{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:E6IX6ADBXS6EFNTODG44VAIBHY","short_pith_number":"pith:E6IX6ADB","canonical_record":{"source":{"id":"1712.06123","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-17T14:42:46Z","cross_cats_sorted":[],"title_canon_sha256":"efc3ef6d7e13ba3ecd86f728af55d134f6b338f104e9b7702d584b4be1a7b9eb","abstract_canon_sha256":"e0f274a242c17785161ebf1bf834df959ad9d1d9e903937de8edbc13d603ed6e"},"schema_version":"1.0"},"canonical_sha256":"27917f0061bcbc42b66e19b9ca81013e1ec8cfcb5d81760de04199899b6771a4","source":{"kind":"arxiv","id":"1712.06123","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.06123","created_at":"2026-05-17T23:59:58Z"},{"alias_kind":"arxiv_version","alias_value":"1712.06123v2","created_at":"2026-05-17T23:59:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06123","created_at":"2026-05-17T23:59:58Z"},{"alias_kind":"pith_short_12","alias_value":"E6IX6ADBXS6E","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"E6IX6ADBXS6EFNTO","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"E6IX6ADB","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:E6IX6ADBXS6EFNTODG44VAIBHY","target":"record","payload":{"canonical_record":{"source":{"id":"1712.06123","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-17T14:42:46Z","cross_cats_sorted":[],"title_canon_sha256":"efc3ef6d7e13ba3ecd86f728af55d134f6b338f104e9b7702d584b4be1a7b9eb","abstract_canon_sha256":"e0f274a242c17785161ebf1bf834df959ad9d1d9e903937de8edbc13d603ed6e"},"schema_version":"1.0"},"canonical_sha256":"27917f0061bcbc42b66e19b9ca81013e1ec8cfcb5d81760de04199899b6771a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:58.197051Z","signature_b64":"EqHg+TrBhBYBFL5sMh1Vscay3b0wZwmTQz/BByqEDUICFEpLDOXi1DGSKJl8emRGqPU9S3GRp4RSb4gTtPsHAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27917f0061bcbc42b66e19b9ca81013e1ec8cfcb5d81760de04199899b6771a4","last_reissued_at":"2026-05-17T23:59:58.196380Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:58.196380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.06123","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":"2026-05-17T23:59:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wC+/5jpx+qg8jjtNMffs6713SD7KJ9peEIUcPvwP91cMdPx5wjKWn2kE/CtneVz4TD/h1l9c1SP1U6TuqdtfBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:25:53.881596Z"},"content_sha256":"7e3ee5db81aa116e74c6e0995c2560e3e99473ed26308caf059dc23c1d6676fc","schema_version":"1.0","event_id":"sha256:7e3ee5db81aa116e74c6e0995c2560e3e99473ed26308caf059dc23c1d6676fc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:E6IX6ADBXS6EFNTODG44VAIBHY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimal non-integer alphabets allowing parallel addition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jan Legersk\\'y","submitted_at":"2017-12-17T14:42:46Z","abstract_excerpt":"Parallel addition, i.e., addition with limited carry propagation, has been so far studied for complex bases and integer alphabets. We focus on alphabets consisting of integer combinations of powers of the base. We give necessary conditions on the alphabet allowing parallel addition. Under certain assumptions, we prove the same lower bound on the size of the generalized alphabet that is known for alphabets consisting of consecutive integers. We also extend the characterization of bases allowing parallel addition to numeration systems with non-integer alphabets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06123","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":"2026-05-17T23:59:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KLhdpORiSOJJQD2inTRyLDsh4SW47ol4Xv8H0BrTCyILfTy2WfVNdYqFD1EQGIdS9NQvNceIzW6T3TLPt9FUDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:25:53.882257Z"},"content_sha256":"5a99a0fc6c53de09e0d223a3fbbee68ee254463af5fa2f4dc5b9411e58fcce7e","schema_version":"1.0","event_id":"sha256:5a99a0fc6c53de09e0d223a3fbbee68ee254463af5fa2f4dc5b9411e58fcce7e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E6IX6ADBXS6EFNTODG44VAIBHY/bundle.json","state_url":"https://pith.science/pith/E6IX6ADBXS6EFNTODG44VAIBHY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E6IX6ADBXS6EFNTODG44VAIBHY/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":"2026-05-25T19:25:53Z","links":{"resolver":"https://pith.science/pith/E6IX6ADBXS6EFNTODG44VAIBHY","bundle":"https://pith.science/pith/E6IX6ADBXS6EFNTODG44VAIBHY/bundle.json","state":"https://pith.science/pith/E6IX6ADBXS6EFNTODG44VAIBHY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E6IX6ADBXS6EFNTODG44VAIBHY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:E6IX6ADBXS6EFNTODG44VAIBHY","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":"e0f274a242c17785161ebf1bf834df959ad9d1d9e903937de8edbc13d603ed6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-17T14:42:46Z","title_canon_sha256":"efc3ef6d7e13ba3ecd86f728af55d134f6b338f104e9b7702d584b4be1a7b9eb"},"schema_version":"1.0","source":{"id":"1712.06123","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.06123","created_at":"2026-05-17T23:59:58Z"},{"alias_kind":"arxiv_version","alias_value":"1712.06123v2","created_at":"2026-05-17T23:59:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06123","created_at":"2026-05-17T23:59:58Z"},{"alias_kind":"pith_short_12","alias_value":"E6IX6ADBXS6E","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"E6IX6ADBXS6EFNTO","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"E6IX6ADB","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:5a99a0fc6c53de09e0d223a3fbbee68ee254463af5fa2f4dc5b9411e58fcce7e","target":"graph","created_at":"2026-05-17T23:59:58Z","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":"Parallel addition, i.e., addition with limited carry propagation, has been so far studied for complex bases and integer alphabets. We focus on alphabets consisting of integer combinations of powers of the base. We give necessary conditions on the alphabet allowing parallel addition. Under certain assumptions, we prove the same lower bound on the size of the generalized alphabet that is known for alphabets consisting of consecutive integers. We also extend the characterization of bases allowing parallel addition to numeration systems with non-integer alphabets.","authors_text":"Jan Legersk\\'y","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-17T14:42:46Z","title":"Minimal non-integer alphabets allowing parallel addition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06123","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":"sha256:7e3ee5db81aa116e74c6e0995c2560e3e99473ed26308caf059dc23c1d6676fc","target":"record","created_at":"2026-05-17T23:59:58Z","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":"e0f274a242c17785161ebf1bf834df959ad9d1d9e903937de8edbc13d603ed6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-17T14:42:46Z","title_canon_sha256":"efc3ef6d7e13ba3ecd86f728af55d134f6b338f104e9b7702d584b4be1a7b9eb"},"schema_version":"1.0","source":{"id":"1712.06123","kind":"arxiv","version":2}},"canonical_sha256":"27917f0061bcbc42b66e19b9ca81013e1ec8cfcb5d81760de04199899b6771a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27917f0061bcbc42b66e19b9ca81013e1ec8cfcb5d81760de04199899b6771a4","first_computed_at":"2026-05-17T23:59:58.196380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:58.196380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EqHg+TrBhBYBFL5sMh1Vscay3b0wZwmTQz/BByqEDUICFEpLDOXi1DGSKJl8emRGqPU9S3GRp4RSb4gTtPsHAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:58.197051Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.06123","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e3ee5db81aa116e74c6e0995c2560e3e99473ed26308caf059dc23c1d6676fc","sha256:5a99a0fc6c53de09e0d223a3fbbee68ee254463af5fa2f4dc5b9411e58fcce7e"],"state_sha256":"2d14e85de498b0e5ed7c0ab635dd98ca8ba531d0c2012fac8a2d367a0f7224e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PPCHO0a1y0npHmcYzvOmtP29bHD2NhDaKJKlNHuZD08uyswOuw9QOGJWHP6tlHFftAIQv5OwPR4+bje6pR6/Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:25:53.885577Z","bundle_sha256":"830bb1f174bf1564277a70b818c65db59fb314b01f22918e980fdfbd825b1030"}}