{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HL52NF55UROGAOPPAIMNGCUBBH","short_pith_number":"pith:HL52NF55","canonical_record":{"source":{"id":"1105.3627","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-05-18T13:41:48Z","cross_cats_sorted":["math.KT","math.RT"],"title_canon_sha256":"dd44259d462f6799bd68445dfdcd41b33eaae69de9933cc5a8bab5123cf3f8ca","abstract_canon_sha256":"70f95809ed647d5b011fd7e97e6d1352159257a2791ff06db6ba61e5c0e4a76a"},"schema_version":"1.0"},"canonical_sha256":"3afba697bda45c6039ef0218d30a8109d535ed344fc7fc82d0d834564e7315b6","source":{"kind":"arxiv","id":"1105.3627","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3627","created_at":"2026-05-18T04:21:52Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3627v1","created_at":"2026-05-18T04:21:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3627","created_at":"2026-05-18T04:21:52Z"},{"alias_kind":"pith_short_12","alias_value":"HL52NF55UROG","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HL52NF55UROGAOPP","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HL52NF55","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HL52NF55UROGAOPPAIMNGCUBBH","target":"record","payload":{"canonical_record":{"source":{"id":"1105.3627","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-05-18T13:41:48Z","cross_cats_sorted":["math.KT","math.RT"],"title_canon_sha256":"dd44259d462f6799bd68445dfdcd41b33eaae69de9933cc5a8bab5123cf3f8ca","abstract_canon_sha256":"70f95809ed647d5b011fd7e97e6d1352159257a2791ff06db6ba61e5c0e4a76a"},"schema_version":"1.0"},"canonical_sha256":"3afba697bda45c6039ef0218d30a8109d535ed344fc7fc82d0d834564e7315b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:52.238874Z","signature_b64":"dAKn68G1FJsLcbDH0IkGbO6zWM1xomWOGqFPH0K9R85YAxian/G5eQIfQi+UCGMsDgxRD6SoJpT+e9ij8ZaMBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3afba697bda45c6039ef0218d30a8109d535ed344fc7fc82d0d834564e7315b6","last_reissued_at":"2026-05-18T04:21:52.238110Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:52.238110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.3627","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:21:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4WpVMZz5oBz1e60ipZ3KQRsVEX2AKAON+lxdlTgrXOETM0YYveQuujVVUypJqawSxyqHh2H3TWTAHaUQU5bmAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:45:58.060442Z"},"content_sha256":"6bf4a30f4932058ee31bf1a8a9b47d84a2a976280bc4f09780ccefe096361547","schema_version":"1.0","event_id":"sha256:6bf4a30f4932058ee31bf1a8a9b47d84a2a976280bc4f09780ccefe096361547"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HL52NF55UROGAOPPAIMNGCUBBH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinitely generated projective modules over pullbacks of rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.RT"],"primary_cat":"math.RA","authors_text":"Dolors Herbera, Pavel Prihoda","submitted_at":"2011-05-18T13:41:48Z","abstract_excerpt":"We use pullbacks of rings to realize the submonoids $M$ of $(\\N_0\\cup\\{\\infty\\})^k$ which are the set of solutions of a finite system of linear diophantine inequalities as the monoid of isomorphism classes of countably generated projective right $R$-modules over a suitable semilocal ring. For these rings, the behavior of countably generated projective left $R$-modules is determined by the monoid $D(M)$ defined by reversing the inequalities determining the monoid $M$. These two monoids are not isomorphic in general. As a consequence of our results we show that there are semilocal rings such tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3627","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:21:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u0V4HYB5Xo21RElrbeh9I2iSYanDQzB4xBKPUOo2r7kDuVLEvKKpQbUEtUt0z3qLNDkHBOD+7wkl38azdi6RBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:45:58.060942Z"},"content_sha256":"f3084971214b4f2e5d9a6328052be9a49f88275c2fb478c8b8b2d8fab4e791f8","schema_version":"1.0","event_id":"sha256:f3084971214b4f2e5d9a6328052be9a49f88275c2fb478c8b8b2d8fab4e791f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HL52NF55UROGAOPPAIMNGCUBBH/bundle.json","state_url":"https://pith.science/pith/HL52NF55UROGAOPPAIMNGCUBBH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HL52NF55UROGAOPPAIMNGCUBBH/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":"2026-06-26T00:45:58Z","links":{"resolver":"https://pith.science/pith/HL52NF55UROGAOPPAIMNGCUBBH","bundle":"https://pith.science/pith/HL52NF55UROGAOPPAIMNGCUBBH/bundle.json","state":"https://pith.science/pith/HL52NF55UROGAOPPAIMNGCUBBH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HL52NF55UROGAOPPAIMNGCUBBH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HL52NF55UROGAOPPAIMNGCUBBH","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":"70f95809ed647d5b011fd7e97e6d1352159257a2791ff06db6ba61e5c0e4a76a","cross_cats_sorted":["math.KT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-05-18T13:41:48Z","title_canon_sha256":"dd44259d462f6799bd68445dfdcd41b33eaae69de9933cc5a8bab5123cf3f8ca"},"schema_version":"1.0","source":{"id":"1105.3627","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3627","created_at":"2026-05-18T04:21:52Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3627v1","created_at":"2026-05-18T04:21:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3627","created_at":"2026-05-18T04:21:52Z"},{"alias_kind":"pith_short_12","alias_value":"HL52NF55UROG","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HL52NF55UROGAOPP","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HL52NF55","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:f3084971214b4f2e5d9a6328052be9a49f88275c2fb478c8b8b2d8fab4e791f8","target":"graph","created_at":"2026-05-18T04:21:52Z","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":"We use pullbacks of rings to realize the submonoids $M$ of $(\\N_0\\cup\\{\\infty\\})^k$ which are the set of solutions of a finite system of linear diophantine inequalities as the monoid of isomorphism classes of countably generated projective right $R$-modules over a suitable semilocal ring. For these rings, the behavior of countably generated projective left $R$-modules is determined by the monoid $D(M)$ defined by reversing the inequalities determining the monoid $M$. These two monoids are not isomorphic in general. As a consequence of our results we show that there are semilocal rings such tha","authors_text":"Dolors Herbera, Pavel Prihoda","cross_cats":["math.KT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-05-18T13:41:48Z","title":"Infinitely generated projective modules over pullbacks of rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3627","kind":"arxiv","version":1},"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":"sha256:6bf4a30f4932058ee31bf1a8a9b47d84a2a976280bc4f09780ccefe096361547","target":"record","created_at":"2026-05-18T04:21:52Z","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":"70f95809ed647d5b011fd7e97e6d1352159257a2791ff06db6ba61e5c0e4a76a","cross_cats_sorted":["math.KT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-05-18T13:41:48Z","title_canon_sha256":"dd44259d462f6799bd68445dfdcd41b33eaae69de9933cc5a8bab5123cf3f8ca"},"schema_version":"1.0","source":{"id":"1105.3627","kind":"arxiv","version":1}},"canonical_sha256":"3afba697bda45c6039ef0218d30a8109d535ed344fc7fc82d0d834564e7315b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3afba697bda45c6039ef0218d30a8109d535ed344fc7fc82d0d834564e7315b6","first_computed_at":"2026-05-18T04:21:52.238110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:52.238110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dAKn68G1FJsLcbDH0IkGbO6zWM1xomWOGqFPH0K9R85YAxian/G5eQIfQi+UCGMsDgxRD6SoJpT+e9ij8ZaMBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:52.238874Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.3627","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6bf4a30f4932058ee31bf1a8a9b47d84a2a976280bc4f09780ccefe096361547","sha256:f3084971214b4f2e5d9a6328052be9a49f88275c2fb478c8b8b2d8fab4e791f8"],"state_sha256":"fc1d2fe6e749928298b4fa45bb3372a46edebf7b5eb233dce3339f7571adf099"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/GCqxvQrmKCp9JudncKwF3zLRsR5XbmOqhz1qVeMUzXAbIdHLzswxfWMGS2UnbndIjhHsPOVHpBX3qQP1KnTAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T00:45:58.063470Z","bundle_sha256":"d5c4f15a8cc90243f899e18a1b6da96e16efe94c79733d835effdcb89032ef76"}}