{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:D2KKAK4WHN62IMXBDLBVJ6UVN3","short_pith_number":"pith:D2KKAK4W","canonical_record":{"source":{"id":"1302.7204","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2013-02-25T16:28:10Z","cross_cats_sorted":[],"title_canon_sha256":"af1b8f61350887cca5b16b267d1f91ec9b5450c689c55f9c2871f73324883a0d","abstract_canon_sha256":"b3cecf4a81b99a1eb13f23d0883e1f56be50191bd9648e8ca2dd6127c6d1bf7f"},"schema_version":"1.0"},"canonical_sha256":"1e94a02b963b7da432e11ac354fa956ed4df8f7aa38faf0c7a8d65e42b6c7a7c","source":{"kind":"arxiv","id":"1302.7204","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.7204","created_at":"2026-05-18T02:19:06Z"},{"alias_kind":"arxiv_version","alias_value":"1302.7204v2","created_at":"2026-05-18T02:19:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.7204","created_at":"2026-05-18T02:19:06Z"},{"alias_kind":"pith_short_12","alias_value":"D2KKAK4WHN62","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"D2KKAK4WHN62IMXB","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"D2KKAK4W","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:D2KKAK4WHN62IMXBDLBVJ6UVN3","target":"record","payload":{"canonical_record":{"source":{"id":"1302.7204","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2013-02-25T16:28:10Z","cross_cats_sorted":[],"title_canon_sha256":"af1b8f61350887cca5b16b267d1f91ec9b5450c689c55f9c2871f73324883a0d","abstract_canon_sha256":"b3cecf4a81b99a1eb13f23d0883e1f56be50191bd9648e8ca2dd6127c6d1bf7f"},"schema_version":"1.0"},"canonical_sha256":"1e94a02b963b7da432e11ac354fa956ed4df8f7aa38faf0c7a8d65e42b6c7a7c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:06.390828Z","signature_b64":"B7LEbHIYpET1JRAvnoOT1/mGTs6kiD5DRQmMCSocC3f1Z1cWoZP9Qr9bhzgFwcYxAgRA3EQnS8zAG8lA/5XaDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e94a02b963b7da432e11ac354fa956ed4df8f7aa38faf0c7a8d65e42b6c7a7c","last_reissued_at":"2026-05-18T02:19:06.390287Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:06.390287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.7204","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:19:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1PPCq5XDvJvUCZYzaeh7tqu7zzMMO6cw8VOPv9J0V5EZjDCywj6gqU0WBIJJS50j/E3rlKlV4jMhybC7snIRAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:11:43.126304Z"},"content_sha256":"76e22a90fec511aa027605f63ccd33a2f1845c9dcaf0c54fafd4dcfd46d5392b","schema_version":"1.0","event_id":"sha256:76e22a90fec511aa027605f63ccd33a2f1845c9dcaf0c54fafd4dcfd46d5392b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:D2KKAK4WHN62IMXBDLBVJ6UVN3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial over Associative D-Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Aleks Kleyn","submitted_at":"2013-02-25T16:28:10Z","abstract_excerpt":"In the paper I considered algebra of polynomials over associative D-algebra with unit. Using the tensor notation allows to simplify the representation of polynomial. I considered questions related to divisibility of polynomial of any power over polynomial of power 1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.7204","kind":"arxiv","version":2},"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":"2026-05-18T02:19:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pi1T8m/EZQZqHJBJ5D7qIVA9eJEzzzJuBnAAcR7KjrGELnBJgUVKA1nvqX5dzkCth1NlvTRQkblt7XycApJtCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:11:43.126999Z"},"content_sha256":"c4fa43736941fa51a7a779eb15e5c04a0679148161bd9e3c31c359b6c1f98e0d","schema_version":"1.0","event_id":"sha256:c4fa43736941fa51a7a779eb15e5c04a0679148161bd9e3c31c359b6c1f98e0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D2KKAK4WHN62IMXBDLBVJ6UVN3/bundle.json","state_url":"https://pith.science/pith/D2KKAK4WHN62IMXBDLBVJ6UVN3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D2KKAK4WHN62IMXBDLBVJ6UVN3/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":"2026-06-09T09:11:43Z","links":{"resolver":"https://pith.science/pith/D2KKAK4WHN62IMXBDLBVJ6UVN3","bundle":"https://pith.science/pith/D2KKAK4WHN62IMXBDLBVJ6UVN3/bundle.json","state":"https://pith.science/pith/D2KKAK4WHN62IMXBDLBVJ6UVN3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D2KKAK4WHN62IMXBDLBVJ6UVN3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:D2KKAK4WHN62IMXBDLBVJ6UVN3","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":"b3cecf4a81b99a1eb13f23d0883e1f56be50191bd9648e8ca2dd6127c6d1bf7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2013-02-25T16:28:10Z","title_canon_sha256":"af1b8f61350887cca5b16b267d1f91ec9b5450c689c55f9c2871f73324883a0d"},"schema_version":"1.0","source":{"id":"1302.7204","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.7204","created_at":"2026-05-18T02:19:06Z"},{"alias_kind":"arxiv_version","alias_value":"1302.7204v2","created_at":"2026-05-18T02:19:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.7204","created_at":"2026-05-18T02:19:06Z"},{"alias_kind":"pith_short_12","alias_value":"D2KKAK4WHN62","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"D2KKAK4WHN62IMXB","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"D2KKAK4W","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:c4fa43736941fa51a7a779eb15e5c04a0679148161bd9e3c31c359b6c1f98e0d","target":"graph","created_at":"2026-05-18T02:19:06Z","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 the paper I considered algebra of polynomials over associative D-algebra with unit. Using the tensor notation allows to simplify the representation of polynomial. I considered questions related to divisibility of polynomial of any power over polynomial of power 1.","authors_text":"Aleks Kleyn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2013-02-25T16:28:10Z","title":"Polynomial over Associative D-Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.7204","kind":"arxiv","version":2},"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":"sha256:76e22a90fec511aa027605f63ccd33a2f1845c9dcaf0c54fafd4dcfd46d5392b","target":"record","created_at":"2026-05-18T02:19:06Z","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":"b3cecf4a81b99a1eb13f23d0883e1f56be50191bd9648e8ca2dd6127c6d1bf7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2013-02-25T16:28:10Z","title_canon_sha256":"af1b8f61350887cca5b16b267d1f91ec9b5450c689c55f9c2871f73324883a0d"},"schema_version":"1.0","source":{"id":"1302.7204","kind":"arxiv","version":2}},"canonical_sha256":"1e94a02b963b7da432e11ac354fa956ed4df8f7aa38faf0c7a8d65e42b6c7a7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e94a02b963b7da432e11ac354fa956ed4df8f7aa38faf0c7a8d65e42b6c7a7c","first_computed_at":"2026-05-18T02:19:06.390287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:06.390287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B7LEbHIYpET1JRAvnoOT1/mGTs6kiD5DRQmMCSocC3f1Z1cWoZP9Qr9bhzgFwcYxAgRA3EQnS8zAG8lA/5XaDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:06.390828Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.7204","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76e22a90fec511aa027605f63ccd33a2f1845c9dcaf0c54fafd4dcfd46d5392b","sha256:c4fa43736941fa51a7a779eb15e5c04a0679148161bd9e3c31c359b6c1f98e0d"],"state_sha256":"8468937122901e5471a99ca3e5f4f2899bd0a52aeabcd3873147d6de469dea7e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zfz0AEITfuexKnbzLRbbTq2VWtpGX+HdXyn3z8lnmlIOEuMKHhBUyHyWNWwBpsCNiUunSysrfbKFK1/SKFoICQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T09:11:43.130888Z","bundle_sha256":"a5e90299c1eee0da45d851b1a1c3bdb7df0178d45cf583cc0ce9ecc72bb7ae28"}}