{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LJF7F3WKEEU6VN5GMEBPJCYMNN","short_pith_number":"pith:LJF7F3WK","canonical_record":{"source":{"id":"1310.3478","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-10-13T13:06:42Z","cross_cats_sorted":[],"title_canon_sha256":"6f07b9545785dc74eb7d60cc944f4c511cf9a79e1cddec8a6ec419f1aead6922","abstract_canon_sha256":"c03c556151ed3184fd3e33eaa5ee960a68e0afbc1c6ceb43d885d49396f20eb4"},"schema_version":"1.0"},"canonical_sha256":"5a4bf2eeca2129eab7a66102f48b0c6b49ffda2311bdea6518ec241f1f27d63c","source":{"kind":"arxiv","id":"1310.3478","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3478","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3478v2","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3478","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"pith_short_12","alias_value":"LJF7F3WKEEU6","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LJF7F3WKEEU6VN5G","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LJF7F3WK","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LJF7F3WKEEU6VN5GMEBPJCYMNN","target":"record","payload":{"canonical_record":{"source":{"id":"1310.3478","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-10-13T13:06:42Z","cross_cats_sorted":[],"title_canon_sha256":"6f07b9545785dc74eb7d60cc944f4c511cf9a79e1cddec8a6ec419f1aead6922","abstract_canon_sha256":"c03c556151ed3184fd3e33eaa5ee960a68e0afbc1c6ceb43d885d49396f20eb4"},"schema_version":"1.0"},"canonical_sha256":"5a4bf2eeca2129eab7a66102f48b0c6b49ffda2311bdea6518ec241f1f27d63c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:04.876296Z","signature_b64":"nf18w2qiEZeB+s6mBdV7OUbuGyZCzSFLOomOCE9KEl30J2wuWauzaFdiqDic4QDk0hJYPi2lmPpOrLsXCQa9Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a4bf2eeca2129eab7a66102f48b0c6b49ffda2311bdea6518ec241f1f27d63c","last_reissued_at":"2026-05-18T00:54:04.875725Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:04.875725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.3478","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":"2026-05-18T00:54:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1bjU/mT4wqSmjqpwT+Prd8Er2ss00PUKJgWnOT6c5XcYNa420D529+dvUTNt9gROPcCxzGLnkzo4+9d+8GTbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:40:03.938624Z"},"content_sha256":"68e9aa454b0f7d8f62b4321216df40eb7fd674596f60db36e228b1319c2357b2","schema_version":"1.0","event_id":"sha256:68e9aa454b0f7d8f62b4321216df40eb7fd674596f60db36e228b1319c2357b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LJF7F3WKEEU6VN5GMEBPJCYMNN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Flat local morphisms of rings with prescribed depth and dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Cristodor Ionescu","submitted_at":"2013-10-13T13:06:42Z","abstract_excerpt":"For pairs of integers (n,m) and (d,e) satisfying some nedesary conditions, we construct a local flat ring morphism of noetherian local rings u:A -->B such that dim(A)=n, depth(A)=d, dim(B)=m, depth(B)=e."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3478","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":"2026-05-18T00:54:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Re1+XcOg8J8coajHUo9eoLnglzmRAX2IqNQlyAXUUEVQ7PNBNK45nE9dkWaGTq9QPrSZBTq35PMHqX7yVHxeBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:40:03.938961Z"},"content_sha256":"9a7c30afe64227da6af34bd8966b3056099c138b0ab0a6da8db753bc0e703984","schema_version":"1.0","event_id":"sha256:9a7c30afe64227da6af34bd8966b3056099c138b0ab0a6da8db753bc0e703984"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LJF7F3WKEEU6VN5GMEBPJCYMNN/bundle.json","state_url":"https://pith.science/pith/LJF7F3WKEEU6VN5GMEBPJCYMNN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LJF7F3WKEEU6VN5GMEBPJCYMNN/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":"2026-06-25T05:40:03Z","links":{"resolver":"https://pith.science/pith/LJF7F3WKEEU6VN5GMEBPJCYMNN","bundle":"https://pith.science/pith/LJF7F3WKEEU6VN5GMEBPJCYMNN/bundle.json","state":"https://pith.science/pith/LJF7F3WKEEU6VN5GMEBPJCYMNN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LJF7F3WKEEU6VN5GMEBPJCYMNN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LJF7F3WKEEU6VN5GMEBPJCYMNN","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":"c03c556151ed3184fd3e33eaa5ee960a68e0afbc1c6ceb43d885d49396f20eb4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-10-13T13:06:42Z","title_canon_sha256":"6f07b9545785dc74eb7d60cc944f4c511cf9a79e1cddec8a6ec419f1aead6922"},"schema_version":"1.0","source":{"id":"1310.3478","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3478","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3478v2","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3478","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"pith_short_12","alias_value":"LJF7F3WKEEU6","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LJF7F3WKEEU6VN5G","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LJF7F3WK","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:9a7c30afe64227da6af34bd8966b3056099c138b0ab0a6da8db753bc0e703984","target":"graph","created_at":"2026-05-18T00:54:04Z","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":"For pairs of integers (n,m) and (d,e) satisfying some nedesary conditions, we construct a local flat ring morphism of noetherian local rings u:A -->B such that dim(A)=n, depth(A)=d, dim(B)=m, depth(B)=e.","authors_text":"Cristodor Ionescu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-10-13T13:06:42Z","title":"Flat local morphisms of rings with prescribed depth and dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3478","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":"sha256:68e9aa454b0f7d8f62b4321216df40eb7fd674596f60db36e228b1319c2357b2","target":"record","created_at":"2026-05-18T00:54:04Z","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":"c03c556151ed3184fd3e33eaa5ee960a68e0afbc1c6ceb43d885d49396f20eb4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-10-13T13:06:42Z","title_canon_sha256":"6f07b9545785dc74eb7d60cc944f4c511cf9a79e1cddec8a6ec419f1aead6922"},"schema_version":"1.0","source":{"id":"1310.3478","kind":"arxiv","version":2}},"canonical_sha256":"5a4bf2eeca2129eab7a66102f48b0c6b49ffda2311bdea6518ec241f1f27d63c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a4bf2eeca2129eab7a66102f48b0c6b49ffda2311bdea6518ec241f1f27d63c","first_computed_at":"2026-05-18T00:54:04.875725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:04.875725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nf18w2qiEZeB+s6mBdV7OUbuGyZCzSFLOomOCE9KEl30J2wuWauzaFdiqDic4QDk0hJYPi2lmPpOrLsXCQa9Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:04.876296Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.3478","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68e9aa454b0f7d8f62b4321216df40eb7fd674596f60db36e228b1319c2357b2","sha256:9a7c30afe64227da6af34bd8966b3056099c138b0ab0a6da8db753bc0e703984"],"state_sha256":"46038c4177806feac6e25bda6666c2a698ab779b2b82bbe3b47479dbd21caa5c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MXdNUKeCKj8ZmcWNrdcKdTrK5UidJMPUC52gCdmpM0VB0V8VHcLOe4UE8CYLx13N2qU+ux/EA2muvZh2m1hGAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T05:40:03.940798Z","bundle_sha256":"a869b42d7d336aa83099d588f8ad855d3ec1b2b92e824b4254c88d2a28d209a2"}}