{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:M5XEAQLYELYGL4VCUVISHUXN4Q","short_pith_number":"pith:M5XEAQLY","canonical_record":{"source":{"id":"1712.04340","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-12-12T15:08:32Z","cross_cats_sorted":[],"title_canon_sha256":"4a743141bc4fa31e736310770f82038630096a828786ab2bb7a5639ddbf23266","abstract_canon_sha256":"790809426dad3b6b8dc39a31f2e3a79d0ee46288b4cc628bf93a00f0707d5fe8"},"schema_version":"1.0"},"canonical_sha256":"676e40417822f065f2a2a55123d2ede409d5b96b13717879f3a324a7eb38bac7","source":{"kind":"arxiv","id":"1712.04340","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04340","created_at":"2026-05-18T00:28:08Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04340v1","created_at":"2026-05-18T00:28:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04340","created_at":"2026-05-18T00:28:08Z"},{"alias_kind":"pith_short_12","alias_value":"M5XEAQLYELYG","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"M5XEAQLYELYGL4VC","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"M5XEAQLY","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:M5XEAQLYELYGL4VCUVISHUXN4Q","target":"record","payload":{"canonical_record":{"source":{"id":"1712.04340","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-12-12T15:08:32Z","cross_cats_sorted":[],"title_canon_sha256":"4a743141bc4fa31e736310770f82038630096a828786ab2bb7a5639ddbf23266","abstract_canon_sha256":"790809426dad3b6b8dc39a31f2e3a79d0ee46288b4cc628bf93a00f0707d5fe8"},"schema_version":"1.0"},"canonical_sha256":"676e40417822f065f2a2a55123d2ede409d5b96b13717879f3a324a7eb38bac7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:08.294306Z","signature_b64":"N+faufW1ApjSiVVk2AqwuCBqipcIh225S3AnUoFmr67UL+o3/UIROVpgJW5pV2zIarNcNebVv9RyftTpr1DIDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"676e40417822f065f2a2a55123d2ede409d5b96b13717879f3a324a7eb38bac7","last_reissued_at":"2026-05-18T00:28:08.293478Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:08.293478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.04340","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":"2026-05-18T00:28:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KI/z8bZqjGk7Ku1i/AuPYX73nV21ErYWCPL/zwVGU08692WX+kkjAr4knEpyISi7OC5hh3ZG3ETlGkGtSzTRDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:20:51.082536Z"},"content_sha256":"af828e3ed0f875d09e0d7f92d20c187da7f53a8e16a976f766f5e65ac30181f7","schema_version":"1.0","event_id":"sha256:af828e3ed0f875d09e0d7f92d20c187da7f53a8e16a976f766f5e65ac30181f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:M5XEAQLYELYGL4VCUVISHUXN4Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification of Rings which admits some special type of Polynomial functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Souvik Dey","submitted_at":"2017-12-12T15:08:32Z","abstract_excerpt":"We know that for a finite field $F$, every function on $F$ can be given by a polynomial with coefficients in $F$. What about the converse? i.e. if $R$ is a ring (not necessarily commutative or with unity) such that every function on $R$ can be given by a polynomial with coefficients in $R$, can we say $R$ is a finite field ? We show that the answer is yes, and that in fact it is enough to only require that all bijections be given by polynomials. If we allow our rings to have unity, we show that the property that all characteristic functions can be given by polynomials actually characterizes fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04340","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":"2026-05-18T00:28:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LxuM4hhlPt+rUguHfmcJ+co+IU5LuSoDVEqoqNed+JEWE/sPDOH5qZ+66jj3lwU4y4GRprb+ljskv7scSz8oCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:20:51.082888Z"},"content_sha256":"9b72a61dea8a0dcd024aaec801f134f10dfbb4d92c9f81e7da50e34f39244c9c","schema_version":"1.0","event_id":"sha256:9b72a61dea8a0dcd024aaec801f134f10dfbb4d92c9f81e7da50e34f39244c9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M5XEAQLYELYGL4VCUVISHUXN4Q/bundle.json","state_url":"https://pith.science/pith/M5XEAQLYELYGL4VCUVISHUXN4Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M5XEAQLYELYGL4VCUVISHUXN4Q/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":"2026-06-25T09:20:51Z","links":{"resolver":"https://pith.science/pith/M5XEAQLYELYGL4VCUVISHUXN4Q","bundle":"https://pith.science/pith/M5XEAQLYELYGL4VCUVISHUXN4Q/bundle.json","state":"https://pith.science/pith/M5XEAQLYELYGL4VCUVISHUXN4Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M5XEAQLYELYGL4VCUVISHUXN4Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:M5XEAQLYELYGL4VCUVISHUXN4Q","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":"790809426dad3b6b8dc39a31f2e3a79d0ee46288b4cc628bf93a00f0707d5fe8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-12-12T15:08:32Z","title_canon_sha256":"4a743141bc4fa31e736310770f82038630096a828786ab2bb7a5639ddbf23266"},"schema_version":"1.0","source":{"id":"1712.04340","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04340","created_at":"2026-05-18T00:28:08Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04340v1","created_at":"2026-05-18T00:28:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04340","created_at":"2026-05-18T00:28:08Z"},{"alias_kind":"pith_short_12","alias_value":"M5XEAQLYELYG","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"M5XEAQLYELYGL4VC","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"M5XEAQLY","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:9b72a61dea8a0dcd024aaec801f134f10dfbb4d92c9f81e7da50e34f39244c9c","target":"graph","created_at":"2026-05-18T00:28:08Z","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 know that for a finite field $F$, every function on $F$ can be given by a polynomial with coefficients in $F$. What about the converse? i.e. if $R$ is a ring (not necessarily commutative or with unity) such that every function on $R$ can be given by a polynomial with coefficients in $R$, can we say $R$ is a finite field ? We show that the answer is yes, and that in fact it is enough to only require that all bijections be given by polynomials. If we allow our rings to have unity, we show that the property that all characteristic functions can be given by polynomials actually characterizes fi","authors_text":"Souvik Dey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-12-12T15:08:32Z","title":"Classification of Rings which admits some special type of Polynomial functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04340","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:af828e3ed0f875d09e0d7f92d20c187da7f53a8e16a976f766f5e65ac30181f7","target":"record","created_at":"2026-05-18T00:28:08Z","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":"790809426dad3b6b8dc39a31f2e3a79d0ee46288b4cc628bf93a00f0707d5fe8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-12-12T15:08:32Z","title_canon_sha256":"4a743141bc4fa31e736310770f82038630096a828786ab2bb7a5639ddbf23266"},"schema_version":"1.0","source":{"id":"1712.04340","kind":"arxiv","version":1}},"canonical_sha256":"676e40417822f065f2a2a55123d2ede409d5b96b13717879f3a324a7eb38bac7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"676e40417822f065f2a2a55123d2ede409d5b96b13717879f3a324a7eb38bac7","first_computed_at":"2026-05-18T00:28:08.293478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:08.293478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N+faufW1ApjSiVVk2AqwuCBqipcIh225S3AnUoFmr67UL+o3/UIROVpgJW5pV2zIarNcNebVv9RyftTpr1DIDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:08.294306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.04340","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af828e3ed0f875d09e0d7f92d20c187da7f53a8e16a976f766f5e65ac30181f7","sha256:9b72a61dea8a0dcd024aaec801f134f10dfbb4d92c9f81e7da50e34f39244c9c"],"state_sha256":"a7bea5f3e4b9faf69c48d0f57f847746c1f664baf68f4785952092742cf47157"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kFHZiZijwfyu8DqR48NVl0NhtRYTPVm/QSWw6bNXPHI0rVnnlyuAtTdZBxcJuat7wQMbEbjS0VKgO5O6woo7Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T09:20:51.084852Z","bundle_sha256":"b3996cb8bd67650afa657d35acbef1dd573899d33722168af373ba3069907d64"}}