{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:EDTWLAZUKDG646ZZCVOLECBMVD","short_pith_number":"pith:EDTWLAZU","canonical_record":{"source":{"id":"1611.02942","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-11-08T20:49:34Z","cross_cats_sorted":[],"title_canon_sha256":"debe30ff58ea98db44f4959730b52146b18954a075daca5f92e74891445e3542","abstract_canon_sha256":"f821c30e05901fe1a6c9b5302f3ba61b3be974a89cb69b162b2d5bda2bd7ba6d"},"schema_version":"1.0"},"canonical_sha256":"20e765833450cdee7b39155cb2082ca8d095beadfd6aa2dc43a21fe459c21298","source":{"kind":"arxiv","id":"1611.02942","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02942","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02942v3","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02942","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"pith_short_12","alias_value":"EDTWLAZUKDG6","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EDTWLAZUKDG646ZZ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EDTWLAZU","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:EDTWLAZUKDG646ZZCVOLECBMVD","target":"record","payload":{"canonical_record":{"source":{"id":"1611.02942","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-11-08T20:49:34Z","cross_cats_sorted":[],"title_canon_sha256":"debe30ff58ea98db44f4959730b52146b18954a075daca5f92e74891445e3542","abstract_canon_sha256":"f821c30e05901fe1a6c9b5302f3ba61b3be974a89cb69b162b2d5bda2bd7ba6d"},"schema_version":"1.0"},"canonical_sha256":"20e765833450cdee7b39155cb2082ca8d095beadfd6aa2dc43a21fe459c21298","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:55.804139Z","signature_b64":"CZk60ycIRjiTzhN6unjCaEHsdLaKKHFehgS+vrxDLCTISmkY7PQEaJhY/ZLBD695HZS7oLgQXWBGW7XDenkzCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20e765833450cdee7b39155cb2082ca8d095beadfd6aa2dc43a21fe459c21298","last_reissued_at":"2026-05-17T23:46:55.803654Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:55.803654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.02942","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:46:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dsLFrFG5MuF3hBk75qqNrMTYVSls0p1PcYY9Tyqy2PuZO8Ia9emZGZMYbFqwOBS0UKXxq34GwT8QVp549oS1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T00:31:56.642387Z"},"content_sha256":"6b1fb0e88fb926836867bc7cabc7d5bf00116bbab51b6cdddc0effea0c7015fd","schema_version":"1.0","event_id":"sha256:6b1fb0e88fb926836867bc7cabc7d5bf00116bbab51b6cdddc0effea0c7015fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:EDTWLAZUKDG646ZZCVOLECBMVD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Alg\\`ebre commutative M\\'ethodes constructives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Claude Quitt\\'e, Henri Lombardi","submitted_at":"2016-11-08T20:49:34Z","abstract_excerpt":"This book is an introductory course to basic commutative algebra with a particular emphasis on finitely generated projective modules, which constitutes the algebraic version of the vector bundles in differential geometry. We adopt the constructive point of view, with which all existence theorems have an explicit algorithmic content. In particular, when a theorem affirms the existence of an object -- the solution of a problem -- a construction algorithm of the object can always be extracted from the given proof. We revisit with a new and often simplifying eye several abstract classical theories"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02942","kind":"arxiv","version":3},"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":"2026-05-17T23:46:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EXv0e8pWTVW2LWaB/9LN8g6x6VWP6k2MzPLMy6iDj3ynpJM7uLaN9OC+24k4BVZqlH+AR0+nSH0SwHVdu+S0Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T00:31:56.642731Z"},"content_sha256":"5b35007d281d7db28f5f49bea0772681ab677cdb2e02c7332384872ac019e2d6","schema_version":"1.0","event_id":"sha256:5b35007d281d7db28f5f49bea0772681ab677cdb2e02c7332384872ac019e2d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EDTWLAZUKDG646ZZCVOLECBMVD/bundle.json","state_url":"https://pith.science/pith/EDTWLAZUKDG646ZZCVOLECBMVD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EDTWLAZUKDG646ZZCVOLECBMVD/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":"2026-06-25T00:31:56Z","links":{"resolver":"https://pith.science/pith/EDTWLAZUKDG646ZZCVOLECBMVD","bundle":"https://pith.science/pith/EDTWLAZUKDG646ZZCVOLECBMVD/bundle.json","state":"https://pith.science/pith/EDTWLAZUKDG646ZZCVOLECBMVD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EDTWLAZUKDG646ZZCVOLECBMVD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EDTWLAZUKDG646ZZCVOLECBMVD","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":"f821c30e05901fe1a6c9b5302f3ba61b3be974a89cb69b162b2d5bda2bd7ba6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-11-08T20:49:34Z","title_canon_sha256":"debe30ff58ea98db44f4959730b52146b18954a075daca5f92e74891445e3542"},"schema_version":"1.0","source":{"id":"1611.02942","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02942","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02942v3","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02942","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"pith_short_12","alias_value":"EDTWLAZUKDG6","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EDTWLAZUKDG646ZZ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EDTWLAZU","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:5b35007d281d7db28f5f49bea0772681ab677cdb2e02c7332384872ac019e2d6","target":"graph","created_at":"2026-05-17T23:46:55Z","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":"This book is an introductory course to basic commutative algebra with a particular emphasis on finitely generated projective modules, which constitutes the algebraic version of the vector bundles in differential geometry. We adopt the constructive point of view, with which all existence theorems have an explicit algorithmic content. In particular, when a theorem affirms the existence of an object -- the solution of a problem -- a construction algorithm of the object can always be extracted from the given proof. We revisit with a new and often simplifying eye several abstract classical theories","authors_text":"Claude Quitt\\'e, Henri Lombardi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-11-08T20:49:34Z","title":"Alg\\`ebre commutative M\\'ethodes constructives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02942","kind":"arxiv","version":3},"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":"sha256:6b1fb0e88fb926836867bc7cabc7d5bf00116bbab51b6cdddc0effea0c7015fd","target":"record","created_at":"2026-05-17T23:46:55Z","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":"f821c30e05901fe1a6c9b5302f3ba61b3be974a89cb69b162b2d5bda2bd7ba6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-11-08T20:49:34Z","title_canon_sha256":"debe30ff58ea98db44f4959730b52146b18954a075daca5f92e74891445e3542"},"schema_version":"1.0","source":{"id":"1611.02942","kind":"arxiv","version":3}},"canonical_sha256":"20e765833450cdee7b39155cb2082ca8d095beadfd6aa2dc43a21fe459c21298","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20e765833450cdee7b39155cb2082ca8d095beadfd6aa2dc43a21fe459c21298","first_computed_at":"2026-05-17T23:46:55.803654Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:55.803654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CZk60ycIRjiTzhN6unjCaEHsdLaKKHFehgS+vrxDLCTISmkY7PQEaJhY/ZLBD695HZS7oLgQXWBGW7XDenkzCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:55.804139Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.02942","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b1fb0e88fb926836867bc7cabc7d5bf00116bbab51b6cdddc0effea0c7015fd","sha256:5b35007d281d7db28f5f49bea0772681ab677cdb2e02c7332384872ac019e2d6"],"state_sha256":"efcb03010d1240e0d8bcb05a28d364d3d5aea3d6d722189673a60b330dbf7357"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YbRaRDVaZHXJZ300X2rT33Np+p6coRfiEfDhEvWmpLca5DVafL0sE23jamraX9tI+/dfJQLHqnzm5sxwqnhjBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T00:31:56.644687Z","bundle_sha256":"6873ccf75315a5f5a794cc52c1e11daf4fc516f8dbaa9bee5aa8f6011321c516"}}