{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ASESDNVEARCOHPUHATMCA5TWXA","short_pith_number":"pith:ASESDNVE","canonical_record":{"source":{"id":"1708.05347","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-08-17T16:11:24Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"3e7f36ff416250ebb898dffe97a4b7d68a1e063b27a430d65bb11316580538d0","abstract_canon_sha256":"4ee421f6fd22e67770c6ff8e8409bbb8941663fa8e7fe424283a9c10119fceab"},"schema_version":"1.0"},"canonical_sha256":"048921b6a40444e3be8704d8207676b80c1034ea9cac0f62d23d66792bf3af09","source":{"kind":"arxiv","id":"1708.05347","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.05347","created_at":"2026-05-18T00:37:53Z"},{"alias_kind":"arxiv_version","alias_value":"1708.05347v1","created_at":"2026-05-18T00:37:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.05347","created_at":"2026-05-18T00:37:53Z"},{"alias_kind":"pith_short_12","alias_value":"ASESDNVEARCO","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"ASESDNVEARCOHPUH","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"ASESDNVE","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ASESDNVEARCOHPUHATMCA5TWXA","target":"record","payload":{"canonical_record":{"source":{"id":"1708.05347","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-08-17T16:11:24Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"3e7f36ff416250ebb898dffe97a4b7d68a1e063b27a430d65bb11316580538d0","abstract_canon_sha256":"4ee421f6fd22e67770c6ff8e8409bbb8941663fa8e7fe424283a9c10119fceab"},"schema_version":"1.0"},"canonical_sha256":"048921b6a40444e3be8704d8207676b80c1034ea9cac0f62d23d66792bf3af09","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:53.184929Z","signature_b64":"uid6q2JXB84yFsdjVHX768VR0gFyhspE+0bo26ke2DVe9ek0TCKj8Qyuj8144u1l19PvwdkKCMEZ3wvTnhcfAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"048921b6a40444e3be8704d8207676b80c1034ea9cac0f62d23d66792bf3af09","last_reissued_at":"2026-05-18T00:37:53.184468Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:53.184468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.05347","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":"2026-05-18T00:37:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LOtQ85YOtauquPETL/K6QCOXgn4mOHhBtoCy2CL2nHwvuLZCLRIu0QyXnmQXpH9vF94eM/hHExRdsTSsJF4TCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:20:51.744191Z"},"content_sha256":"a967874a5229fa7932d03e44241c3446bed22d80dc3690ea88b59eb705deafce","schema_version":"1.0","event_id":"sha256:a967874a5229fa7932d03e44241c3446bed22d80dc3690ea88b59eb705deafce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ASESDNVEARCOHPUHATMCA5TWXA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two weight $\\mathbb{Z}_{p^k}$-codes, $p$ odd prime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Minjia Shi, Patrick Sol\\'e, Rongsheng Wu, Zahra Sepasdar","submitted_at":"2017-08-17T16:11:24Z","abstract_excerpt":"We show that regular homogeneous two-weight $\\mathbb{Z}_{p^k}$-codes where $p$ is odd and $k\\geqslant 2$ with dual Hamming distance at least four do not exist. The proof relies on existence conditions for the strongly regular graph built on the cosets of the dual code."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05347","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":"2026-05-18T00:37:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WIg+nH5E+6XrGA7MVT5Nz0uGSOjcpw8WEwSm5z+T3ovPC+r/QLL7VvzUNiyNsX3XJMJWdrnWqCtPgmvacpSECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:20:51.744794Z"},"content_sha256":"9cf54e0853fd03c8d52912d32f970e19491684b46ca8ed7776c696844a8d5296","schema_version":"1.0","event_id":"sha256:9cf54e0853fd03c8d52912d32f970e19491684b46ca8ed7776c696844a8d5296"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ASESDNVEARCOHPUHATMCA5TWXA/bundle.json","state_url":"https://pith.science/pith/ASESDNVEARCOHPUHATMCA5TWXA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ASESDNVEARCOHPUHATMCA5TWXA/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":"2026-05-27T12:20:51Z","links":{"resolver":"https://pith.science/pith/ASESDNVEARCOHPUHATMCA5TWXA","bundle":"https://pith.science/pith/ASESDNVEARCOHPUHATMCA5TWXA/bundle.json","state":"https://pith.science/pith/ASESDNVEARCOHPUHATMCA5TWXA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ASESDNVEARCOHPUHATMCA5TWXA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ASESDNVEARCOHPUHATMCA5TWXA","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":"4ee421f6fd22e67770c6ff8e8409bbb8941663fa8e7fe424283a9c10119fceab","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-08-17T16:11:24Z","title_canon_sha256":"3e7f36ff416250ebb898dffe97a4b7d68a1e063b27a430d65bb11316580538d0"},"schema_version":"1.0","source":{"id":"1708.05347","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.05347","created_at":"2026-05-18T00:37:53Z"},{"alias_kind":"arxiv_version","alias_value":"1708.05347v1","created_at":"2026-05-18T00:37:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.05347","created_at":"2026-05-18T00:37:53Z"},{"alias_kind":"pith_short_12","alias_value":"ASESDNVEARCO","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"ASESDNVEARCOHPUH","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"ASESDNVE","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:9cf54e0853fd03c8d52912d32f970e19491684b46ca8ed7776c696844a8d5296","target":"graph","created_at":"2026-05-18T00:37:53Z","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 show that regular homogeneous two-weight $\\mathbb{Z}_{p^k}$-codes where $p$ is odd and $k\\geqslant 2$ with dual Hamming distance at least four do not exist. The proof relies on existence conditions for the strongly regular graph built on the cosets of the dual code.","authors_text":"Minjia Shi, Patrick Sol\\'e, Rongsheng Wu, Zahra Sepasdar","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-08-17T16:11:24Z","title":"Two weight $\\mathbb{Z}_{p^k}$-codes, $p$ odd prime"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05347","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:a967874a5229fa7932d03e44241c3446bed22d80dc3690ea88b59eb705deafce","target":"record","created_at":"2026-05-18T00:37:53Z","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":"4ee421f6fd22e67770c6ff8e8409bbb8941663fa8e7fe424283a9c10119fceab","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-08-17T16:11:24Z","title_canon_sha256":"3e7f36ff416250ebb898dffe97a4b7d68a1e063b27a430d65bb11316580538d0"},"schema_version":"1.0","source":{"id":"1708.05347","kind":"arxiv","version":1}},"canonical_sha256":"048921b6a40444e3be8704d8207676b80c1034ea9cac0f62d23d66792bf3af09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"048921b6a40444e3be8704d8207676b80c1034ea9cac0f62d23d66792bf3af09","first_computed_at":"2026-05-18T00:37:53.184468Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:53.184468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uid6q2JXB84yFsdjVHX768VR0gFyhspE+0bo26ke2DVe9ek0TCKj8Qyuj8144u1l19PvwdkKCMEZ3wvTnhcfAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:53.184929Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.05347","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a967874a5229fa7932d03e44241c3446bed22d80dc3690ea88b59eb705deafce","sha256:9cf54e0853fd03c8d52912d32f970e19491684b46ca8ed7776c696844a8d5296"],"state_sha256":"68806611ff5bea4f4933d65e2a2b2778d4893c907ce2d87e5a23e61132a933c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8lHTdHhX/5YK8WOKXmHuawATcjjfYcaCg8N90xzzFB8UKO/6mO44F8/imNhIIz+J6SoHRla7+vvK5haprx9fDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T12:20:51.748175Z","bundle_sha256":"4e66d5457a74766cb37104b82a7559e4f0cd819dba087406e2a3aacc2c031f16"}}