{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:DKG5SB4WELZ24BJMBLXAEGLKFM","short_pith_number":"pith:DKG5SB4W","canonical_record":{"source":{"id":"1605.00813","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-03T09:36:28Z","cross_cats_sorted":[],"title_canon_sha256":"80f615c37d67ea46c1333f35845b7ad0d54207b44882509b79dbc9a2ea7c49ff","abstract_canon_sha256":"6e2a8893d59a02e468690299163587566cb7e5e844e486367579aedbddedb65e"},"schema_version":"1.0"},"canonical_sha256":"1a8dd9079622f3ae052c0aee02196a2b2811696776463184241b7fd067093295","source":{"kind":"arxiv","id":"1605.00813","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00813","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00813v1","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00813","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"pith_short_12","alias_value":"DKG5SB4WELZ2","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DKG5SB4WELZ24BJM","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DKG5SB4W","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:DKG5SB4WELZ24BJMBLXAEGLKFM","target":"record","payload":{"canonical_record":{"source":{"id":"1605.00813","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-03T09:36:28Z","cross_cats_sorted":[],"title_canon_sha256":"80f615c37d67ea46c1333f35845b7ad0d54207b44882509b79dbc9a2ea7c49ff","abstract_canon_sha256":"6e2a8893d59a02e468690299163587566cb7e5e844e486367579aedbddedb65e"},"schema_version":"1.0"},"canonical_sha256":"1a8dd9079622f3ae052c0aee02196a2b2811696776463184241b7fd067093295","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:47.972394Z","signature_b64":"c/LaJFQZpA1nPOJOfdbKeeqx7X/5Ie5sfXqEq1VCo2YwKViy6u3azEito9FZzvj+t+J/tPtyY/wUu8s1gwqEAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a8dd9079622f3ae052c0aee02196a2b2811696776463184241b7fd067093295","last_reissued_at":"2026-05-18T01:15:47.971854Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:47.971854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.00813","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":"2026-05-18T01:15:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Doi3X6JR2HBO+KwdCWYEauNVhP9bUVKHS7Fh+YyXkTqX5JwARgLVeodBuKVSKdlWP890NzpRMOoocb3Z8BJiDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:12:48.005749Z"},"content_sha256":"615e2038d3db721c48342a9a182add35b7711c48c619ac24b5666acc9de476d3","schema_version":"1.0","event_id":"sha256:615e2038d3db721c48342a9a182add35b7711c48c619ac24b5666acc9de476d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:DKG5SB4WELZ24BJMBLXAEGLKFM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On certain recurrent and automatic sequences in finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alain Lasjaunias, Jia-Yan Yao","submitted_at":"2016-05-03T09:36:28Z","abstract_excerpt":"In this work we extend our study on a link between automaticity and certain algebraic power series over finite fields. Our starting point is a family of sequences in a finite field of characteristic $2$, recently introduced by the first author in connection with algebraic continued fractions. By including it in a large family of recurrent sequences in an arbitrary finite field, we prove its automaticity. Then we give a criterion on automatic sequences, generalizing a previous result and this allows us to present new families of automatic sequences in an arbitrary finite field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00813","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":"2026-05-18T01:15:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NB7BC0W+VoYzVvde4OY/2RCO5S1E4SXcRC2SKYkrR8R89PYZ9mM4gLH29yMHkPb6UT2Z5q7CTpiIJQVC6MFACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:12:48.006085Z"},"content_sha256":"cca003d06f9d5b63588ad72db0464a8aaa27cab66f634a7dd3e2e4eeb11bedbe","schema_version":"1.0","event_id":"sha256:cca003d06f9d5b63588ad72db0464a8aaa27cab66f634a7dd3e2e4eeb11bedbe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DKG5SB4WELZ24BJMBLXAEGLKFM/bundle.json","state_url":"https://pith.science/pith/DKG5SB4WELZ24BJMBLXAEGLKFM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DKG5SB4WELZ24BJMBLXAEGLKFM/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":"2026-06-02T02:12:48Z","links":{"resolver":"https://pith.science/pith/DKG5SB4WELZ24BJMBLXAEGLKFM","bundle":"https://pith.science/pith/DKG5SB4WELZ24BJMBLXAEGLKFM/bundle.json","state":"https://pith.science/pith/DKG5SB4WELZ24BJMBLXAEGLKFM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DKG5SB4WELZ24BJMBLXAEGLKFM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DKG5SB4WELZ24BJMBLXAEGLKFM","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":"6e2a8893d59a02e468690299163587566cb7e5e844e486367579aedbddedb65e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-03T09:36:28Z","title_canon_sha256":"80f615c37d67ea46c1333f35845b7ad0d54207b44882509b79dbc9a2ea7c49ff"},"schema_version":"1.0","source":{"id":"1605.00813","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00813","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00813v1","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00813","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"pith_short_12","alias_value":"DKG5SB4WELZ2","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DKG5SB4WELZ24BJM","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DKG5SB4W","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:cca003d06f9d5b63588ad72db0464a8aaa27cab66f634a7dd3e2e4eeb11bedbe","target":"graph","created_at":"2026-05-18T01:15:47Z","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 this work we extend our study on a link between automaticity and certain algebraic power series over finite fields. Our starting point is a family of sequences in a finite field of characteristic $2$, recently introduced by the first author in connection with algebraic continued fractions. By including it in a large family of recurrent sequences in an arbitrary finite field, we prove its automaticity. Then we give a criterion on automatic sequences, generalizing a previous result and this allows us to present new families of automatic sequences in an arbitrary finite field.","authors_text":"Alain Lasjaunias, Jia-Yan Yao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-03T09:36:28Z","title":"On certain recurrent and automatic sequences in finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00813","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":"sha256:615e2038d3db721c48342a9a182add35b7711c48c619ac24b5666acc9de476d3","target":"record","created_at":"2026-05-18T01:15:47Z","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":"6e2a8893d59a02e468690299163587566cb7e5e844e486367579aedbddedb65e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-03T09:36:28Z","title_canon_sha256":"80f615c37d67ea46c1333f35845b7ad0d54207b44882509b79dbc9a2ea7c49ff"},"schema_version":"1.0","source":{"id":"1605.00813","kind":"arxiv","version":1}},"canonical_sha256":"1a8dd9079622f3ae052c0aee02196a2b2811696776463184241b7fd067093295","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a8dd9079622f3ae052c0aee02196a2b2811696776463184241b7fd067093295","first_computed_at":"2026-05-18T01:15:47.971854Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:47.971854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c/LaJFQZpA1nPOJOfdbKeeqx7X/5Ie5sfXqEq1VCo2YwKViy6u3azEito9FZzvj+t+J/tPtyY/wUu8s1gwqEAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:47.972394Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.00813","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:615e2038d3db721c48342a9a182add35b7711c48c619ac24b5666acc9de476d3","sha256:cca003d06f9d5b63588ad72db0464a8aaa27cab66f634a7dd3e2e4eeb11bedbe"],"state_sha256":"9288c024c12bb964005367e996044e1d9d66eca5a45ec15acd6823eee87052eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HV1xOkoWE7T0ZqePCTDabpII5lO8sAfTbeebsiArKji3EiOjgUVPdce8wVMlqdDDcApNhgLesvxVIpPpDO/7Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T02:12:48.007933Z","bundle_sha256":"da25a775402e3285ea55ab964f1eb5c6ce1b9e48bf40bd5e86903facc797e4d8"}}