{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:644CMMO3OPIGFZXVROEUOJNX3N","short_pith_number":"pith:644CMMO3","schema_version":"1.0","canonical_sha256":"f7382631db73d062e6f58b894725b7db68143dc2bc56b586f1cccd3ea56494b7","source":{"kind":"arxiv","id":"1509.08812","version":1},"attestation_state":"computed","paper":{"title":"An isomorphism lemma for graded rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"James J. Zhang, Jason Bell","submitted_at":"2015-09-29T15:42:02Z","abstract_excerpt":"Let $A$ and $B$ be two connected graded algebras finitely generated in degree one. If $A$ is isomorphic to $B$ as ungraded algebras, then they are also isomorphic to each other as graded algebras."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1509.08812","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-09-29T15:42:02Z","cross_cats_sorted":[],"title_canon_sha256":"023c35308488fdab925e64991b0a28c177b50aa6fc8b170bacf1737742b91eba","abstract_canon_sha256":"c9cce20468d24bef488d9dac2190d59bcb453a7c335bc71d5cbd495feae40d94"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:47.041836Z","signature_b64":"3EkVakNgm6orpla2mkMHWkURBSmoq2IZaE9LgUbRH0WtdcusaqUs1eOfV/c9Grqj82a6lYd4NNtk0WbTs71HAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7382631db73d062e6f58b894725b7db68143dc2bc56b586f1cccd3ea56494b7","last_reissued_at":"2026-05-18T01:31:47.041245Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:47.041245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An isomorphism lemma for graded rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"James J. Zhang, Jason Bell","submitted_at":"2015-09-29T15:42:02Z","abstract_excerpt":"Let $A$ and $B$ be two connected graded algebras finitely generated in degree one. If $A$ is isomorphic to $B$ as ungraded algebras, then they are also isomorphic to each other as graded algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08812","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1509.08812","created_at":"2026-05-18T01:31:47.041347+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.08812v1","created_at":"2026-05-18T01:31:47.041347+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08812","created_at":"2026-05-18T01:31:47.041347+00:00"},{"alias_kind":"pith_short_12","alias_value":"644CMMO3OPIG","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"644CMMO3OPIGFZXV","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"644CMMO3","created_at":"2026-05-18T12:29:07.941421+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/644CMMO3OPIGFZXVROEUOJNX3N","json":"https://pith.science/pith/644CMMO3OPIGFZXVROEUOJNX3N.json","graph_json":"https://pith.science/api/pith-number/644CMMO3OPIGFZXVROEUOJNX3N/graph.json","events_json":"https://pith.science/api/pith-number/644CMMO3OPIGFZXVROEUOJNX3N/events.json","paper":"https://pith.science/paper/644CMMO3"},"agent_actions":{"view_html":"https://pith.science/pith/644CMMO3OPIGFZXVROEUOJNX3N","download_json":"https://pith.science/pith/644CMMO3OPIGFZXVROEUOJNX3N.json","view_paper":"https://pith.science/paper/644CMMO3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.08812&json=true","fetch_graph":"https://pith.science/api/pith-number/644CMMO3OPIGFZXVROEUOJNX3N/graph.json","fetch_events":"https://pith.science/api/pith-number/644CMMO3OPIGFZXVROEUOJNX3N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/644CMMO3OPIGFZXVROEUOJNX3N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/644CMMO3OPIGFZXVROEUOJNX3N/action/storage_attestation","attest_author":"https://pith.science/pith/644CMMO3OPIGFZXVROEUOJNX3N/action/author_attestation","sign_citation":"https://pith.science/pith/644CMMO3OPIGFZXVROEUOJNX3N/action/citation_signature","submit_replication":"https://pith.science/pith/644CMMO3OPIGFZXVROEUOJNX3N/action/replication_record"}},"created_at":"2026-05-18T01:31:47.041347+00:00","updated_at":"2026-05-18T01:31:47.041347+00:00"}