{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:W66AGIRUTMCFRCBV675PS52DN6","short_pith_number":"pith:W66AGIRU","canonical_record":{"source":{"id":"1905.13190","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2019-05-30T17:21:26Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"0044d5f281eb2302df9c8aed30979a74ca0a42624df686d51b0fd4f05c0668df","abstract_canon_sha256":"ab4db207fe892a19477433dea1f3068f777f804e9969a34de2996ab632e811c9"},"schema_version":"1.0"},"canonical_sha256":"b7bc0322349b04588835f7faf977436f83e4bec6439b7d2f277399761e41b1c3","source":{"kind":"arxiv","id":"1905.13190","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.13190","created_at":"2026-05-17T23:44:38Z"},{"alias_kind":"arxiv_version","alias_value":"1905.13190v1","created_at":"2026-05-17T23:44:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.13190","created_at":"2026-05-17T23:44:38Z"},{"alias_kind":"pith_short_12","alias_value":"W66AGIRUTMCF","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"W66AGIRUTMCFRCBV","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"W66AGIRU","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:W66AGIRUTMCFRCBV675PS52DN6","target":"record","payload":{"canonical_record":{"source":{"id":"1905.13190","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2019-05-30T17:21:26Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"0044d5f281eb2302df9c8aed30979a74ca0a42624df686d51b0fd4f05c0668df","abstract_canon_sha256":"ab4db207fe892a19477433dea1f3068f777f804e9969a34de2996ab632e811c9"},"schema_version":"1.0"},"canonical_sha256":"b7bc0322349b04588835f7faf977436f83e4bec6439b7d2f277399761e41b1c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:38.697301Z","signature_b64":"Uqen6fMbQmo28w+DbELJb0/DsdM1Uhz15BMOc4QCauXblEZ7k5kYJnpTdcFYzbJn/yjkSz8ezarX3aczc3aGBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7bc0322349b04588835f7faf977436f83e4bec6439b7d2f277399761e41b1c3","last_reissued_at":"2026-05-17T23:44:38.696800Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:38.696800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.13190","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":"2026-05-17T23:44:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HtZUkgNPOhy9Y2lvUXYLBzjZZslMptZuTr8Wx1R642HiFYgC9fM7MXXXD0RCOiS6WqU3QUPbd9/bmDfPom8sCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:10:14.664060Z"},"content_sha256":"b902ffd07f2849cb14eb5490ed9931b34c377d484013b9bf0d3661e5ebeeaa8c","schema_version":"1.0","event_id":"sha256:b902ffd07f2849cb14eb5490ed9931b34c377d484013b9bf0d3661e5ebeeaa8c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:W66AGIRUTMCFRCBV675PS52DN6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"String-to-String Interpretations with Polynomial-Size Output","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.FL","authors_text":"Miko{\\l}aj Boja\\'nczyk, Nathan Lhote, Sandra Kiefer","submitted_at":"2019-05-30T17:21:26Z","abstract_excerpt":"String-to-string MSO interpretations are like Courcelle's MSO transductions, except that a single output position can be represented using a tuple of input positions instead of just a single input position. In particular, the output length is polynomial in the input length, as opposed to MSO transductions, which have output of linear length. We show that string-to-string MSO interpretations are exactly the polyregular functions. The latter class has various characterizations, one of which is that it consists of the string-to-string functions recognized by pebble transducers.\n  Our main result "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.13190","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":"2026-05-17T23:44:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7SC7H0cQzjzw4GTr2U4tFSn5IqcUD+vJtPxjaW62ZbTpRqQV0NGFMkTKPlIqdwRSbXhmS/0wj9jFOEJ/ARdwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:10:14.664769Z"},"content_sha256":"3cb51f28b0c88fdee876f88f27e3a2c400a8941316a25466221b26746ee6b56d","schema_version":"1.0","event_id":"sha256:3cb51f28b0c88fdee876f88f27e3a2c400a8941316a25466221b26746ee6b56d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W66AGIRUTMCFRCBV675PS52DN6/bundle.json","state_url":"https://pith.science/pith/W66AGIRUTMCFRCBV675PS52DN6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W66AGIRUTMCFRCBV675PS52DN6/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":"2026-05-28T00:10:14Z","links":{"resolver":"https://pith.science/pith/W66AGIRUTMCFRCBV675PS52DN6","bundle":"https://pith.science/pith/W66AGIRUTMCFRCBV675PS52DN6/bundle.json","state":"https://pith.science/pith/W66AGIRUTMCFRCBV675PS52DN6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W66AGIRUTMCFRCBV675PS52DN6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:W66AGIRUTMCFRCBV675PS52DN6","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":"ab4db207fe892a19477433dea1f3068f777f804e9969a34de2996ab632e811c9","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2019-05-30T17:21:26Z","title_canon_sha256":"0044d5f281eb2302df9c8aed30979a74ca0a42624df686d51b0fd4f05c0668df"},"schema_version":"1.0","source":{"id":"1905.13190","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.13190","created_at":"2026-05-17T23:44:38Z"},{"alias_kind":"arxiv_version","alias_value":"1905.13190v1","created_at":"2026-05-17T23:44:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.13190","created_at":"2026-05-17T23:44:38Z"},{"alias_kind":"pith_short_12","alias_value":"W66AGIRUTMCF","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"W66AGIRUTMCFRCBV","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"W66AGIRU","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:3cb51f28b0c88fdee876f88f27e3a2c400a8941316a25466221b26746ee6b56d","target":"graph","created_at":"2026-05-17T23:44:38Z","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":"String-to-string MSO interpretations are like Courcelle's MSO transductions, except that a single output position can be represented using a tuple of input positions instead of just a single input position. In particular, the output length is polynomial in the input length, as opposed to MSO transductions, which have output of linear length. We show that string-to-string MSO interpretations are exactly the polyregular functions. The latter class has various characterizations, one of which is that it consists of the string-to-string functions recognized by pebble transducers.\n  Our main result ","authors_text":"Miko{\\l}aj Boja\\'nczyk, Nathan Lhote, Sandra Kiefer","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2019-05-30T17:21:26Z","title":"String-to-String Interpretations with Polynomial-Size Output"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.13190","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:b902ffd07f2849cb14eb5490ed9931b34c377d484013b9bf0d3661e5ebeeaa8c","target":"record","created_at":"2026-05-17T23:44:38Z","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":"ab4db207fe892a19477433dea1f3068f777f804e9969a34de2996ab632e811c9","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2019-05-30T17:21:26Z","title_canon_sha256":"0044d5f281eb2302df9c8aed30979a74ca0a42624df686d51b0fd4f05c0668df"},"schema_version":"1.0","source":{"id":"1905.13190","kind":"arxiv","version":1}},"canonical_sha256":"b7bc0322349b04588835f7faf977436f83e4bec6439b7d2f277399761e41b1c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7bc0322349b04588835f7faf977436f83e4bec6439b7d2f277399761e41b1c3","first_computed_at":"2026-05-17T23:44:38.696800Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:38.696800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Uqen6fMbQmo28w+DbELJb0/DsdM1Uhz15BMOc4QCauXblEZ7k5kYJnpTdcFYzbJn/yjkSz8ezarX3aczc3aGBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:38.697301Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.13190","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b902ffd07f2849cb14eb5490ed9931b34c377d484013b9bf0d3661e5ebeeaa8c","sha256:3cb51f28b0c88fdee876f88f27e3a2c400a8941316a25466221b26746ee6b56d"],"state_sha256":"39d7b5b3df626a3091e957c4261d45d7eb79daccd9a7d4fb208f6427fdb85b65"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rvUdItKCdFJC/swQBIxsH1yIw5LEYVtoYK+afQf8+HaYeM8N9VLOf5e7BhL4Jn15Uw3lTKbSrd2cIqnhtbv8Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T00:10:14.668095Z","bundle_sha256":"cb5416a3d262b9efd30d55718bb9f69962a85a9546207791a08fab3c056d62c8"}}