{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6T5NJLBQXGN7EH7IEFRBXJN2R4","short_pith_number":"pith:6T5NJLBQ","canonical_record":{"source":{"id":"1301.1873","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-01-09T14:46:33Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"312dd7376ab998e4f324fc93a7302581474219a683489be719a53f78fe890eea","abstract_canon_sha256":"78b49175bdcd2d875d683eb1235b522d1da84bd824753c2beaac6eebc1a49cf9"},"schema_version":"1.0"},"canonical_sha256":"f4fad4ac30b99bf21fe821621ba5ba8f19a913b96423189d2f20a1995985efec","source":{"kind":"arxiv","id":"1301.1873","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1873","created_at":"2026-05-18T03:36:55Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1873v1","created_at":"2026-05-18T03:36:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1873","created_at":"2026-05-18T03:36:55Z"},{"alias_kind":"pith_short_12","alias_value":"6T5NJLBQXGN7","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6T5NJLBQXGN7EH7I","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6T5NJLBQ","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6T5NJLBQXGN7EH7IEFRBXJN2R4","target":"record","payload":{"canonical_record":{"source":{"id":"1301.1873","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-01-09T14:46:33Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"312dd7376ab998e4f324fc93a7302581474219a683489be719a53f78fe890eea","abstract_canon_sha256":"78b49175bdcd2d875d683eb1235b522d1da84bd824753c2beaac6eebc1a49cf9"},"schema_version":"1.0"},"canonical_sha256":"f4fad4ac30b99bf21fe821621ba5ba8f19a913b96423189d2f20a1995985efec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:55.790063Z","signature_b64":"ggSFeLCfCXoc5bzNn/hlN11SCXxm8o/t/GcjE/da+JiOvRc715u2xBw03lAFI4/GVcVjis0YpcEY2vlU+cR1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4fad4ac30b99bf21fe821621ba5ba8f19a913b96423189d2f20a1995985efec","last_reissued_at":"2026-05-18T03:36:55.789660Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:55.789660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.1873","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":"2026-05-18T03:36:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JXeNaCnq6cCEGjncPVqQCx9LUu7IZ5841o7Wqedg8yxz2nw+ZDsVBEf8vh2EF8yQ/7R8ZIbU33Bt4gBzdEzHAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:50:13.845860Z"},"content_sha256":"f77960b2972126830521ad27372e70836468edd183e8cba955ef89a9e3723c92","schema_version":"1.0","event_id":"sha256:f77960b2972126830521ad27372e70836468edd183e8cba955ef89a9e3723c92"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6T5NJLBQXGN7EH7IEFRBXJN2R4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Application of entropy compression in pattern avoidance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Alexandre Pinlou, Pascal Ochem","submitted_at":"2013-01-09T14:46:33Z","abstract_excerpt":"In combinatorics on words, a word $w$ over an alphabet $\\Sigma$ is said to avoid a pattern $p$ over an alphabet $\\Delta$ if there is no factor $f$ of $w$ such that $f= (p)$ where $h: \\Delta^*\\to\\Sigma^*$ is a non-erasing morphism. A pattern $p$ is said to be $k$-avoidable if there exists an infinite word over a $k$-letter alphabet that avoids $p$. We give a positive answer to Problem 3.3.2 in Lothaire's book \"Algebraic combinatorics on words\", that is, every pattern with $k$ variables of length at least $2^k$ (resp. $3\\times2^{k-1}$) is 3-avoidable (resp. 2-avoidable). This improves previous b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1873","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":"2026-05-18T03:36:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B6SjUP7NaSKnHpfoMZ2ZjmLbLXll8LtOBl2ib/ATT3BWi2JFE2Avfro6ZYR8pUOXL94I9fVSTjboJ0QrQJQUBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:50:13.846728Z"},"content_sha256":"f0f9ad6840a3655883b125d1d2cdf55280c13ecff5af802dbe7cc9b0e9bc8bb6","schema_version":"1.0","event_id":"sha256:f0f9ad6840a3655883b125d1d2cdf55280c13ecff5af802dbe7cc9b0e9bc8bb6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6T5NJLBQXGN7EH7IEFRBXJN2R4/bundle.json","state_url":"https://pith.science/pith/6T5NJLBQXGN7EH7IEFRBXJN2R4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6T5NJLBQXGN7EH7IEFRBXJN2R4/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":"2026-05-28T23:50:13Z","links":{"resolver":"https://pith.science/pith/6T5NJLBQXGN7EH7IEFRBXJN2R4","bundle":"https://pith.science/pith/6T5NJLBQXGN7EH7IEFRBXJN2R4/bundle.json","state":"https://pith.science/pith/6T5NJLBQXGN7EH7IEFRBXJN2R4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6T5NJLBQXGN7EH7IEFRBXJN2R4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6T5NJLBQXGN7EH7IEFRBXJN2R4","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":"78b49175bdcd2d875d683eb1235b522d1da84bd824753c2beaac6eebc1a49cf9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-01-09T14:46:33Z","title_canon_sha256":"312dd7376ab998e4f324fc93a7302581474219a683489be719a53f78fe890eea"},"schema_version":"1.0","source":{"id":"1301.1873","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1873","created_at":"2026-05-18T03:36:55Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1873v1","created_at":"2026-05-18T03:36:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1873","created_at":"2026-05-18T03:36:55Z"},{"alias_kind":"pith_short_12","alias_value":"6T5NJLBQXGN7","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6T5NJLBQXGN7EH7I","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6T5NJLBQ","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:f0f9ad6840a3655883b125d1d2cdf55280c13ecff5af802dbe7cc9b0e9bc8bb6","target":"graph","created_at":"2026-05-18T03:36:55Z","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":"In combinatorics on words, a word $w$ over an alphabet $\\Sigma$ is said to avoid a pattern $p$ over an alphabet $\\Delta$ if there is no factor $f$ of $w$ such that $f= (p)$ where $h: \\Delta^*\\to\\Sigma^*$ is a non-erasing morphism. A pattern $p$ is said to be $k$-avoidable if there exists an infinite word over a $k$-letter alphabet that avoids $p$. We give a positive answer to Problem 3.3.2 in Lothaire's book \"Algebraic combinatorics on words\", that is, every pattern with $k$ variables of length at least $2^k$ (resp. $3\\times2^{k-1}$) is 3-avoidable (resp. 2-avoidable). This improves previous b","authors_text":"Alexandre Pinlou, Pascal Ochem","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-01-09T14:46:33Z","title":"Application of entropy compression in pattern avoidance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1873","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:f77960b2972126830521ad27372e70836468edd183e8cba955ef89a9e3723c92","target":"record","created_at":"2026-05-18T03:36:55Z","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":"78b49175bdcd2d875d683eb1235b522d1da84bd824753c2beaac6eebc1a49cf9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-01-09T14:46:33Z","title_canon_sha256":"312dd7376ab998e4f324fc93a7302581474219a683489be719a53f78fe890eea"},"schema_version":"1.0","source":{"id":"1301.1873","kind":"arxiv","version":1}},"canonical_sha256":"f4fad4ac30b99bf21fe821621ba5ba8f19a913b96423189d2f20a1995985efec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4fad4ac30b99bf21fe821621ba5ba8f19a913b96423189d2f20a1995985efec","first_computed_at":"2026-05-18T03:36:55.789660Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:55.789660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ggSFeLCfCXoc5bzNn/hlN11SCXxm8o/t/GcjE/da+JiOvRc715u2xBw03lAFI4/GVcVjis0YpcEY2vlU+cR1Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:55.790063Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1873","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f77960b2972126830521ad27372e70836468edd183e8cba955ef89a9e3723c92","sha256:f0f9ad6840a3655883b125d1d2cdf55280c13ecff5af802dbe7cc9b0e9bc8bb6"],"state_sha256":"8f486ad747a2fb952c886c59f01fd49528b60c95dbb54f693ccdc229825f45ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rTkbU28cr1A9iuy07fTBlf3vFQbNcTBoiPno5YDHQCtqs65Er/DHTspeBb3txSQaBOFDxm+sLv3KOOoLSYZRAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:50:13.850260Z","bundle_sha256":"cb90a55efe8656132ad525030dab592f9986b9d112e6c0efdd87df114ad19b69"}}