{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Q2N3KKJ75QKYEUT3J4K6RQPL2K","short_pith_number":"pith:Q2N3KKJ7","canonical_record":{"source":{"id":"1308.1694","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-08-07T20:50:39Z","cross_cats_sorted":[],"title_canon_sha256":"31963f368d596c076c30e8191586f902267179df7802b67fb42025b94a9d476e","abstract_canon_sha256":"af52cc36ffd89aab6bbe719aebd30446579656133bc36d5a457fb794a798b7e5"},"schema_version":"1.0"},"canonical_sha256":"869bb5293fec1582527b4f15e8c1ebd2a6ee905659922254c494b5a6e0fe1967","source":{"kind":"arxiv","id":"1308.1694","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1694","created_at":"2026-05-18T03:16:28Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1694v1","created_at":"2026-05-18T03:16:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1694","created_at":"2026-05-18T03:16:28Z"},{"alias_kind":"pith_short_12","alias_value":"Q2N3KKJ75QKY","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q2N3KKJ75QKYEUT3","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q2N3KKJ7","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Q2N3KKJ75QKYEUT3J4K6RQPL2K","target":"record","payload":{"canonical_record":{"source":{"id":"1308.1694","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-08-07T20:50:39Z","cross_cats_sorted":[],"title_canon_sha256":"31963f368d596c076c30e8191586f902267179df7802b67fb42025b94a9d476e","abstract_canon_sha256":"af52cc36ffd89aab6bbe719aebd30446579656133bc36d5a457fb794a798b7e5"},"schema_version":"1.0"},"canonical_sha256":"869bb5293fec1582527b4f15e8c1ebd2a6ee905659922254c494b5a6e0fe1967","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:28.032910Z","signature_b64":"5E6NaUNjyqzhevKMn3QiDP4cJmeZ9UOdBymc3wuG+qLpti02AEKsURIFgQaFm6WkRqng34wvU8nWJHsNvRRWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"869bb5293fec1582527b4f15e8c1ebd2a6ee905659922254c494b5a6e0fe1967","last_reissued_at":"2026-05-18T03:16:28.032432Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:28.032432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.1694","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":"2026-05-18T03:16:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"38GPCRohTpgqRb3fSbyRSo+ra9i0MJxWZdjAbTC46zh/Ss9QJm1Di1xCDddj66cDQIlqxmHp0EOCMELdSJW8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:31:01.252380Z"},"content_sha256":"e31d91724ad87f54e3c27438636307765653ad026c03b03dd38ab3fb90e712fd","schema_version":"1.0","event_id":"sha256:e31d91724ad87f54e3c27438636307765653ad026c03b03dd38ab3fb90e712fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Q2N3KKJ75QKYEUT3J4K6RQPL2K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Free subalgebras of the skew polynomial rings k[x,y][t;\\sigma] and k[x,x^{-1},y,y^{-1}][t;\\sigma]","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"S. Paul Smith","submitted_at":"2013-08-07T20:50:39Z","abstract_excerpt":"Let \\sigma be an automorphism of a commutative k-algebra R. The skew polynomial ring R[t;\\sigma] is generated by R and an indeterminate t subject to the relations ta=\\sigma(a)t for all a in R. For certain R and appropriate \\sigma there are elements a and b in R such that the subalgebra of R[t;\\sigma] generated by at and bt is a free algebra. If \\sigma is an automorphism of the polynomial ring k[x,y], then the subalgebra of k[x,y][t;\\sigma] generated by xt and yt is free if and only if \\sigma is not conjugate to an elementary automorphism. If \\sigma is an automorphism of k[x,x^{-1},y,y^{- 1}] o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1694","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":"2026-05-18T03:16:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q7dwLF220D7aquFybUZeNFWPxKhwFOmFA1QymA3Wc+rPtH66e5PK4CMMK3R6U/cPhcRREIyg2u+rUe15Ph3uAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:31:01.252956Z"},"content_sha256":"f0fe7d6c5ea28ed66e30995cb1c2d166d4bf858cb724b8f15583c39d0f7cd57c","schema_version":"1.0","event_id":"sha256:f0fe7d6c5ea28ed66e30995cb1c2d166d4bf858cb724b8f15583c39d0f7cd57c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q2N3KKJ75QKYEUT3J4K6RQPL2K/bundle.json","state_url":"https://pith.science/pith/Q2N3KKJ75QKYEUT3J4K6RQPL2K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q2N3KKJ75QKYEUT3J4K6RQPL2K/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":"2026-05-31T21:31:01Z","links":{"resolver":"https://pith.science/pith/Q2N3KKJ75QKYEUT3J4K6RQPL2K","bundle":"https://pith.science/pith/Q2N3KKJ75QKYEUT3J4K6RQPL2K/bundle.json","state":"https://pith.science/pith/Q2N3KKJ75QKYEUT3J4K6RQPL2K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q2N3KKJ75QKYEUT3J4K6RQPL2K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Q2N3KKJ75QKYEUT3J4K6RQPL2K","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":"af52cc36ffd89aab6bbe719aebd30446579656133bc36d5a457fb794a798b7e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-08-07T20:50:39Z","title_canon_sha256":"31963f368d596c076c30e8191586f902267179df7802b67fb42025b94a9d476e"},"schema_version":"1.0","source":{"id":"1308.1694","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1694","created_at":"2026-05-18T03:16:28Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1694v1","created_at":"2026-05-18T03:16:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1694","created_at":"2026-05-18T03:16:28Z"},{"alias_kind":"pith_short_12","alias_value":"Q2N3KKJ75QKY","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q2N3KKJ75QKYEUT3","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q2N3KKJ7","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:f0fe7d6c5ea28ed66e30995cb1c2d166d4bf858cb724b8f15583c39d0f7cd57c","target":"graph","created_at":"2026-05-18T03:16:28Z","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":"Let \\sigma be an automorphism of a commutative k-algebra R. The skew polynomial ring R[t;\\sigma] is generated by R and an indeterminate t subject to the relations ta=\\sigma(a)t for all a in R. For certain R and appropriate \\sigma there are elements a and b in R such that the subalgebra of R[t;\\sigma] generated by at and bt is a free algebra. If \\sigma is an automorphism of the polynomial ring k[x,y], then the subalgebra of k[x,y][t;\\sigma] generated by xt and yt is free if and only if \\sigma is not conjugate to an elementary automorphism. If \\sigma is an automorphism of k[x,x^{-1},y,y^{- 1}] o","authors_text":"S. Paul Smith","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-08-07T20:50:39Z","title":"Free subalgebras of the skew polynomial rings k[x,y][t;\\sigma] and k[x,x^{-1},y,y^{-1}][t;\\sigma]"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1694","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:e31d91724ad87f54e3c27438636307765653ad026c03b03dd38ab3fb90e712fd","target":"record","created_at":"2026-05-18T03:16:28Z","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":"af52cc36ffd89aab6bbe719aebd30446579656133bc36d5a457fb794a798b7e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-08-07T20:50:39Z","title_canon_sha256":"31963f368d596c076c30e8191586f902267179df7802b67fb42025b94a9d476e"},"schema_version":"1.0","source":{"id":"1308.1694","kind":"arxiv","version":1}},"canonical_sha256":"869bb5293fec1582527b4f15e8c1ebd2a6ee905659922254c494b5a6e0fe1967","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"869bb5293fec1582527b4f15e8c1ebd2a6ee905659922254c494b5a6e0fe1967","first_computed_at":"2026-05-18T03:16:28.032432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:28.032432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5E6NaUNjyqzhevKMn3QiDP4cJmeZ9UOdBymc3wuG+qLpti02AEKsURIFgQaFm6WkRqng34wvU8nWJHsNvRRWBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:28.032910Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.1694","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e31d91724ad87f54e3c27438636307765653ad026c03b03dd38ab3fb90e712fd","sha256:f0fe7d6c5ea28ed66e30995cb1c2d166d4bf858cb724b8f15583c39d0f7cd57c"],"state_sha256":"dc97341f998646626caeddc13f3d994d5138766d34d74a34ebd22e996918d49d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MhH7OM7ghiTfi0AV8QwTseGBBAYm2k/smvGZTRYRbHuVbDXOOBkI0W0j7RwRirXBWwSjNhvPlxuu5iXNitBRCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T21:31:01.255200Z","bundle_sha256":"624cc8665c2701abc807e18e0fc42f96c280bd08aab9803641407e891901c3d3"}}