{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:4KK3RHWHCTDSB6FKCW2Y3C6FWI","short_pith_number":"pith:4KK3RHWH","canonical_record":{"source":{"id":"1407.4286","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-07-16T12:48:48Z","cross_cats_sorted":["cs.CC","cs.FL"],"title_canon_sha256":"4c47020c35a247a1b8e3d832ac30ea4f33f386cca1c596c463d91a2d10facc92","abstract_canon_sha256":"65e9794589523755a2853073702ccad5f1b10d47826b817f168130c7ddbfdc53"},"schema_version":"1.0"},"canonical_sha256":"e295b89ec714c720f8aa15b58d8bc5b21cc99276238cc65a5be645efcc01ff0c","source":{"kind":"arxiv","id":"1407.4286","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4286","created_at":"2026-05-18T01:32:41Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4286v3","created_at":"2026-05-18T01:32:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4286","created_at":"2026-05-18T01:32:41Z"},{"alias_kind":"pith_short_12","alias_value":"4KK3RHWHCTDS","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4KK3RHWHCTDSB6FK","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4KK3RHWH","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:4KK3RHWHCTDSB6FKCW2Y3C6FWI","target":"record","payload":{"canonical_record":{"source":{"id":"1407.4286","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-07-16T12:48:48Z","cross_cats_sorted":["cs.CC","cs.FL"],"title_canon_sha256":"4c47020c35a247a1b8e3d832ac30ea4f33f386cca1c596c463d91a2d10facc92","abstract_canon_sha256":"65e9794589523755a2853073702ccad5f1b10d47826b817f168130c7ddbfdc53"},"schema_version":"1.0"},"canonical_sha256":"e295b89ec714c720f8aa15b58d8bc5b21cc99276238cc65a5be645efcc01ff0c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:41.839562Z","signature_b64":"OM9GekxUm2oMYf00RewY18u/s+iSAkJDgg+dQnWu2OC3bQPHBeUi/C8XHMVXoCwAF3CssORnhS6m9TnPL+ZKDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e295b89ec714c720f8aa15b58d8bc5b21cc99276238cc65a5be645efcc01ff0c","last_reissued_at":"2026-05-18T01:32:41.839036Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:41.839036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.4286","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":"2026-05-18T01:32:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lOaVYeMRW3HAhb7s9fh49HyZgsxnoCOCQJ1IjqxutGVJBWtplpI9eTKVuyuRFCeVSJuJreNnnXobyvDIGI2yDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T17:53:46.465631Z"},"content_sha256":"2c609a32aa1fe524cef985c3c5d50d4d8cc81604f5296cff0aee634710722b73","schema_version":"1.0","event_id":"sha256:2c609a32aa1fe524cef985c3c5d50d4d8cc81604f5296cff0aee634710722b73"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:4KK3RHWHCTDSB6FKCW2Y3C6FWI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constructing small tree grammars and small circuits for formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.FL"],"primary_cat":"cs.DS","authors_text":"Artur Jez, Danny Hucke, Eric Noeth, Markus Lohrey, Moses Ganardi","submitted_at":"2014-07-16T12:48:48Z","abstract_excerpt":"It is shown that every tree of size $n$ over a fixed set of $\\sigma$ different ranked symbols can be decomposed (in linear time as well as in logspace) into $O\\big(\\frac{n}{\\log_\\sigma n}\\big) = O\\big(\\frac{n \\log \\sigma}{\\log n}\\big)$ many hierarchically defined pieces. Formally, such a hierarchical decomposition has the form of a straight-line linear context-free tree grammar of size $O\\big(\\frac{n}{\\log_\\sigma n}\\big)$, which can be used as a compressed representation of the input tree. This generalizes an analogous result for strings. Previous grammar-based tree compressors were not analyz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4286","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":"2026-05-18T01:32:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z3SKUilznYl03u0hxMo/jLX2k7ZnZDJujnXb3UiEB5whZfVxlCIu6NC1rNLx8TlmajuH3f+Ia43xBcGHnQ0GBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T17:53:46.466343Z"},"content_sha256":"61997aa0251acdfe8ee015a7f941af64a8e427b2b490fca72e05ac955cea7f69","schema_version":"1.0","event_id":"sha256:61997aa0251acdfe8ee015a7f941af64a8e427b2b490fca72e05ac955cea7f69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4KK3RHWHCTDSB6FKCW2Y3C6FWI/bundle.json","state_url":"https://pith.science/pith/4KK3RHWHCTDSB6FKCW2Y3C6FWI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4KK3RHWHCTDSB6FKCW2Y3C6FWI/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":"2026-05-26T17:53:46Z","links":{"resolver":"https://pith.science/pith/4KK3RHWHCTDSB6FKCW2Y3C6FWI","bundle":"https://pith.science/pith/4KK3RHWHCTDSB6FKCW2Y3C6FWI/bundle.json","state":"https://pith.science/pith/4KK3RHWHCTDSB6FKCW2Y3C6FWI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4KK3RHWHCTDSB6FKCW2Y3C6FWI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4KK3RHWHCTDSB6FKCW2Y3C6FWI","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":"65e9794589523755a2853073702ccad5f1b10d47826b817f168130c7ddbfdc53","cross_cats_sorted":["cs.CC","cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-07-16T12:48:48Z","title_canon_sha256":"4c47020c35a247a1b8e3d832ac30ea4f33f386cca1c596c463d91a2d10facc92"},"schema_version":"1.0","source":{"id":"1407.4286","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4286","created_at":"2026-05-18T01:32:41Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4286v3","created_at":"2026-05-18T01:32:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4286","created_at":"2026-05-18T01:32:41Z"},{"alias_kind":"pith_short_12","alias_value":"4KK3RHWHCTDS","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4KK3RHWHCTDSB6FK","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4KK3RHWH","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:61997aa0251acdfe8ee015a7f941af64a8e427b2b490fca72e05ac955cea7f69","target":"graph","created_at":"2026-05-18T01:32:41Z","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":"It is shown that every tree of size $n$ over a fixed set of $\\sigma$ different ranked symbols can be decomposed (in linear time as well as in logspace) into $O\\big(\\frac{n}{\\log_\\sigma n}\\big) = O\\big(\\frac{n \\log \\sigma}{\\log n}\\big)$ many hierarchically defined pieces. Formally, such a hierarchical decomposition has the form of a straight-line linear context-free tree grammar of size $O\\big(\\frac{n}{\\log_\\sigma n}\\big)$, which can be used as a compressed representation of the input tree. This generalizes an analogous result for strings. Previous grammar-based tree compressors were not analyz","authors_text":"Artur Jez, Danny Hucke, Eric Noeth, Markus Lohrey, Moses Ganardi","cross_cats":["cs.CC","cs.FL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-07-16T12:48:48Z","title":"Constructing small tree grammars and small circuits for formulas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4286","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":"sha256:2c609a32aa1fe524cef985c3c5d50d4d8cc81604f5296cff0aee634710722b73","target":"record","created_at":"2026-05-18T01:32:41Z","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":"65e9794589523755a2853073702ccad5f1b10d47826b817f168130c7ddbfdc53","cross_cats_sorted":["cs.CC","cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-07-16T12:48:48Z","title_canon_sha256":"4c47020c35a247a1b8e3d832ac30ea4f33f386cca1c596c463d91a2d10facc92"},"schema_version":"1.0","source":{"id":"1407.4286","kind":"arxiv","version":3}},"canonical_sha256":"e295b89ec714c720f8aa15b58d8bc5b21cc99276238cc65a5be645efcc01ff0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e295b89ec714c720f8aa15b58d8bc5b21cc99276238cc65a5be645efcc01ff0c","first_computed_at":"2026-05-18T01:32:41.839036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:41.839036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OM9GekxUm2oMYf00RewY18u/s+iSAkJDgg+dQnWu2OC3bQPHBeUi/C8XHMVXoCwAF3CssORnhS6m9TnPL+ZKDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:41.839562Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.4286","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c609a32aa1fe524cef985c3c5d50d4d8cc81604f5296cff0aee634710722b73","sha256:61997aa0251acdfe8ee015a7f941af64a8e427b2b490fca72e05ac955cea7f69"],"state_sha256":"bb8051e64ef0c118c2de4af2593231618fe80cd5e55e8bb2756d7ba05987274b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1/cTlflku6H4OMm1m1KXAIby20RcSXhRECoToAaPIhHZJrj7SumGBFdCCh/5e2vjRb/Vr7bfeJc+8lU07ylsAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T17:53:46.470188Z","bundle_sha256":"e7293a1a5f10d07a6f42aaaf91b457cf5c739e44411eaaec586fa0bd79ab4b30"}}