{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:DSLASFREL4FPUYDNEZARQMB7ZQ","short_pith_number":"pith:DSLASFRE","canonical_record":{"source":{"id":"1109.4387","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-09-20T18:32:19Z","cross_cats_sorted":[],"title_canon_sha256":"ab01ae76ab716866fd67875e05b894a6d0a21d71f68753bb615e7f5641856cc5","abstract_canon_sha256":"5ddf0261c4e77b5704c30b1778706ff3d46b1d72813fb07801ca75a91b9d92da"},"schema_version":"1.0"},"canonical_sha256":"1c960916245f0afa606d264118303fcc106c740ed41c578662f45c6e07cf06bb","source":{"kind":"arxiv","id":"1109.4387","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4387","created_at":"2026-05-18T04:11:07Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4387v2","created_at":"2026-05-18T04:11:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4387","created_at":"2026-05-18T04:11:07Z"},{"alias_kind":"pith_short_12","alias_value":"DSLASFREL4FP","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DSLASFREL4FPUYDN","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DSLASFRE","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:DSLASFREL4FPUYDNEZARQMB7ZQ","target":"record","payload":{"canonical_record":{"source":{"id":"1109.4387","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-09-20T18:32:19Z","cross_cats_sorted":[],"title_canon_sha256":"ab01ae76ab716866fd67875e05b894a6d0a21d71f68753bb615e7f5641856cc5","abstract_canon_sha256":"5ddf0261c4e77b5704c30b1778706ff3d46b1d72813fb07801ca75a91b9d92da"},"schema_version":"1.0"},"canonical_sha256":"1c960916245f0afa606d264118303fcc106c740ed41c578662f45c6e07cf06bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:07.079120Z","signature_b64":"JUB1pLZkE/L7u67OIL/rvFXim+6TYhiDFfa6vQow4++9tXoEOWt/JHFQ6uQaN16LxMg9AaEp09wMZd1AR+hGBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c960916245f0afa606d264118303fcc106c740ed41c578662f45c6e07cf06bb","last_reissued_at":"2026-05-18T04:11:07.078585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:07.078585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.4387","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":"2026-05-18T04:11:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b0L14KAzAM2R9YFOM3axXduJA/e5iG2FQQHcSkfAr10lV4NF3/vO82o037DlwOWu3rVCGqT2ftzcj7onVkZHDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:52:30.778337Z"},"content_sha256":"ef135c12f04154bca080affb33b97bb79f2e9c73ccc418fc947803bffb6b6cfe","schema_version":"1.0","event_id":"sha256:ef135c12f04154bca080affb33b97bb79f2e9c73ccc418fc947803bffb6b6cfe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:DSLASFREL4FPUYDNEZARQMB7ZQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An equivalence of categories for graded modules over monomial algebras and path algebras of quivers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Cody Holdaway, S. Paul Smith","submitted_at":"2011-09-20T18:32:19Z","abstract_excerpt":"Let A be a finitely generated connected graded k-algebra defined by a finite number of monomial relations. Then there is a finite directed graph, Q, the Ufnarovskii graph of A, for which the categories QGr(A) and QGr(kQ) are equivalent: QGr(A) denotes the quotient category of graded A-modules modulo the subcategory consisting of those that are the sum of their finite dimensional submodules; QGr(kQ) has a similar definition. The proof makes use of an algebra homomorphism A--->kQ that may be of independent interest."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4387","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":"2026-05-18T04:11:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mchI14So+GTUhBmRCfT9l8UK9rAMruLNfPN832Re5rxHxk4w1dEbdauikT0Q0IHDUJ9STVYxikpSdwkHnQOOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:52:30.779037Z"},"content_sha256":"effc8b1ee809d24722252a90801bb08989274e0c61e7ff7d0930e68a429a1c67","schema_version":"1.0","event_id":"sha256:effc8b1ee809d24722252a90801bb08989274e0c61e7ff7d0930e68a429a1c67"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DSLASFREL4FPUYDNEZARQMB7ZQ/bundle.json","state_url":"https://pith.science/pith/DSLASFREL4FPUYDNEZARQMB7ZQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DSLASFREL4FPUYDNEZARQMB7ZQ/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":"2026-05-31T12:52:30Z","links":{"resolver":"https://pith.science/pith/DSLASFREL4FPUYDNEZARQMB7ZQ","bundle":"https://pith.science/pith/DSLASFREL4FPUYDNEZARQMB7ZQ/bundle.json","state":"https://pith.science/pith/DSLASFREL4FPUYDNEZARQMB7ZQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DSLASFREL4FPUYDNEZARQMB7ZQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DSLASFREL4FPUYDNEZARQMB7ZQ","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":"5ddf0261c4e77b5704c30b1778706ff3d46b1d72813fb07801ca75a91b9d92da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-09-20T18:32:19Z","title_canon_sha256":"ab01ae76ab716866fd67875e05b894a6d0a21d71f68753bb615e7f5641856cc5"},"schema_version":"1.0","source":{"id":"1109.4387","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4387","created_at":"2026-05-18T04:11:07Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4387v2","created_at":"2026-05-18T04:11:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4387","created_at":"2026-05-18T04:11:07Z"},{"alias_kind":"pith_short_12","alias_value":"DSLASFREL4FP","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DSLASFREL4FPUYDN","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DSLASFRE","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:effc8b1ee809d24722252a90801bb08989274e0c61e7ff7d0930e68a429a1c67","target":"graph","created_at":"2026-05-18T04:11:07Z","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 A be a finitely generated connected graded k-algebra defined by a finite number of monomial relations. Then there is a finite directed graph, Q, the Ufnarovskii graph of A, for which the categories QGr(A) and QGr(kQ) are equivalent: QGr(A) denotes the quotient category of graded A-modules modulo the subcategory consisting of those that are the sum of their finite dimensional submodules; QGr(kQ) has a similar definition. The proof makes use of an algebra homomorphism A--->kQ that may be of independent interest.","authors_text":"Cody Holdaway, S. Paul Smith","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-09-20T18:32:19Z","title":"An equivalence of categories for graded modules over monomial algebras and path algebras of quivers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4387","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:ef135c12f04154bca080affb33b97bb79f2e9c73ccc418fc947803bffb6b6cfe","target":"record","created_at":"2026-05-18T04:11:07Z","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":"5ddf0261c4e77b5704c30b1778706ff3d46b1d72813fb07801ca75a91b9d92da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-09-20T18:32:19Z","title_canon_sha256":"ab01ae76ab716866fd67875e05b894a6d0a21d71f68753bb615e7f5641856cc5"},"schema_version":"1.0","source":{"id":"1109.4387","kind":"arxiv","version":2}},"canonical_sha256":"1c960916245f0afa606d264118303fcc106c740ed41c578662f45c6e07cf06bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c960916245f0afa606d264118303fcc106c740ed41c578662f45c6e07cf06bb","first_computed_at":"2026-05-18T04:11:07.078585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:07.078585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JUB1pLZkE/L7u67OIL/rvFXim+6TYhiDFfa6vQow4++9tXoEOWt/JHFQ6uQaN16LxMg9AaEp09wMZd1AR+hGBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:07.079120Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4387","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef135c12f04154bca080affb33b97bb79f2e9c73ccc418fc947803bffb6b6cfe","sha256:effc8b1ee809d24722252a90801bb08989274e0c61e7ff7d0930e68a429a1c67"],"state_sha256":"d93d2a8c5f85b505241ba5ff0211cc892d2a028dbc8d0252466afe669155b90b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CulklZs+9/mKRAvc0uEYQRB+K71rnkUzS4gAHKKKXuP5ldkuc9bA+xLie6E7uL4UMVchbKzyu5K466JCLK0QBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T12:52:30.783616Z","bundle_sha256":"20a7c9368cc5f0a8018f5aa8ef45d45d5fdbfc31d23561229d982ec9831be630"}}