{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6WFIVW4I3O5QD6WS6NU5F66S45","short_pith_number":"pith:6WFIVW4I","canonical_record":{"source":{"id":"1511.06230","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-11-19T16:12:17Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"65ff55d3536659e2f060b6dcaea8ef17432dd6f5a0eb110a55eda116a2994253","abstract_canon_sha256":"61093db0842f00fd09d56f6c84d2848a3eb02764687043ccec812ac01627617e"},"schema_version":"1.0"},"canonical_sha256":"f58a8adb88dbbb01fad2f369d2fbd2e76bebc0492bbdd89215dcceae56be157d","source":{"kind":"arxiv","id":"1511.06230","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.06230","created_at":"2026-05-18T01:26:26Z"},{"alias_kind":"arxiv_version","alias_value":"1511.06230v1","created_at":"2026-05-18T01:26:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06230","created_at":"2026-05-18T01:26:26Z"},{"alias_kind":"pith_short_12","alias_value":"6WFIVW4I3O5Q","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6WFIVW4I3O5QD6WS","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6WFIVW4I","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6WFIVW4I3O5QD6WS6NU5F66S45","target":"record","payload":{"canonical_record":{"source":{"id":"1511.06230","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-11-19T16:12:17Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"65ff55d3536659e2f060b6dcaea8ef17432dd6f5a0eb110a55eda116a2994253","abstract_canon_sha256":"61093db0842f00fd09d56f6c84d2848a3eb02764687043ccec812ac01627617e"},"schema_version":"1.0"},"canonical_sha256":"f58a8adb88dbbb01fad2f369d2fbd2e76bebc0492bbdd89215dcceae56be157d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:26.067881Z","signature_b64":"ykM8Ule4cGE28S34vpqtrkyrO4+yukZvb8qG9hV2pCcPbFg1yL7jcy7jMNS0dlOU81DYjtSjugp31SJHjmXEAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f58a8adb88dbbb01fad2f369d2fbd2e76bebc0492bbdd89215dcceae56be157d","last_reissued_at":"2026-05-18T01:26:26.067538Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:26.067538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.06230","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":"2026-05-18T01:26:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d3e3dmJn3XKJZm9Kn5tZ9wubIQ8jGalS2ZMnGLND5CY2avGnkLmTOz+jvSSoiMhe11HfWQI2OyorrNgWHXxUBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:02:11.859525Z"},"content_sha256":"2ee824e738c2e2a7eaa6d3acdb2b1e138dcaeead150a18de822ec2db39e0ddd2","schema_version":"1.0","event_id":"sha256:2ee824e738c2e2a7eaa6d3acdb2b1e138dcaeead150a18de822ec2db39e0ddd2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6WFIVW4I3O5QD6WS6NU5F66S45","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth's second tower","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Diego Ruano, Olav Geil, Stefano Martin, Umberto Mart\\'inez-Pe\\~nas","submitted_at":"2015-11-19T16:12:17Z","abstract_excerpt":"Asymptotically good sequences of ramp secret sharing schemes were given in [Asymptotically good ramp secret sharing schemes, arXiv:1502.05507] by using one-point algebraic geometric codes defined from asymptotically good towers of function fields. Their security is given by the relative generalized Hamming weights of the corresponding codes. In this paper we demonstrate how to obtain refined information on the RGHWs when the codimension of the codes is small. For general codimension, we give an improved estimate for the highest RGHW."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06230","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":"2026-05-18T01:26:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M0yJC8L8M/tiKtTxGdtjxavaP5B6qwMQy7LVwjoXHPsHhr2dz5mzReBoNfvKqHznLkY7KOhY80JfPUec4HYwCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:02:11.860224Z"},"content_sha256":"eb7e0a00e30836010e0a5b0dc70455e7e509fa038d1239a0582cc088fe6530e2","schema_version":"1.0","event_id":"sha256:eb7e0a00e30836010e0a5b0dc70455e7e509fa038d1239a0582cc088fe6530e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6WFIVW4I3O5QD6WS6NU5F66S45/bundle.json","state_url":"https://pith.science/pith/6WFIVW4I3O5QD6WS6NU5F66S45/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6WFIVW4I3O5QD6WS6NU5F66S45/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":"2026-06-09T05:02:11Z","links":{"resolver":"https://pith.science/pith/6WFIVW4I3O5QD6WS6NU5F66S45","bundle":"https://pith.science/pith/6WFIVW4I3O5QD6WS6NU5F66S45/bundle.json","state":"https://pith.science/pith/6WFIVW4I3O5QD6WS6NU5F66S45/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6WFIVW4I3O5QD6WS6NU5F66S45/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6WFIVW4I3O5QD6WS6NU5F66S45","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":"61093db0842f00fd09d56f6c84d2848a3eb02764687043ccec812ac01627617e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-11-19T16:12:17Z","title_canon_sha256":"65ff55d3536659e2f060b6dcaea8ef17432dd6f5a0eb110a55eda116a2994253"},"schema_version":"1.0","source":{"id":"1511.06230","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.06230","created_at":"2026-05-18T01:26:26Z"},{"alias_kind":"arxiv_version","alias_value":"1511.06230v1","created_at":"2026-05-18T01:26:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06230","created_at":"2026-05-18T01:26:26Z"},{"alias_kind":"pith_short_12","alias_value":"6WFIVW4I3O5Q","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6WFIVW4I3O5QD6WS","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6WFIVW4I","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:eb7e0a00e30836010e0a5b0dc70455e7e509fa038d1239a0582cc088fe6530e2","target":"graph","created_at":"2026-05-18T01:26:26Z","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":"Asymptotically good sequences of ramp secret sharing schemes were given in [Asymptotically good ramp secret sharing schemes, arXiv:1502.05507] by using one-point algebraic geometric codes defined from asymptotically good towers of function fields. Their security is given by the relative generalized Hamming weights of the corresponding codes. In this paper we demonstrate how to obtain refined information on the RGHWs when the codimension of the codes is small. For general codimension, we give an improved estimate for the highest RGHW.","authors_text":"Diego Ruano, Olav Geil, Stefano Martin, Umberto Mart\\'inez-Pe\\~nas","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-11-19T16:12:17Z","title":"Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth's second tower"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06230","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":"sha256:2ee824e738c2e2a7eaa6d3acdb2b1e138dcaeead150a18de822ec2db39e0ddd2","target":"record","created_at":"2026-05-18T01:26:26Z","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":"61093db0842f00fd09d56f6c84d2848a3eb02764687043ccec812ac01627617e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-11-19T16:12:17Z","title_canon_sha256":"65ff55d3536659e2f060b6dcaea8ef17432dd6f5a0eb110a55eda116a2994253"},"schema_version":"1.0","source":{"id":"1511.06230","kind":"arxiv","version":1}},"canonical_sha256":"f58a8adb88dbbb01fad2f369d2fbd2e76bebc0492bbdd89215dcceae56be157d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f58a8adb88dbbb01fad2f369d2fbd2e76bebc0492bbdd89215dcceae56be157d","first_computed_at":"2026-05-18T01:26:26.067538Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:26.067538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ykM8Ule4cGE28S34vpqtrkyrO4+yukZvb8qG9hV2pCcPbFg1yL7jcy7jMNS0dlOU81DYjtSjugp31SJHjmXEAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:26.067881Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.06230","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ee824e738c2e2a7eaa6d3acdb2b1e138dcaeead150a18de822ec2db39e0ddd2","sha256:eb7e0a00e30836010e0a5b0dc70455e7e509fa038d1239a0582cc088fe6530e2"],"state_sha256":"5d9ecb4dbb0306c5dfe71cf4573c922678ee928cc9b1858ec5c6dedfbc01c3c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1vXk66FJj/xO3wtIeIF8SS6IMqTTk6h1OoUrX1kLjx/mXrT2ph1t/hDnxkE5ZexDneKraFy1UW6j9rEp12m6Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T05:02:11.864141Z","bundle_sha256":"c06fab6b831ede2e1d12c68c4ce9d960dc6c5b17c3858e6de5d84ea95fbf75db"}}