{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RD5PXRTPDK54H2KZIUA6PTNYA6","short_pith_number":"pith:RD5PXRTP","canonical_record":{"source":{"id":"1611.03535","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-10T22:40:53Z","cross_cats_sorted":[],"title_canon_sha256":"d29afde5eaf63e6e1814d916ac2084eb6ff077f106f710f81dece1b571c87aac","abstract_canon_sha256":"70cb66855050bda56b8cb845bbcf23f98cb20387f1a1fcc2bbf0d093ce817293"},"schema_version":"1.0"},"canonical_sha256":"88fafbc66f1abbc3e9594501e7cdb807806df0aa7eca545f9d342cac82f5e3d9","source":{"kind":"arxiv","id":"1611.03535","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03535","created_at":"2026-05-18T00:23:46Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03535v1","created_at":"2026-05-18T00:23:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03535","created_at":"2026-05-18T00:23:46Z"},{"alias_kind":"pith_short_12","alias_value":"RD5PXRTPDK54","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RD5PXRTPDK54H2KZ","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RD5PXRTP","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RD5PXRTPDK54H2KZIUA6PTNYA6","target":"record","payload":{"canonical_record":{"source":{"id":"1611.03535","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-10T22:40:53Z","cross_cats_sorted":[],"title_canon_sha256":"d29afde5eaf63e6e1814d916ac2084eb6ff077f106f710f81dece1b571c87aac","abstract_canon_sha256":"70cb66855050bda56b8cb845bbcf23f98cb20387f1a1fcc2bbf0d093ce817293"},"schema_version":"1.0"},"canonical_sha256":"88fafbc66f1abbc3e9594501e7cdb807806df0aa7eca545f9d342cac82f5e3d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:46.048816Z","signature_b64":"aXxvX70w8D/C7SMsl1OGoH1iBrTEGjLh3vroLhyf4pTKW2kjLxeM6NQ+v8XL9fAE/8aF+2ciQ8K3eQwAIQoDDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88fafbc66f1abbc3e9594501e7cdb807806df0aa7eca545f9d342cac82f5e3d9","last_reissued_at":"2026-05-18T00:23:46.048285Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:46.048285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.03535","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":"2026-05-18T00:23:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/g+nklVe9TxtjFZW4rbTartd/Hdp7xVVmTJq3iDFtgGZHGK40B29FzCC2sYs9rfkR4X5h8Ul+D7Q3CIX9n/ICQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:41:05.592748Z"},"content_sha256":"8aa85203583eef40b2b52f67e46cb2748b442831c9302da097f39ccf7d166dbd","schema_version":"1.0","event_id":"sha256:8aa85203583eef40b2b52f67e46cb2748b442831c9302da097f39ccf7d166dbd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RD5PXRTPDK54H2KZIUA6PTNYA6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A family of formulas with reversal of high avoidability index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"James Currie, Lucas Mol, Narad Rampersad","submitted_at":"2016-11-10T22:40:53Z","abstract_excerpt":"We present an infinite family of formulas with reversal whose avoidability index is bounded between 4 and 5, and we show that several members of the family have avoidability index 5. This family is particularly interesting due to its size and the simple structure of its members. For each $k\\in\\{4,5\\}$, there are several previously known avoidable formulas (without reversal) of avoidability index $k$, but they are small in number and they all have rather complex structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03535","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":"2026-05-18T00:23:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hYmw/yw83z1Ex0aH7jGGoW3iwRzU2WuDmNVcdiBqtfkJL97UrooSOzPfUTb6mLJk8EhtfKI5+7Eqv5/h/Tx+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:41:05.593094Z"},"content_sha256":"b0034d149c8124038d63429969d097e057ad63eea59e70ccb6376267272f7941","schema_version":"1.0","event_id":"sha256:b0034d149c8124038d63429969d097e057ad63eea59e70ccb6376267272f7941"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RD5PXRTPDK54H2KZIUA6PTNYA6/bundle.json","state_url":"https://pith.science/pith/RD5PXRTPDK54H2KZIUA6PTNYA6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RD5PXRTPDK54H2KZIUA6PTNYA6/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":"2026-06-24T20:41:05Z","links":{"resolver":"https://pith.science/pith/RD5PXRTPDK54H2KZIUA6PTNYA6","bundle":"https://pith.science/pith/RD5PXRTPDK54H2KZIUA6PTNYA6/bundle.json","state":"https://pith.science/pith/RD5PXRTPDK54H2KZIUA6PTNYA6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RD5PXRTPDK54H2KZIUA6PTNYA6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RD5PXRTPDK54H2KZIUA6PTNYA6","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":"70cb66855050bda56b8cb845bbcf23f98cb20387f1a1fcc2bbf0d093ce817293","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-10T22:40:53Z","title_canon_sha256":"d29afde5eaf63e6e1814d916ac2084eb6ff077f106f710f81dece1b571c87aac"},"schema_version":"1.0","source":{"id":"1611.03535","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03535","created_at":"2026-05-18T00:23:46Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03535v1","created_at":"2026-05-18T00:23:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03535","created_at":"2026-05-18T00:23:46Z"},{"alias_kind":"pith_short_12","alias_value":"RD5PXRTPDK54","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RD5PXRTPDK54H2KZ","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RD5PXRTP","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:b0034d149c8124038d63429969d097e057ad63eea59e70ccb6376267272f7941","target":"graph","created_at":"2026-05-18T00:23:46Z","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":"We present an infinite family of formulas with reversal whose avoidability index is bounded between 4 and 5, and we show that several members of the family have avoidability index 5. This family is particularly interesting due to its size and the simple structure of its members. For each $k\\in\\{4,5\\}$, there are several previously known avoidable formulas (without reversal) of avoidability index $k$, but they are small in number and they all have rather complex structure.","authors_text":"James Currie, Lucas Mol, Narad Rampersad","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-10T22:40:53Z","title":"A family of formulas with reversal of high avoidability index"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03535","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":"sha256:8aa85203583eef40b2b52f67e46cb2748b442831c9302da097f39ccf7d166dbd","target":"record","created_at":"2026-05-18T00:23:46Z","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":"70cb66855050bda56b8cb845bbcf23f98cb20387f1a1fcc2bbf0d093ce817293","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-10T22:40:53Z","title_canon_sha256":"d29afde5eaf63e6e1814d916ac2084eb6ff077f106f710f81dece1b571c87aac"},"schema_version":"1.0","source":{"id":"1611.03535","kind":"arxiv","version":1}},"canonical_sha256":"88fafbc66f1abbc3e9594501e7cdb807806df0aa7eca545f9d342cac82f5e3d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88fafbc66f1abbc3e9594501e7cdb807806df0aa7eca545f9d342cac82f5e3d9","first_computed_at":"2026-05-18T00:23:46.048285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:46.048285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aXxvX70w8D/C7SMsl1OGoH1iBrTEGjLh3vroLhyf4pTKW2kjLxeM6NQ+v8XL9fAE/8aF+2ciQ8K3eQwAIQoDDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:46.048816Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.03535","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8aa85203583eef40b2b52f67e46cb2748b442831c9302da097f39ccf7d166dbd","sha256:b0034d149c8124038d63429969d097e057ad63eea59e70ccb6376267272f7941"],"state_sha256":"a5cb2f46c66e9ab8dc72295869312fdf5bd84517340176c793ae23f177f98ec9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4XpRfATmvI6LIpsDbnwC8gclfp/rIRLMO1kK4zW8OGs++C/dQrfqBSuIgXg/DPOpmV+4cFc1agAKnJ2Syu0uDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T20:41:05.595181Z","bundle_sha256":"0afb952723f76b3d7c7856c41f84eaa99fc9290bd78a861b1b7134257d4ab7b9"}}