{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZMLXEAS7KNLDQCOJJNKFYVJTZA","short_pith_number":"pith:ZMLXEAS7","canonical_record":{"source":{"id":"1507.07038","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-24T22:40:14Z","cross_cats_sorted":[],"title_canon_sha256":"26a1c9fe0be2928a94e638c0393f539d1d325c1f7db7795aed15e95afc2a7431","abstract_canon_sha256":"73669bf0efae12efdb846a7a81697ec72cd54624a759840579beb1a63050f4d2"},"schema_version":"1.0"},"canonical_sha256":"cb1772025f53563809c94b545c5533c82d82aedaed72e6dbc2864a3c2f292565","source":{"kind":"arxiv","id":"1507.07038","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.07038","created_at":"2026-05-18T01:36:17Z"},{"alias_kind":"arxiv_version","alias_value":"1507.07038v1","created_at":"2026-05-18T01:36:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07038","created_at":"2026-05-18T01:36:17Z"},{"alias_kind":"pith_short_12","alias_value":"ZMLXEAS7KNLD","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZMLXEAS7KNLDQCOJ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZMLXEAS7","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZMLXEAS7KNLDQCOJJNKFYVJTZA","target":"record","payload":{"canonical_record":{"source":{"id":"1507.07038","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-24T22:40:14Z","cross_cats_sorted":[],"title_canon_sha256":"26a1c9fe0be2928a94e638c0393f539d1d325c1f7db7795aed15e95afc2a7431","abstract_canon_sha256":"73669bf0efae12efdb846a7a81697ec72cd54624a759840579beb1a63050f4d2"},"schema_version":"1.0"},"canonical_sha256":"cb1772025f53563809c94b545c5533c82d82aedaed72e6dbc2864a3c2f292565","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:17.457712Z","signature_b64":"MbvEG/Lqsi6lfZLPHFIjaLtfTVUUMu85xVIFBwYDCaUlfcpI3PLNErxezEi+0/MPxYjaJJs7Nkoq3AMrbBpwAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb1772025f53563809c94b545c5533c82d82aedaed72e6dbc2864a3c2f292565","last_reissued_at":"2026-05-18T01:36:17.457153Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:17.457153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.07038","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":"2026-05-18T01:36:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MtClmBAXK8HB7OlBtiTLv0SXqp4PatVf5SV1+5Jjht8FGYsFXEShpyRkWHX1GflsPYe1s6yiGkeY3vkGp5vlBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:59:01.732625Z"},"content_sha256":"a53af59653091cc7956e19fa7ca5dd8a25770bc472a6eac8981c28926852f30b","schema_version":"1.0","event_id":"sha256:a53af59653091cc7956e19fa7ca5dd8a25770bc472a6eac8981c28926852f30b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZMLXEAS7KNLDQCOJJNKFYVJTZA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"String Comparison in $V$-Order: New Lexicographic Properties & On-line Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ali Alatabbi, Jacqueline W. Daykin, M. Sohel Rahman, W. F. Smyth","submitted_at":"2015-07-24T22:40:14Z","abstract_excerpt":"$V$-order is a global order on strings related to Unique Maximal Factorization Families (UMFFs), which are themselves generalizations of Lyndon words. $V$-order has recently been proposed as an alternative to lexicographical order in the computation of suffix arrays and in the suffix-sorting induced by the Burrows-Wheeler transform. Efficient $V$-ordering of strings thus becomes a matter of considerable interest. In this paper we present new and surprising results on $V$-order in strings, then go on to explore the algorithmic consequences."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07038","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":"2026-05-18T01:36:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lybCEG8jq3HXUHpqYbjr+iBaTCwHvjZ4Sbm31acTv5AGUBeAq313ER3VLaU73tbU52vhamvpIggIz1Tw9LLeCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:59:01.733387Z"},"content_sha256":"a0bd2afb100dff4e22c647804ee523f5c2a8805889b81594a0be46f8702176e7","schema_version":"1.0","event_id":"sha256:a0bd2afb100dff4e22c647804ee523f5c2a8805889b81594a0be46f8702176e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZMLXEAS7KNLDQCOJJNKFYVJTZA/bundle.json","state_url":"https://pith.science/pith/ZMLXEAS7KNLDQCOJJNKFYVJTZA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZMLXEAS7KNLDQCOJJNKFYVJTZA/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":"2026-06-09T06:59:01Z","links":{"resolver":"https://pith.science/pith/ZMLXEAS7KNLDQCOJJNKFYVJTZA","bundle":"https://pith.science/pith/ZMLXEAS7KNLDQCOJJNKFYVJTZA/bundle.json","state":"https://pith.science/pith/ZMLXEAS7KNLDQCOJJNKFYVJTZA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZMLXEAS7KNLDQCOJJNKFYVJTZA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZMLXEAS7KNLDQCOJJNKFYVJTZA","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":"73669bf0efae12efdb846a7a81697ec72cd54624a759840579beb1a63050f4d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-24T22:40:14Z","title_canon_sha256":"26a1c9fe0be2928a94e638c0393f539d1d325c1f7db7795aed15e95afc2a7431"},"schema_version":"1.0","source":{"id":"1507.07038","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.07038","created_at":"2026-05-18T01:36:17Z"},{"alias_kind":"arxiv_version","alias_value":"1507.07038v1","created_at":"2026-05-18T01:36:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07038","created_at":"2026-05-18T01:36:17Z"},{"alias_kind":"pith_short_12","alias_value":"ZMLXEAS7KNLD","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZMLXEAS7KNLDQCOJ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZMLXEAS7","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:a0bd2afb100dff4e22c647804ee523f5c2a8805889b81594a0be46f8702176e7","target":"graph","created_at":"2026-05-18T01:36:17Z","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":"$V$-order is a global order on strings related to Unique Maximal Factorization Families (UMFFs), which are themselves generalizations of Lyndon words. $V$-order has recently been proposed as an alternative to lexicographical order in the computation of suffix arrays and in the suffix-sorting induced by the Burrows-Wheeler transform. Efficient $V$-ordering of strings thus becomes a matter of considerable interest. In this paper we present new and surprising results on $V$-order in strings, then go on to explore the algorithmic consequences.","authors_text":"Ali Alatabbi, Jacqueline W. Daykin, M. Sohel Rahman, W. F. Smyth","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-24T22:40:14Z","title":"String Comparison in $V$-Order: New Lexicographic Properties & On-line Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07038","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:a53af59653091cc7956e19fa7ca5dd8a25770bc472a6eac8981c28926852f30b","target":"record","created_at":"2026-05-18T01:36:17Z","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":"73669bf0efae12efdb846a7a81697ec72cd54624a759840579beb1a63050f4d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-24T22:40:14Z","title_canon_sha256":"26a1c9fe0be2928a94e638c0393f539d1d325c1f7db7795aed15e95afc2a7431"},"schema_version":"1.0","source":{"id":"1507.07038","kind":"arxiv","version":1}},"canonical_sha256":"cb1772025f53563809c94b545c5533c82d82aedaed72e6dbc2864a3c2f292565","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb1772025f53563809c94b545c5533c82d82aedaed72e6dbc2864a3c2f292565","first_computed_at":"2026-05-18T01:36:17.457153Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:17.457153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MbvEG/Lqsi6lfZLPHFIjaLtfTVUUMu85xVIFBwYDCaUlfcpI3PLNErxezEi+0/MPxYjaJJs7Nkoq3AMrbBpwAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:17.457712Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.07038","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a53af59653091cc7956e19fa7ca5dd8a25770bc472a6eac8981c28926852f30b","sha256:a0bd2afb100dff4e22c647804ee523f5c2a8805889b81594a0be46f8702176e7"],"state_sha256":"0d1cab4b32c7ceb66e463c93788a0f352020f05a3bb591cb4f636f9a456b2a05"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kAHsutj+zkqXEgL3KcQcoELNE2AOOTrthFA4GfME6UHhSkKWDwCHAan/hMiYLKN6LBdAjNQM0tXalpTzBPVZAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:59:01.737355Z","bundle_sha256":"2f3b803af6787aa850e13fbd4409f4797876ea6c443df9617436d867256ad4eb"}}