{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:A3OABQTQ6JDBWDV57UJLQIIJKJ","short_pith_number":"pith:A3OABQTQ","canonical_record":{"source":{"id":"1207.0302","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-02T07:54:10Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"dad70281a4c4648ee1343736e94af44389538e41da3febfc4768f13c0311845d","abstract_canon_sha256":"fad56d16db80c5847d192e65fae40b409e592fcae5433c922db975cdd34c9c78"},"schema_version":"1.0"},"canonical_sha256":"06dc00c270f2461b0ebdfd12b82109526ba0157ccc8e00e0085b56457d552ba9","source":{"kind":"arxiv","id":"1207.0302","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0302","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0302v3","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0302","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"A3OABQTQ6JDB","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"A3OABQTQ6JDBWDV5","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"A3OABQTQ","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:A3OABQTQ6JDBWDV57UJLQIIJKJ","target":"record","payload":{"canonical_record":{"source":{"id":"1207.0302","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-02T07:54:10Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"dad70281a4c4648ee1343736e94af44389538e41da3febfc4768f13c0311845d","abstract_canon_sha256":"fad56d16db80c5847d192e65fae40b409e592fcae5433c922db975cdd34c9c78"},"schema_version":"1.0"},"canonical_sha256":"06dc00c270f2461b0ebdfd12b82109526ba0157ccc8e00e0085b56457d552ba9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:21.666435Z","signature_b64":"McU3tcnd3dceZgtu7iJh6XYyhHc1SinSjJoHaTCeBVhyod+V1Am0+OO7hwLJ4B2aBasW/K64TK3/yY+uBvh+Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06dc00c270f2461b0ebdfd12b82109526ba0157ccc8e00e0085b56457d552ba9","last_reissued_at":"2026-05-18T03:45:21.665646Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:21.665646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.0302","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:45:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PNRb1G7xKelV2TtYoTDvDvuVqvjW4UgKFGVmCkbYnKQY7ZwV7eqiMrI7Ub/oHIcukLDgkV0n30haKV8fLDoABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:28:44.428099Z"},"content_sha256":"6d6edd5ce1cdbb0aa9b1aa3043ee77ac97d38db9a7ac3a82e4646f51568bb580","schema_version":"1.0","event_id":"sha256:6d6edd5ce1cdbb0aa9b1aa3043ee77ac97d38db9a7ac3a82e4646f51568bb580"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:A3OABQTQ6JDBWDV57UJLQIIJKJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards More Realistic Probabilistic Models for Data Structures: The External Path Length in Tries under the Markov Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.PR","authors_text":"Kevin Leckey, Ralph Neininger, Wojciech Szpankowski","submitted_at":"2012-07-02T07:54:10Z","abstract_excerpt":"Tries are among the most versatile and widely used data structures on words. They are pertinent to the (internal) structure of (stored) words and several splitting procedures used in diverse contexts ranging from document taxonomy to IP addresses lookup, from data compression (i.e., Lempel-Ziv'77 scheme) to dynamic hashing, from partial-match queries to speech recognition, from leader election algorithms to distributed hashing tables and graph compression. While the performance of tries under a realistic probabilistic model is of significant importance, its analysis, even for simplest memoryle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0302","kind":"arxiv","version":3},"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":"2026-05-18T03:45:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xKRdwzk8n1XA70g6TnJ4tvmNrALQQYexElGm7AvhmSqUa9mwJAtwTIGpUxBnlU5WFIa8v0uBbTR3F3kJblJnBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:28:44.428463Z"},"content_sha256":"5e1e200d40b2fb27d547b7a1432f96703e1daac88cc6f14a644038ff6e2525a8","schema_version":"1.0","event_id":"sha256:5e1e200d40b2fb27d547b7a1432f96703e1daac88cc6f14a644038ff6e2525a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A3OABQTQ6JDBWDV57UJLQIIJKJ/bundle.json","state_url":"https://pith.science/pith/A3OABQTQ6JDBWDV57UJLQIIJKJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A3OABQTQ6JDBWDV57UJLQIIJKJ/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":"2026-05-31T17:28:44Z","links":{"resolver":"https://pith.science/pith/A3OABQTQ6JDBWDV57UJLQIIJKJ","bundle":"https://pith.science/pith/A3OABQTQ6JDBWDV57UJLQIIJKJ/bundle.json","state":"https://pith.science/pith/A3OABQTQ6JDBWDV57UJLQIIJKJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A3OABQTQ6JDBWDV57UJLQIIJKJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:A3OABQTQ6JDBWDV57UJLQIIJKJ","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":"fad56d16db80c5847d192e65fae40b409e592fcae5433c922db975cdd34c9c78","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-02T07:54:10Z","title_canon_sha256":"dad70281a4c4648ee1343736e94af44389538e41da3febfc4768f13c0311845d"},"schema_version":"1.0","source":{"id":"1207.0302","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0302","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0302v3","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0302","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"A3OABQTQ6JDB","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"A3OABQTQ6JDBWDV5","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"A3OABQTQ","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:5e1e200d40b2fb27d547b7a1432f96703e1daac88cc6f14a644038ff6e2525a8","target":"graph","created_at":"2026-05-18T03:45:21Z","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":"Tries are among the most versatile and widely used data structures on words. They are pertinent to the (internal) structure of (stored) words and several splitting procedures used in diverse contexts ranging from document taxonomy to IP addresses lookup, from data compression (i.e., Lempel-Ziv'77 scheme) to dynamic hashing, from partial-match queries to speech recognition, from leader election algorithms to distributed hashing tables and graph compression. While the performance of tries under a realistic probabilistic model is of significant importance, its analysis, even for simplest memoryle","authors_text":"Kevin Leckey, Ralph Neininger, Wojciech Szpankowski","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-02T07:54:10Z","title":"Towards More Realistic Probabilistic Models for Data Structures: The External Path Length in Tries under the Markov Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0302","kind":"arxiv","version":3},"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":"sha256:6d6edd5ce1cdbb0aa9b1aa3043ee77ac97d38db9a7ac3a82e4646f51568bb580","target":"record","created_at":"2026-05-18T03:45:21Z","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":"fad56d16db80c5847d192e65fae40b409e592fcae5433c922db975cdd34c9c78","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-02T07:54:10Z","title_canon_sha256":"dad70281a4c4648ee1343736e94af44389538e41da3febfc4768f13c0311845d"},"schema_version":"1.0","source":{"id":"1207.0302","kind":"arxiv","version":3}},"canonical_sha256":"06dc00c270f2461b0ebdfd12b82109526ba0157ccc8e00e0085b56457d552ba9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06dc00c270f2461b0ebdfd12b82109526ba0157ccc8e00e0085b56457d552ba9","first_computed_at":"2026-05-18T03:45:21.665646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:21.665646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"McU3tcnd3dceZgtu7iJh6XYyhHc1SinSjJoHaTCeBVhyod+V1Am0+OO7hwLJ4B2aBasW/K64TK3/yY+uBvh+Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:21.666435Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.0302","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d6edd5ce1cdbb0aa9b1aa3043ee77ac97d38db9a7ac3a82e4646f51568bb580","sha256:5e1e200d40b2fb27d547b7a1432f96703e1daac88cc6f14a644038ff6e2525a8"],"state_sha256":"2a717286a295bf1965de664047f92d4748b105d7f83c9c7dc3625f373d2a003c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A3EkqQz4zMGSwqrJTsR3pzClg9eQ+vK8vP/nv0Q+8fMyFrIZRM+B9Z5QLYM/8cq3LZ+hmZ3F7djCown/ONggAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T17:28:44.430636Z","bundle_sha256":"ba3a9b8053492c40af1002807ebfbb868a70071e007d4ad254978fdce0a9f75b"}}