb08b49ade8e251d3a42fb44eaa6aee8e44a7c20"},"schema_version":"1.0"},"canonical_sha256":"eab50e8977a302f85fb2aeb95126b0feb2f4cd3b1281f89ea20efd5f4e7fa330","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:56.892505Z","signature_b64":"ypOYxh+iF18OY62eBMwyFHbIREWSBmaDlcKmliGEvfDuR1YUerm5nm0vIEuHOtgZ/jgvxo4syMqki4kTEmFQAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eab50e8977a302f85fb2aeb95126b0feb2f4cd3b1281f89ea20efd5f4e7fa330","last_reissued_at":"2026-05-18T00:57:56.892003Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:56.892003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.6006","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":"2026-05-18T00:57:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nR/Un33vgSB7Cgz3EGLWbwtNpF5NSZJs19eWoXBhCnJmXw9VocaXYxaBtoro/hulyB0hSufEX4JTJEFfiioqBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:08:16.006964Z"},"content_sha256":"b66023900f32118c0d5f300d8ba2fd85edb63d2afd554f770ab53f1481b3d6dd","schema_version":"1.0","event_id":"sha256:b66023900f32118c0d5f300d8ba2fd85edb63d2afd554f770ab53f1481b3d6dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:5K2Q5CLXUMBPQX5SV24VCJVQ72","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some bounds on the size of codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Eleonora Guerrini, Emanuele Bellini, Massimiliano Sala","submitted_at":"2012-06-26T14:38:40Z","abstract_excerpt":"We present some upper bounds on the size of non-linear codes and their restriction to systematic codes and linear codes. These bounds are independent of other known theoretical bounds, e.g. the Griesmer bound, the Johnson bound or the Plotkin bound, and one of these is actually an improvement of a bound by Litsyn and Laihonen. Our experiments show that in some cases (the majority of cases for some q) our bounds provide the best value, compared to all other theoretical bounds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6006","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":"2026-05-18T00:57:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZdKmhIm18jAANujeGHFcFVMrWYunQINDJ1oHPavRDLMXBCaplls9OCENBavee5dw9REXf6CLZ67eNdcfugLtBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:08:16.007310Z"},"content_sha256":"267457ab5d43bee52f7548178665d1927ef3586d709c144dd6c6b5c17e9154da","schema_version":"1.0","event_id":"sha256:267457ab5d43bee52f7548178665d1927ef3586d709c144dd6c6b5c17e9154da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5K2Q5CLXUMBPQX5SV24VCJVQ72/bundle.json","state_url":"https://pith.science/pith/5K2Q5CLXUMBPQX5SV24VCJVQ72/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5K2Q5CLXUMBPQX5SV24VCJVQ72/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":"2026-06-01T20:08:16Z","links":{"resolver":"https://pith.science/pith/5K2Q5CLXUMBPQX5SV24VCJVQ72","bundle":"https://pith.science/pith/5K2Q5CLXUMBPQX5SV24VCJVQ72/bundle.json","state":"https://pith.science/pith/5K2Q5CLXUMBPQX5SV24VCJVQ72/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5K2Q5CLXUMBPQX5SV24VCJVQ72/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5K2Q5CLXUMBPQX5SV24VCJVQ72","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":"2e5568ccdfa3690a847e2a3adb08b49ade8e251d3a42fb44eaa6aee8e44a7c20","cross_cats_sorted":["cs.DM","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-06-26T14:38:40Z","title_canon_sha256":"5cc0fb6fa03214759ccfd47e7d47f4ea8e60afdfd5b393cbf78d082a428daba6"},"schema_version":"1.0","source":{"id":"1206.6006","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.6006","created_at":"2026-05-18T00:57:56Z"},{"alias_kind":"arxiv_version","alias_value":"1206.6006v2","created_at":"2026-05-18T00:57:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.6006","created_at":"2026-05-18T00:57:56Z"},{"alias_kind":"pith_short_12","alias_value":"5K2Q5CLXUMBP","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5K2Q5CLXUMBPQX5S","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5K2Q5CLX","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:267457ab5d43bee52f7548178665d1927ef3586d709c144dd6c6b5c17e9154da","target":"graph","created_at":"2026-05-18T00:57:56Z","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 present some upper bounds on the size of non-linear codes and their restriction to systematic codes and linear codes. These bounds are independent of other known theoretical bounds, e.g. the Griesmer bound, the Johnson bound or the Plotkin bound, and one of these is actually an improvement of a bound by Litsyn and Laihonen. Our experiments show that in some cases (the majority of cases for some q) our bounds provide the best value, compared to all other theoretical bounds.","authors_text":"Eleonora Guerrini, Emanuele Bellini, Massimiliano Sala","cross_cats":["cs.DM","math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-06-26T14:38:40Z","title":"Some bounds on the size of codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6006","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:b66023900f32118c0d5f300d8ba2fd85edb63d2afd554f770ab53f1481b3d6dd","target":"record","created_at":"2026-05-18T00:57:56Z","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":"2e5568ccdfa3690a847e2a3adb08b49ade8e251d3a42fb44eaa6aee8e44a7c20","cross_cats_sorted":["cs.DM","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-06-26T14:38:40Z","title_canon_sha256":"5cc0fb6fa03214759ccfd47e7d47f4ea8e60afdfd5b393cbf78d082a428daba6"},"schema_version":"1.0","source":{"id":"1206.6006","kind":"arxiv","version":2}},"canonical_sha256":"eab50e8977a302f85fb2aeb95126b0feb2f4cd3b1281f89ea20efd5f4e7fa330","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eab50e8977a302f85fb2aeb95126b0feb2f4cd3b1281f89ea20efd5f4e7fa330","first_computed_at":"2026-05-18T00:57:56.892003Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:56.892003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ypOYxh+iF18OY62eBMwyFHbIREWSBmaDlcKmliGEvfDuR1YUerm5nm0vIEuHOtgZ/jgvxo4syMqki4kTEmFQAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:56.892505Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.6006","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b66023900f32118c0d5f300d8ba2fd85edb63d2afd554f770ab53f1481b3d6dd","sha256:267457ab5d43bee52f7548178665d1927ef3586d709c144dd6c6b5c17e9154da"],"state_sha256":"b09c7c3cc89e2e18742f1f7d1fff9af3b43c10129fec37b6954a54c249290835"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VVABvh30Nju2/qou3HrZYVh8hbLAyLhaC+iiqsQu+jFzw6Ae/FJvcUcX9zhDH8qcfQIqkLyiLkJIHTX2D8lbDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T20:08:16.009305Z","bundle_sha256":"8c5fc82ba6a063cb88de57c1553685a1c18317eee70f851885518ce37b1941e2"}}