{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:GHJUR7XU5GZUUMUHQ77FC3LWYB","short_pith_number":"pith:GHJUR7XU","canonical_record":{"source":{"id":"1901.03149","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-10T13:33:47Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"33d1892ded8c16c067f3f8b67521dfb30481d95e4660782ed7ac8742362e82de","abstract_canon_sha256":"24789e77f3293344d90afed1fcfc099e4bf0a90c377ba7d18cc12441466a0ab4"},"schema_version":"1.0"},"canonical_sha256":"31d348fef4e9b34a328787fe516d76c07bcb36493fe65111cff1c928e8087169","source":{"kind":"arxiv","id":"1901.03149","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.03149","created_at":"2026-05-17T23:41:36Z"},{"alias_kind":"arxiv_version","alias_value":"1901.03149v2","created_at":"2026-05-17T23:41:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.03149","created_at":"2026-05-17T23:41:36Z"},{"alias_kind":"pith_short_12","alias_value":"GHJUR7XU5GZU","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"GHJUR7XU5GZUUMUH","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"GHJUR7XU","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:GHJUR7XU5GZUUMUHQ77FC3LWYB","target":"record","payload":{"canonical_record":{"source":{"id":"1901.03149","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-10T13:33:47Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"33d1892ded8c16c067f3f8b67521dfb30481d95e4660782ed7ac8742362e82de","abstract_canon_sha256":"24789e77f3293344d90afed1fcfc099e4bf0a90c377ba7d18cc12441466a0ab4"},"schema_version":"1.0"},"canonical_sha256":"31d348fef4e9b34a328787fe516d76c07bcb36493fe65111cff1c928e8087169","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:36.684610Z","signature_b64":"upf5XnEYVTmz7+rvrriIhJXSwV7oYFJYldckZNcr9EmusEpPV22isoLKMmBjhQiUHB8HQ0vBQYPt88mVjHOgAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31d348fef4e9b34a328787fe516d76c07bcb36493fe65111cff1c928e8087169","last_reissued_at":"2026-05-17T23:41:36.683889Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:36.683889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.03149","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":"2026-05-17T23:41:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QLso7h21Jgh9sdVVTsCjhZnOhVdlG6BCtgBhenwlErC6ifkEP+RW2FTV95CDgaVYMWZtjoLUxzt1Yo+v4U+XCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:31:58.675213Z"},"content_sha256":"9987954e7ab4f4a18b040847c1da5053d5cf44bab39dd5e3e6f5a2b37b57db3d","schema_version":"1.0","event_id":"sha256:9987954e7ab4f4a18b040847c1da5053d5cf44bab39dd5e3e6f5a2b37b57db3d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:GHJUR7XU5GZUUMUHQ77FC3LWYB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Complete Hierarchical Locality of the Punctured Simplex Code","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Camilla Hollanti, Matthias Grezet","submitted_at":"2019-01-10T13:33:47Z","abstract_excerpt":"This paper presents a new alphabet-dependent bound for codes with hierarchical locality. Then, the complete list of possible localities is derived for a class of codes obtained by deleting specific columns from a Simplex code. This list is used to show that these codes are optimal codes with hierarchical locality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03149","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":"2026-05-17T23:41:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l8EA6gNUJg3MU8VX/Hk+j/5E/U9XR1RFRZC9rGk4PAS61NGisMtw+A1pKQxTEU/FSVJpXEfRlVpi/JcrPSXQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:31:58.675943Z"},"content_sha256":"68dee57422fbddca84f48188645b9dfd9e2e1909e6e9ec5d405ca5adb4c71d9e","schema_version":"1.0","event_id":"sha256:68dee57422fbddca84f48188645b9dfd9e2e1909e6e9ec5d405ca5adb4c71d9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GHJUR7XU5GZUUMUHQ77FC3LWYB/bundle.json","state_url":"https://pith.science/pith/GHJUR7XU5GZUUMUHQ77FC3LWYB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GHJUR7XU5GZUUMUHQ77FC3LWYB/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":"2026-06-08T17:31:58Z","links":{"resolver":"https://pith.science/pith/GHJUR7XU5GZUUMUHQ77FC3LWYB","bundle":"https://pith.science/pith/GHJUR7XU5GZUUMUHQ77FC3LWYB/bundle.json","state":"https://pith.science/pith/GHJUR7XU5GZUUMUHQ77FC3LWYB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GHJUR7XU5GZUUMUHQ77FC3LWYB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GHJUR7XU5GZUUMUHQ77FC3LWYB","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":"24789e77f3293344d90afed1fcfc099e4bf0a90c377ba7d18cc12441466a0ab4","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-10T13:33:47Z","title_canon_sha256":"33d1892ded8c16c067f3f8b67521dfb30481d95e4660782ed7ac8742362e82de"},"schema_version":"1.0","source":{"id":"1901.03149","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.03149","created_at":"2026-05-17T23:41:36Z"},{"alias_kind":"arxiv_version","alias_value":"1901.03149v2","created_at":"2026-05-17T23:41:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.03149","created_at":"2026-05-17T23:41:36Z"},{"alias_kind":"pith_short_12","alias_value":"GHJUR7XU5GZU","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"GHJUR7XU5GZUUMUH","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"GHJUR7XU","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:68dee57422fbddca84f48188645b9dfd9e2e1909e6e9ec5d405ca5adb4c71d9e","target":"graph","created_at":"2026-05-17T23:41:36Z","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":"This paper presents a new alphabet-dependent bound for codes with hierarchical locality. Then, the complete list of possible localities is derived for a class of codes obtained by deleting specific columns from a Simplex code. This list is used to show that these codes are optimal codes with hierarchical locality.","authors_text":"Camilla Hollanti, Matthias Grezet","cross_cats":["math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-10T13:33:47Z","title":"The Complete Hierarchical Locality of the Punctured Simplex Code"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03149","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":"sha256:9987954e7ab4f4a18b040847c1da5053d5cf44bab39dd5e3e6f5a2b37b57db3d","target":"record","created_at":"2026-05-17T23:41:36Z","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":"24789e77f3293344d90afed1fcfc099e4bf0a90c377ba7d18cc12441466a0ab4","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-10T13:33:47Z","title_canon_sha256":"33d1892ded8c16c067f3f8b67521dfb30481d95e4660782ed7ac8742362e82de"},"schema_version":"1.0","source":{"id":"1901.03149","kind":"arxiv","version":2}},"canonical_sha256":"31d348fef4e9b34a328787fe516d76c07bcb36493fe65111cff1c928e8087169","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31d348fef4e9b34a328787fe516d76c07bcb36493fe65111cff1c928e8087169","first_computed_at":"2026-05-17T23:41:36.683889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:36.683889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"upf5XnEYVTmz7+rvrriIhJXSwV7oYFJYldckZNcr9EmusEpPV22isoLKMmBjhQiUHB8HQ0vBQYPt88mVjHOgAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:36.684610Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.03149","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9987954e7ab4f4a18b040847c1da5053d5cf44bab39dd5e3e6f5a2b37b57db3d","sha256:68dee57422fbddca84f48188645b9dfd9e2e1909e6e9ec5d405ca5adb4c71d9e"],"state_sha256":"4b55804a990f144c78cd47c3cee56856b68c5bf307b6630eb8174dd42d1c0c54"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HJvo+2xUIW/EP8qyc5xWim1qUISSFG8EXUXcPPglPZ9U7pR1eEzfB9jkfo7QlMxRqN9lfrmN152VTSoBMrwuCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:31:58.679099Z","bundle_sha256":"dca36724babc258f73e5a1dbd5053ad6ec73ca87b1fffc7bbb9732b13638c56c"}}