{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6UU2MUP6ZNEW4FPO22PU22NEMX","short_pith_number":"pith:6UU2MUP6","canonical_record":{"source":{"id":"1610.03900","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-12T23:38:30Z","cross_cats_sorted":["cs.FL","math.CO","math.DS"],"title_canon_sha256":"5984876d3b0fb2ca51393016679b2e84d43a0225da3b6966c9ecdbe16d13c817","abstract_canon_sha256":"177e1a416409b852eefad18e4c51a407a0e1767c9868598be94efe7b300b2834"},"schema_version":"1.0"},"canonical_sha256":"f529a651fecb496e15eed69f4d69a465c574286f3eef57b1fcab528065b18ecf","source":{"kind":"arxiv","id":"1610.03900","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03900","created_at":"2026-05-18T01:02:23Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03900v1","created_at":"2026-05-18T01:02:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03900","created_at":"2026-05-18T01:02:23Z"},{"alias_kind":"pith_short_12","alias_value":"6UU2MUP6ZNEW","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6UU2MUP6ZNEW4FPO","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6UU2MUP6","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6UU2MUP6ZNEW4FPO22PU22NEMX","target":"record","payload":{"canonical_record":{"source":{"id":"1610.03900","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-12T23:38:30Z","cross_cats_sorted":["cs.FL","math.CO","math.DS"],"title_canon_sha256":"5984876d3b0fb2ca51393016679b2e84d43a0225da3b6966c9ecdbe16d13c817","abstract_canon_sha256":"177e1a416409b852eefad18e4c51a407a0e1767c9868598be94efe7b300b2834"},"schema_version":"1.0"},"canonical_sha256":"f529a651fecb496e15eed69f4d69a465c574286f3eef57b1fcab528065b18ecf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:23.102354Z","signature_b64":"N50p8ntJbazwjg1UJbB7Ew4WI06q9VCcTkGh5jk+iGdiS3mBxqGa0EdpG3+0bQONBR9cuBc4cJ/L8SzLiioqAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f529a651fecb496e15eed69f4d69a465c574286f3eef57b1fcab528065b18ecf","last_reissued_at":"2026-05-18T01:02:23.101705Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:23.101705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.03900","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":"2026-05-18T01:02:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WjNEBECKKQsv65LP++xiGYrZe5gR3hwT9Zhbx4JGMuOKEfRWG+ECpOnGkRFxpbfTC+EZ174wCxEAo9BP7pgEDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:37:11.059974Z"},"content_sha256":"36a589a6b36998822bb0d38ad2e8119678c11990d1e67d7e787eb232775f3d22","schema_version":"1.0","event_id":"sha256:36a589a6b36998822bb0d38ad2e8119678c11990d1e67d7e787eb232775f3d22"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6UU2MUP6ZNEW4FPO22PU22NEMX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Automatic sequences, generalised polynomials, and nilmanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL","math.CO","math.DS"],"primary_cat":"math.NT","authors_text":"Jakub Byszewski, Jakub Konieczny","submitted_at":"2016-10-12T23:38:30Z","abstract_excerpt":"We conjecture that bounded generalised polynomial functions cannot be generated by finite automata, except for the trivial case when they are periodic away from a finite set. Using methods from ergodic theory, we are able to partially resolve this conjecture, proving that any hypothetical counterexample is periodic away from a very sparse and structured set. In particular, we show that for a polynomial $p(n)$ with at least one irrational coefficient (except for the constant one) and integer $m$, the sequence $\\lfloor p(n) \\rfloor \\bmod{m}$ is never automatic. We also obtain a conditional resul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03900","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":"2026-05-18T01:02:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PqnCVExqMj6bKXRcJMybWb7Bt239Ieu1KLSKJjzRr9sy/STjJDHW9Ti+8k3q+sWmpFDMTfTBFBsiIUaT1byaCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:37:11.060676Z"},"content_sha256":"9675a7bdda8bad5401b3b300bb9d1e5f67952cd3094e64f08b2471050550c138","schema_version":"1.0","event_id":"sha256:9675a7bdda8bad5401b3b300bb9d1e5f67952cd3094e64f08b2471050550c138"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6UU2MUP6ZNEW4FPO22PU22NEMX/bundle.json","state_url":"https://pith.science/pith/6UU2MUP6ZNEW4FPO22PU22NEMX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6UU2MUP6ZNEW4FPO22PU22NEMX/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":"2026-06-10T23:37:11Z","links":{"resolver":"https://pith.science/pith/6UU2MUP6ZNEW4FPO22PU22NEMX","bundle":"https://pith.science/pith/6UU2MUP6ZNEW4FPO22PU22NEMX/bundle.json","state":"https://pith.science/pith/6UU2MUP6ZNEW4FPO22PU22NEMX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6UU2MUP6ZNEW4FPO22PU22NEMX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6UU2MUP6ZNEW4FPO22PU22NEMX","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":"177e1a416409b852eefad18e4c51a407a0e1767c9868598be94efe7b300b2834","cross_cats_sorted":["cs.FL","math.CO","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-12T23:38:30Z","title_canon_sha256":"5984876d3b0fb2ca51393016679b2e84d43a0225da3b6966c9ecdbe16d13c817"},"schema_version":"1.0","source":{"id":"1610.03900","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03900","created_at":"2026-05-18T01:02:23Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03900v1","created_at":"2026-05-18T01:02:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03900","created_at":"2026-05-18T01:02:23Z"},{"alias_kind":"pith_short_12","alias_value":"6UU2MUP6ZNEW","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6UU2MUP6ZNEW4FPO","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6UU2MUP6","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:9675a7bdda8bad5401b3b300bb9d1e5f67952cd3094e64f08b2471050550c138","target":"graph","created_at":"2026-05-18T01:02:23Z","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 conjecture that bounded generalised polynomial functions cannot be generated by finite automata, except for the trivial case when they are periodic away from a finite set. Using methods from ergodic theory, we are able to partially resolve this conjecture, proving that any hypothetical counterexample is periodic away from a very sparse and structured set. In particular, we show that for a polynomial $p(n)$ with at least one irrational coefficient (except for the constant one) and integer $m$, the sequence $\\lfloor p(n) \\rfloor \\bmod{m}$ is never automatic. We also obtain a conditional resul","authors_text":"Jakub Byszewski, Jakub Konieczny","cross_cats":["cs.FL","math.CO","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-12T23:38:30Z","title":"Automatic sequences, generalised polynomials, and nilmanifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03900","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":"sha256:36a589a6b36998822bb0d38ad2e8119678c11990d1e67d7e787eb232775f3d22","target":"record","created_at":"2026-05-18T01:02:23Z","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":"177e1a416409b852eefad18e4c51a407a0e1767c9868598be94efe7b300b2834","cross_cats_sorted":["cs.FL","math.CO","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-12T23:38:30Z","title_canon_sha256":"5984876d3b0fb2ca51393016679b2e84d43a0225da3b6966c9ecdbe16d13c817"},"schema_version":"1.0","source":{"id":"1610.03900","kind":"arxiv","version":1}},"canonical_sha256":"f529a651fecb496e15eed69f4d69a465c574286f3eef57b1fcab528065b18ecf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f529a651fecb496e15eed69f4d69a465c574286f3eef57b1fcab528065b18ecf","first_computed_at":"2026-05-18T01:02:23.101705Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:23.101705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N50p8ntJbazwjg1UJbB7Ew4WI06q9VCcTkGh5jk+iGdiS3mBxqGa0EdpG3+0bQONBR9cuBc4cJ/L8SzLiioqAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:23.102354Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.03900","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36a589a6b36998822bb0d38ad2e8119678c11990d1e67d7e787eb232775f3d22","sha256:9675a7bdda8bad5401b3b300bb9d1e5f67952cd3094e64f08b2471050550c138"],"state_sha256":"5d29c01bc8a5b0c4edc43abd5a981b1150473897c539215c595f467992efc20c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ea6xt+c1U4FDnRZwxraJFdMPAIaeP6xZrcg2MRKH2htL+gkthfkd+IpZjceOoYTcMRg3LNwb8ReQkPW9hvtsDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T23:37:11.065004Z","bundle_sha256":"991337048c62566c95786781d15266ea8f91ee411c53747f14c5f3a369ea217f"}}