{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:WZBZJBFMAPL4HGITH322YNTMHX","short_pith_number":"pith:WZBZJBFM","canonical_record":{"source":{"id":"1602.08579","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-02-27T10:06:46Z","cross_cats_sorted":[],"title_canon_sha256":"2be93578d2f0a4d57009815a8a15f8e6f28b953da2dfa77d5297cb93682b592e","abstract_canon_sha256":"38cddaf2cd2a756210f6d5d61343c7a65fd6da7ad497474e074581b01256d2c2"},"schema_version":"1.0"},"canonical_sha256":"b6439484ac03d7c399133ef5ac366c3df54765f3039ead96999eae132bf426d1","source":{"kind":"arxiv","id":"1602.08579","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.08579","created_at":"2026-05-18T01:07:56Z"},{"alias_kind":"arxiv_version","alias_value":"1602.08579v3","created_at":"2026-05-18T01:07:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.08579","created_at":"2026-05-18T01:07:56Z"},{"alias_kind":"pith_short_12","alias_value":"WZBZJBFMAPL4","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WZBZJBFMAPL4HGIT","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WZBZJBFM","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:WZBZJBFMAPL4HGITH322YNTMHX","target":"record","payload":{"canonical_record":{"source":{"id":"1602.08579","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-02-27T10:06:46Z","cross_cats_sorted":[],"title_canon_sha256":"2be93578d2f0a4d57009815a8a15f8e6f28b953da2dfa77d5297cb93682b592e","abstract_canon_sha256":"38cddaf2cd2a756210f6d5d61343c7a65fd6da7ad497474e074581b01256d2c2"},"schema_version":"1.0"},"canonical_sha256":"b6439484ac03d7c399133ef5ac366c3df54765f3039ead96999eae132bf426d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:56.787199Z","signature_b64":"ToabmwgXwQQ4Rrq+CQp2C54g1DVSB5ZP4Rdnh1DvbxhHLH67svCAuIq7kEZoYN2zzm5e6QSaG5Ta6WNIJMmUCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6439484ac03d7c399133ef5ac366c3df54765f3039ead96999eae132bf426d1","last_reissued_at":"2026-05-18T01:07:56.786645Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:56.786645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.08579","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":"2026-05-18T01:07:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LDiGvsHLxePUhOYFOyeTnQ4L+AEXL7fxQgMpRlXpx4eDdwWZPPJ+DLRgCiB4bYRbWQOle8GJhe3Lb2CowFD7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:41:28.348846Z"},"content_sha256":"b79a4e152f584508f262ee79d56524306298aa7a1ecbcb0bea89cc28d75e6432","schema_version":"1.0","event_id":"sha256:b79a4e152f584508f262ee79d56524306298aa7a1ecbcb0bea89cc28d75e6432"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:WZBZJBFMAPL4HGITH322YNTMHX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On automatic subsets of the Gaussian integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Robbert Fokkink, Thijmen Krebs, Wieb Bosma","submitted_at":"2016-02-27T10:06:46Z","abstract_excerpt":"Suppose that $a$ and $b$ are multiplicatively independent Gaussian integers, that are both of modulus~$\\geq \\sqrt 5$. We prove that there exist a $X\\subset \\mathbb Z[i]$ which is $a$-automatic but not $b$-automatic. This settles a problem of Allouche, Cateland, Gilbert, Peitgen, Shallit, and Skordev."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08579","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":"2026-05-18T01:07:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"apDvZJfNuusph7fvcPu/r0nBtlh+wiyKaumWBqSTv2xI/hIdMS0J+xePSujFGfBHFaW2N9TL9pALi81y7DirBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:41:28.349562Z"},"content_sha256":"2d14038a25826ecb23afdc2f7ba9f36f12409c1d7354ef29b6eb4cdeff8368f2","schema_version":"1.0","event_id":"sha256:2d14038a25826ecb23afdc2f7ba9f36f12409c1d7354ef29b6eb4cdeff8368f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WZBZJBFMAPL4HGITH322YNTMHX/bundle.json","state_url":"https://pith.science/pith/WZBZJBFMAPL4HGITH322YNTMHX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WZBZJBFMAPL4HGITH322YNTMHX/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":"2026-05-27T16:41:28Z","links":{"resolver":"https://pith.science/pith/WZBZJBFMAPL4HGITH322YNTMHX","bundle":"https://pith.science/pith/WZBZJBFMAPL4HGITH322YNTMHX/bundle.json","state":"https://pith.science/pith/WZBZJBFMAPL4HGITH322YNTMHX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WZBZJBFMAPL4HGITH322YNTMHX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WZBZJBFMAPL4HGITH322YNTMHX","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":"38cddaf2cd2a756210f6d5d61343c7a65fd6da7ad497474e074581b01256d2c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-02-27T10:06:46Z","title_canon_sha256":"2be93578d2f0a4d57009815a8a15f8e6f28b953da2dfa77d5297cb93682b592e"},"schema_version":"1.0","source":{"id":"1602.08579","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.08579","created_at":"2026-05-18T01:07:56Z"},{"alias_kind":"arxiv_version","alias_value":"1602.08579v3","created_at":"2026-05-18T01:07:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.08579","created_at":"2026-05-18T01:07:56Z"},{"alias_kind":"pith_short_12","alias_value":"WZBZJBFMAPL4","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WZBZJBFMAPL4HGIT","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WZBZJBFM","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:2d14038a25826ecb23afdc2f7ba9f36f12409c1d7354ef29b6eb4cdeff8368f2","target":"graph","created_at":"2026-05-18T01:07:56Z","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":"Suppose that $a$ and $b$ are multiplicatively independent Gaussian integers, that are both of modulus~$\\geq \\sqrt 5$. We prove that there exist a $X\\subset \\mathbb Z[i]$ which is $a$-automatic but not $b$-automatic. This settles a problem of Allouche, Cateland, Gilbert, Peitgen, Shallit, and Skordev.","authors_text":"Robbert Fokkink, Thijmen Krebs, Wieb Bosma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-02-27T10:06:46Z","title":"On automatic subsets of the Gaussian integers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08579","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:b79a4e152f584508f262ee79d56524306298aa7a1ecbcb0bea89cc28d75e6432","target":"record","created_at":"2026-05-18T01:07:56Z","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":"38cddaf2cd2a756210f6d5d61343c7a65fd6da7ad497474e074581b01256d2c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-02-27T10:06:46Z","title_canon_sha256":"2be93578d2f0a4d57009815a8a15f8e6f28b953da2dfa77d5297cb93682b592e"},"schema_version":"1.0","source":{"id":"1602.08579","kind":"arxiv","version":3}},"canonical_sha256":"b6439484ac03d7c399133ef5ac366c3df54765f3039ead96999eae132bf426d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6439484ac03d7c399133ef5ac366c3df54765f3039ead96999eae132bf426d1","first_computed_at":"2026-05-18T01:07:56.786645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:56.786645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ToabmwgXwQQ4Rrq+CQp2C54g1DVSB5ZP4Rdnh1DvbxhHLH67svCAuIq7kEZoYN2zzm5e6QSaG5Ta6WNIJMmUCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:56.787199Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.08579","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b79a4e152f584508f262ee79d56524306298aa7a1ecbcb0bea89cc28d75e6432","sha256:2d14038a25826ecb23afdc2f7ba9f36f12409c1d7354ef29b6eb4cdeff8368f2"],"state_sha256":"df91f7e4b8bc3f234438a3ed5a068f194c8344a72e904f59f77a52b391441988"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6noLPc9RE7NMAO5s5hbghXLU5F76R9sWxJpTGkmWzsYMdle/54/prytQ3AgnxCIrVg++zj6tpdMd2/Lchq05Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T16:41:28.353393Z","bundle_sha256":"e492a883de6cd06bb37bb97fcfe9657b219ea79ee53822652c8bb8cac3a1e42c"}}