{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MXJBY7KQ2DQR7KGQSSD5NCTVM4","short_pith_number":"pith:MXJBY7KQ","canonical_record":{"source":{"id":"1605.03841","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-05-11T10:21:17Z","cross_cats_sorted":[],"title_canon_sha256":"187ecdaa3a84ee3168a3c386405a079e2d5d2acbb62186079c8c19a5a07101ee","abstract_canon_sha256":"b0e947d8acb9e12a0f2327c10a9e6f998be1cda6557a9e5e3cbba4427fc69140"},"schema_version":"1.0"},"canonical_sha256":"65d21c7d50d0e11fa8d09487d68a756726a367a8debc8a6a1253218775ee1616","source":{"kind":"arxiv","id":"1605.03841","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03841","created_at":"2026-05-18T00:52:23Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03841v2","created_at":"2026-05-18T00:52:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03841","created_at":"2026-05-18T00:52:23Z"},{"alias_kind":"pith_short_12","alias_value":"MXJBY7KQ2DQR","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MXJBY7KQ2DQR7KGQ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MXJBY7KQ","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MXJBY7KQ2DQR7KGQSSD5NCTVM4","target":"record","payload":{"canonical_record":{"source":{"id":"1605.03841","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-05-11T10:21:17Z","cross_cats_sorted":[],"title_canon_sha256":"187ecdaa3a84ee3168a3c386405a079e2d5d2acbb62186079c8c19a5a07101ee","abstract_canon_sha256":"b0e947d8acb9e12a0f2327c10a9e6f998be1cda6557a9e5e3cbba4427fc69140"},"schema_version":"1.0"},"canonical_sha256":"65d21c7d50d0e11fa8d09487d68a756726a367a8debc8a6a1253218775ee1616","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:23.354683Z","signature_b64":"H5P0TdBOgAoZzNLP4TFyjPomNrrUygWhX+4+uc/nn+eYZKPIE94zo9uXupFqy4VpuIouJi3grPCo1cBzZbsGCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65d21c7d50d0e11fa8d09487d68a756726a367a8debc8a6a1253218775ee1616","last_reissued_at":"2026-05-18T00:52:23.353919Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:23.353919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.03841","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":"2026-05-18T00:52:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0N2KrrOxjqhzP7HU4YCxsdt9WfXHyxA8ALxWn5ZtmyU6NNXdf+Rd8RY+VQiJnEoJIOHjAYZc/CV0sTfp2j5/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T21:47:00.263212Z"},"content_sha256":"198e772ed5c94b292096bd09a475ca52371fe0008c070c4c4ca8aece5e0e5cc4","schema_version":"1.0","event_id":"sha256:198e772ed5c94b292096bd09a475ca52371fe0008c070c4c4ca8aece5e0e5cc4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MXJBY7KQ2DQR7KGQSSD5NCTVM4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the homological dimensions of Leavitt path algebras with coefficients in commutative rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"T.G. Nam, V. Lopatkin","submitted_at":"2016-05-11T10:21:17Z","abstract_excerpt":"In this paper, we give sharp bounds for the homological dimensions of the Leavitt path algebra $L_K(E)$ of a finite graph $E$ with coefficients in a commutative ring $K$, as well as establish a formula for calculating the homological dimensions of $L_K(E)$ when $K$ is a commutative unital algebra over a field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03841","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":"2026-05-18T00:52:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yFHRb4CZNK8NHTPpyQDUZrRqqKxixQ9U3X7/guWZIOQeMB7kfskhSN8mwXR3TAhZgtSZT9VIEgO1a3SO77MTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T21:47:00.263554Z"},"content_sha256":"798ff9aea24f7b2f354f2c2ba7d3a4d9ef0e4629d66edf4b32040ddd9d493f73","schema_version":"1.0","event_id":"sha256:798ff9aea24f7b2f354f2c2ba7d3a4d9ef0e4629d66edf4b32040ddd9d493f73"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MXJBY7KQ2DQR7KGQSSD5NCTVM4/bundle.json","state_url":"https://pith.science/pith/MXJBY7KQ2DQR7KGQSSD5NCTVM4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MXJBY7KQ2DQR7KGQSSD5NCTVM4/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":"2026-06-26T21:47:00Z","links":{"resolver":"https://pith.science/pith/MXJBY7KQ2DQR7KGQSSD5NCTVM4","bundle":"https://pith.science/pith/MXJBY7KQ2DQR7KGQSSD5NCTVM4/bundle.json","state":"https://pith.science/pith/MXJBY7KQ2DQR7KGQSSD5NCTVM4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MXJBY7KQ2DQR7KGQSSD5NCTVM4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MXJBY7KQ2DQR7KGQSSD5NCTVM4","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":"b0e947d8acb9e12a0f2327c10a9e6f998be1cda6557a9e5e3cbba4427fc69140","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-05-11T10:21:17Z","title_canon_sha256":"187ecdaa3a84ee3168a3c386405a079e2d5d2acbb62186079c8c19a5a07101ee"},"schema_version":"1.0","source":{"id":"1605.03841","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03841","created_at":"2026-05-18T00:52:23Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03841v2","created_at":"2026-05-18T00:52:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03841","created_at":"2026-05-18T00:52:23Z"},{"alias_kind":"pith_short_12","alias_value":"MXJBY7KQ2DQR","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MXJBY7KQ2DQR7KGQ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MXJBY7KQ","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:798ff9aea24f7b2f354f2c2ba7d3a4d9ef0e4629d66edf4b32040ddd9d493f73","target":"graph","created_at":"2026-05-18T00:52:23Z","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 this paper, we give sharp bounds for the homological dimensions of the Leavitt path algebra $L_K(E)$ of a finite graph $E$ with coefficients in a commutative ring $K$, as well as establish a formula for calculating the homological dimensions of $L_K(E)$ when $K$ is a commutative unital algebra over a field.","authors_text":"T.G. Nam, V. Lopatkin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-05-11T10:21:17Z","title":"On the homological dimensions of Leavitt path algebras with coefficients in commutative rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03841","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":"sha256:198e772ed5c94b292096bd09a475ca52371fe0008c070c4c4ca8aece5e0e5cc4","target":"record","created_at":"2026-05-18T00:52:23Z","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":"b0e947d8acb9e12a0f2327c10a9e6f998be1cda6557a9e5e3cbba4427fc69140","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-05-11T10:21:17Z","title_canon_sha256":"187ecdaa3a84ee3168a3c386405a079e2d5d2acbb62186079c8c19a5a07101ee"},"schema_version":"1.0","source":{"id":"1605.03841","kind":"arxiv","version":2}},"canonical_sha256":"65d21c7d50d0e11fa8d09487d68a756726a367a8debc8a6a1253218775ee1616","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65d21c7d50d0e11fa8d09487d68a756726a367a8debc8a6a1253218775ee1616","first_computed_at":"2026-05-18T00:52:23.353919Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:23.353919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H5P0TdBOgAoZzNLP4TFyjPomNrrUygWhX+4+uc/nn+eYZKPIE94zo9uXupFqy4VpuIouJi3grPCo1cBzZbsGCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:23.354683Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.03841","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:198e772ed5c94b292096bd09a475ca52371fe0008c070c4c4ca8aece5e0e5cc4","sha256:798ff9aea24f7b2f354f2c2ba7d3a4d9ef0e4629d66edf4b32040ddd9d493f73"],"state_sha256":"b1bbea55da9fce6ddd2c6f72d5a1739619a0a96651e40a4389949e0b135ebcf2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P/Ckedm2/K+rNVoO7fOAaDbviWtBr7cGYLByJVucrvdTseh4qLx456zJKlc8acCgmH1MJSalokAKU2Ij3eUsBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T21:47:00.265312Z","bundle_sha256":"32d15bf1d12b33055ceaed9307c0d60715c970d290e862456eb9460fd4297eb3"}}