{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:DTJQJKBLKTKOD2SISDS3V5J4HK","short_pith_number":"pith:DTJQJKBL","canonical_record":{"source":{"id":"1105.4083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-05-20T13:24:55Z","cross_cats_sorted":[],"title_canon_sha256":"2db6a8f5baa41d06e7a061ec7ed260442c3585675273cc1d238cbf4c3719404e","abstract_canon_sha256":"c3c7e5a165a7184e65aed69cf04a21baa917d888a4fff7e4920bcd259fc6c916"},"schema_version":"1.0"},"canonical_sha256":"1cd304a82b54d4e1ea4890e5baf53c3a9a34cd892234df668db0801b2a4ac19c","source":{"kind":"arxiv","id":"1105.4083","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4083","created_at":"2026-05-18T04:21:43Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4083v1","created_at":"2026-05-18T04:21:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4083","created_at":"2026-05-18T04:21:43Z"},{"alias_kind":"pith_short_12","alias_value":"DTJQJKBLKTKO","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DTJQJKBLKTKOD2SI","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DTJQJKBL","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:DTJQJKBLKTKOD2SISDS3V5J4HK","target":"record","payload":{"canonical_record":{"source":{"id":"1105.4083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-05-20T13:24:55Z","cross_cats_sorted":[],"title_canon_sha256":"2db6a8f5baa41d06e7a061ec7ed260442c3585675273cc1d238cbf4c3719404e","abstract_canon_sha256":"c3c7e5a165a7184e65aed69cf04a21baa917d888a4fff7e4920bcd259fc6c916"},"schema_version":"1.0"},"canonical_sha256":"1cd304a82b54d4e1ea4890e5baf53c3a9a34cd892234df668db0801b2a4ac19c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:43.006601Z","signature_b64":"v5+oJPHFBTv8DLqA8WLrDqs5cQwDhCTT+Lu4TAyxYm8D4OM+fp1GIFUyZfWFbr4ZrkKz4rgc2VRm5Jb7AdqlCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cd304a82b54d4e1ea4890e5baf53c3a9a34cd892234df668db0801b2a4ac19c","last_reissued_at":"2026-05-18T04:21:43.006053Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:43.006053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.4083","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":"2026-05-18T04:21:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i3qtoqviZqDqFoBzZVABtU7V2HhGhhlJAZ9f6daqazlPBMW7KWN+WwIO/qHC/vwqSr87Y7S+toFYMZmqbR84DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T23:00:36.842981Z"},"content_sha256":"6036f66c993aaba21b01fbe33cfc5fc932a80ac462707372d4aab173e23054b2","schema_version":"1.0","event_id":"sha256:6036f66c993aaba21b01fbe33cfc5fc932a80ac462707372d4aab173e23054b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:DTJQJKBLKTKOD2SISDS3V5J4HK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Semi-characteristic polynomials, {\\phi}-modules and skew polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"J\\'er\\'emy Le Borgne (IRMAR)","submitted_at":"2011-05-20T13:24:55Z","abstract_excerpt":"We introduce the notion of semi-characteristic polynomial for a semi-linear map of a finite- dimensional vector space over a field of characteristic p. This polynomial has some properties in common with the classical characteristic polynomial of a linear map. We use this notion to study skew polynomials and linearized polynomials over a finite field, giving an algorithm to compute the splitting field of a linearized polynomial over a finite field and the Galois action on this field. We also give a way to compute the optimal bound of a skew polynomial. We then look at properties of the factoriz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4083","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":"2026-05-18T04:21:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jkOCL2K2oxKGrSPLnXmEh6McDL8V8xvV+BgStzs0P/uShY75nNRdHeLr6dUHrSGrN50QQZALlbnju4utJ1X8Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T23:00:36.843578Z"},"content_sha256":"83049c7c1f4d1b9153b0aaf9bc34c2d6adefd3fc2fac75bdc3c5ed3cca52f850","schema_version":"1.0","event_id":"sha256:83049c7c1f4d1b9153b0aaf9bc34c2d6adefd3fc2fac75bdc3c5ed3cca52f850"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DTJQJKBLKTKOD2SISDS3V5J4HK/bundle.json","state_url":"https://pith.science/pith/DTJQJKBLKTKOD2SISDS3V5J4HK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DTJQJKBLKTKOD2SISDS3V5J4HK/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":"2026-07-03T23:00:36Z","links":{"resolver":"https://pith.science/pith/DTJQJKBLKTKOD2SISDS3V5J4HK","bundle":"https://pith.science/pith/DTJQJKBLKTKOD2SISDS3V5J4HK/bundle.json","state":"https://pith.science/pith/DTJQJKBLKTKOD2SISDS3V5J4HK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DTJQJKBLKTKOD2SISDS3V5J4HK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DTJQJKBLKTKOD2SISDS3V5J4HK","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":"c3c7e5a165a7184e65aed69cf04a21baa917d888a4fff7e4920bcd259fc6c916","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-05-20T13:24:55Z","title_canon_sha256":"2db6a8f5baa41d06e7a061ec7ed260442c3585675273cc1d238cbf4c3719404e"},"schema_version":"1.0","source":{"id":"1105.4083","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4083","created_at":"2026-05-18T04:21:43Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4083v1","created_at":"2026-05-18T04:21:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4083","created_at":"2026-05-18T04:21:43Z"},{"alias_kind":"pith_short_12","alias_value":"DTJQJKBLKTKO","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DTJQJKBLKTKOD2SI","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DTJQJKBL","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:83049c7c1f4d1b9153b0aaf9bc34c2d6adefd3fc2fac75bdc3c5ed3cca52f850","target":"graph","created_at":"2026-05-18T04:21:43Z","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 introduce the notion of semi-characteristic polynomial for a semi-linear map of a finite- dimensional vector space over a field of characteristic p. This polynomial has some properties in common with the classical characteristic polynomial of a linear map. We use this notion to study skew polynomials and linearized polynomials over a finite field, giving an algorithm to compute the splitting field of a linearized polynomial over a finite field and the Galois action on this field. We also give a way to compute the optimal bound of a skew polynomial. We then look at properties of the factoriz","authors_text":"J\\'er\\'emy Le Borgne (IRMAR)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-05-20T13:24:55Z","title":"Semi-characteristic polynomials, {\\phi}-modules and skew polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4083","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":"sha256:6036f66c993aaba21b01fbe33cfc5fc932a80ac462707372d4aab173e23054b2","target":"record","created_at":"2026-05-18T04:21:43Z","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":"c3c7e5a165a7184e65aed69cf04a21baa917d888a4fff7e4920bcd259fc6c916","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-05-20T13:24:55Z","title_canon_sha256":"2db6a8f5baa41d06e7a061ec7ed260442c3585675273cc1d238cbf4c3719404e"},"schema_version":"1.0","source":{"id":"1105.4083","kind":"arxiv","version":1}},"canonical_sha256":"1cd304a82b54d4e1ea4890e5baf53c3a9a34cd892234df668db0801b2a4ac19c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cd304a82b54d4e1ea4890e5baf53c3a9a34cd892234df668db0801b2a4ac19c","first_computed_at":"2026-05-18T04:21:43.006053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:43.006053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v5+oJPHFBTv8DLqA8WLrDqs5cQwDhCTT+Lu4TAyxYm8D4OM+fp1GIFUyZfWFbr4ZrkKz4rgc2VRm5Jb7AdqlCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:43.006601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4083","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6036f66c993aaba21b01fbe33cfc5fc932a80ac462707372d4aab173e23054b2","sha256:83049c7c1f4d1b9153b0aaf9bc34c2d6adefd3fc2fac75bdc3c5ed3cca52f850"],"state_sha256":"2b32af36d2c72554923cc549c30badeab57b8a52bbab5033b7ae22f94f42ac9f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g3bgZjse3T2ZazjBvVh/vdiSe7vtYiYhtoEiJsVL2XJcUCMX6sKzcrjze0pxZVzLwVdlf5B2wSHDdGEA4xROAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T23:00:36.847033Z","bundle_sha256":"66e5a2d84f612926950c4fb5134a3712fc4b5f95e021ebc15519daefe01f7ec4"}}