{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6LY5AYL6ZQ2JOWSN4EHNDX4HK2","short_pith_number":"pith:6LY5AYL6","canonical_record":{"source":{"id":"1801.10091","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-01-30T16:51:10Z","cross_cats_sorted":[],"title_canon_sha256":"80dff15960c8dd42ae3a922e08e8c424a4ad1cf08a5bfe3ec6a543c7c0e1e1df","abstract_canon_sha256":"51c246d98d8006cfcc8d9556c7951adbf337a4568279ad6c40dd8e38407b06c6"},"schema_version":"1.0"},"canonical_sha256":"f2f1d0617ecc34975a4de10ed1df8756b3c966a9787c3ee22806ab03ee0b50c4","source":{"kind":"arxiv","id":"1801.10091","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.10091","created_at":"2026-05-17T23:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"1801.10091v2","created_at":"2026-05-17T23:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.10091","created_at":"2026-05-17T23:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"6LY5AYL6ZQ2J","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6LY5AYL6ZQ2JOWSN","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6LY5AYL6","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6LY5AYL6ZQ2JOWSN4EHNDX4HK2","target":"record","payload":{"canonical_record":{"source":{"id":"1801.10091","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-01-30T16:51:10Z","cross_cats_sorted":[],"title_canon_sha256":"80dff15960c8dd42ae3a922e08e8c424a4ad1cf08a5bfe3ec6a543c7c0e1e1df","abstract_canon_sha256":"51c246d98d8006cfcc8d9556c7951adbf337a4568279ad6c40dd8e38407b06c6"},"schema_version":"1.0"},"canonical_sha256":"f2f1d0617ecc34975a4de10ed1df8756b3c966a9787c3ee22806ab03ee0b50c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:04.310629Z","signature_b64":"1DUaeD3DJto3Xm2/MMyo/T9u9s5Z1B5mlsIIB9Cqd2sx6oNlB5VlLWAvSfmQJeN400Yn5cQ8Z0SVnpeMesh3AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2f1d0617ecc34975a4de10ed1df8756b3c966a9787c3ee22806ab03ee0b50c4","last_reissued_at":"2026-05-17T23:46:04.309915Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:04.309915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.10091","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":"2026-05-17T23:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ix1h8Zbc6gQw+da3s5kIUzOz/AEjwbtyeOWQR5zRy9rj87JXo6pQmCFF8FQ5ghr0m/kKNOuzxPB/Nlj7QLrFDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:31:26.032795Z"},"content_sha256":"79bc02a81f454b93d1077e20fadf1b0e8cdfb78a28e0731f3ac0fc615f4e6b18","schema_version":"1.0","event_id":"sha256:79bc02a81f454b93d1077e20fadf1b0e8cdfb78a28e0731f3ac0fc615f4e6b18"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6LY5AYL6ZQ2JOWSN4EHNDX4HK2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Efficient Generalized Shift-Rule for the Prefer-Max De Bruijn Sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Amir Rubin, Gal Amram","submitted_at":"2018-01-30T16:51:10Z","abstract_excerpt":"One of the fundamental ways to construct De Bruijn sequences is by using a shift-rule. A shift-rule receives a word as an argument and computes the symbol that appears after it in the sequence. An optimal shift-rule for an $(n,k)$-De Bruijn sequence runs in time $O(n)$. We propose an extended notion we name a generalized-shift-rule, which receives a word, $w$, and an integer, $c$, and outputs the $c$ symbols that comes after $w$. An optimal generalized-shift-rule for an $(n,k)$-De Bruijn sequence runs in time $O(n+c)$. We show that, unlike in the case of a shift-rule, a time optimal generalize"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10091","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":"2026-05-17T23:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QOoM62b7Vi3HIMhWBA/4STExqSeq0YoKFC6D1exQdPZkcH+JL6L2zkKojXnD3GELl1wGVUw8/6ZLlnhrvqN9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:31:26.033132Z"},"content_sha256":"ed4f70639e35733b485ee71cf481a3e534976f95790370f54cf446dfb66dcd22","schema_version":"1.0","event_id":"sha256:ed4f70639e35733b485ee71cf481a3e534976f95790370f54cf446dfb66dcd22"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6LY5AYL6ZQ2JOWSN4EHNDX4HK2/bundle.json","state_url":"https://pith.science/pith/6LY5AYL6ZQ2JOWSN4EHNDX4HK2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6LY5AYL6ZQ2JOWSN4EHNDX4HK2/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":"2026-06-21T22:31:26Z","links":{"resolver":"https://pith.science/pith/6LY5AYL6ZQ2JOWSN4EHNDX4HK2","bundle":"https://pith.science/pith/6LY5AYL6ZQ2JOWSN4EHNDX4HK2/bundle.json","state":"https://pith.science/pith/6LY5AYL6ZQ2JOWSN4EHNDX4HK2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6LY5AYL6ZQ2JOWSN4EHNDX4HK2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6LY5AYL6ZQ2JOWSN4EHNDX4HK2","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":"51c246d98d8006cfcc8d9556c7951adbf337a4568279ad6c40dd8e38407b06c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-01-30T16:51:10Z","title_canon_sha256":"80dff15960c8dd42ae3a922e08e8c424a4ad1cf08a5bfe3ec6a543c7c0e1e1df"},"schema_version":"1.0","source":{"id":"1801.10091","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.10091","created_at":"2026-05-17T23:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"1801.10091v2","created_at":"2026-05-17T23:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.10091","created_at":"2026-05-17T23:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"6LY5AYL6ZQ2J","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6LY5AYL6ZQ2JOWSN","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6LY5AYL6","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:ed4f70639e35733b485ee71cf481a3e534976f95790370f54cf446dfb66dcd22","target":"graph","created_at":"2026-05-17T23:46:04Z","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":"One of the fundamental ways to construct De Bruijn sequences is by using a shift-rule. A shift-rule receives a word as an argument and computes the symbol that appears after it in the sequence. An optimal shift-rule for an $(n,k)$-De Bruijn sequence runs in time $O(n)$. We propose an extended notion we name a generalized-shift-rule, which receives a word, $w$, and an integer, $c$, and outputs the $c$ symbols that comes after $w$. An optimal generalized-shift-rule for an $(n,k)$-De Bruijn sequence runs in time $O(n+c)$. We show that, unlike in the case of a shift-rule, a time optimal generalize","authors_text":"Amir Rubin, Gal Amram","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-01-30T16:51:10Z","title":"An Efficient Generalized Shift-Rule for the Prefer-Max De Bruijn Sequence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10091","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":"sha256:79bc02a81f454b93d1077e20fadf1b0e8cdfb78a28e0731f3ac0fc615f4e6b18","target":"record","created_at":"2026-05-17T23:46:04Z","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":"51c246d98d8006cfcc8d9556c7951adbf337a4568279ad6c40dd8e38407b06c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-01-30T16:51:10Z","title_canon_sha256":"80dff15960c8dd42ae3a922e08e8c424a4ad1cf08a5bfe3ec6a543c7c0e1e1df"},"schema_version":"1.0","source":{"id":"1801.10091","kind":"arxiv","version":2}},"canonical_sha256":"f2f1d0617ecc34975a4de10ed1df8756b3c966a9787c3ee22806ab03ee0b50c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2f1d0617ecc34975a4de10ed1df8756b3c966a9787c3ee22806ab03ee0b50c4","first_computed_at":"2026-05-17T23:46:04.309915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:04.309915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1DUaeD3DJto3Xm2/MMyo/T9u9s5Z1B5mlsIIB9Cqd2sx6oNlB5VlLWAvSfmQJeN400Yn5cQ8Z0SVnpeMesh3AQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:04.310629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.10091","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79bc02a81f454b93d1077e20fadf1b0e8cdfb78a28e0731f3ac0fc615f4e6b18","sha256:ed4f70639e35733b485ee71cf481a3e534976f95790370f54cf446dfb66dcd22"],"state_sha256":"861574a940b45eef62aea57ae931e59fd2cdfcea111c94713cd197bf28646d42"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6N3udtdojG/SeqSEcHEP6UDM/y9MEvs41udDN3/SeCL0Pps1Dq+Ks25tSy7vvc7KKlyHg9L5N+zB129cQ/B9Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T22:31:26.035066Z","bundle_sha256":"c7a1f427b2b44c4020c368222603f6b7a97101c960948d03991d3bfc76c88d41"}}