{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CGKUVD5LU53Z2BSQKTZUBQJBLW","short_pith_number":"pith:CGKUVD5L","canonical_record":{"source":{"id":"1611.07726","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-11-23T10:25:54Z","cross_cats_sorted":[],"title_canon_sha256":"c9c448a7fb5aa956768e2e6a3a41203f3ed6d0cffa11ec7a5babd00bc66d61b3","abstract_canon_sha256":"e52467009742a0bc2842eb090470d03d1c4dd93177b463c546a50fc9139e1001"},"schema_version":"1.0"},"canonical_sha256":"11954a8faba7779d065054f340c1215d98143e1d631f47ab495aff9c1ce615c6","source":{"kind":"arxiv","id":"1611.07726","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07726","created_at":"2026-05-18T00:56:59Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07726v1","created_at":"2026-05-18T00:56:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07726","created_at":"2026-05-18T00:56:59Z"},{"alias_kind":"pith_short_12","alias_value":"CGKUVD5LU53Z","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CGKUVD5LU53Z2BSQ","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CGKUVD5L","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CGKUVD5LU53Z2BSQKTZUBQJBLW","target":"record","payload":{"canonical_record":{"source":{"id":"1611.07726","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-11-23T10:25:54Z","cross_cats_sorted":[],"title_canon_sha256":"c9c448a7fb5aa956768e2e6a3a41203f3ed6d0cffa11ec7a5babd00bc66d61b3","abstract_canon_sha256":"e52467009742a0bc2842eb090470d03d1c4dd93177b463c546a50fc9139e1001"},"schema_version":"1.0"},"canonical_sha256":"11954a8faba7779d065054f340c1215d98143e1d631f47ab495aff9c1ce615c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:59.989772Z","signature_b64":"GkVksBm0Z0k6IfIWscWn/faUQp9R7Ddtk3f+5spzx30006M9u1oc91jpW1KB+npltC7kMcQw4K9pVhZ9pI8dDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11954a8faba7779d065054f340c1215d98143e1d631f47ab495aff9c1ce615c6","last_reissued_at":"2026-05-18T00:56:59.989192Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:59.989192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.07726","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":"2026-05-18T00:56:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p2KQ6Oea6zX6tD0jaqTCr3jdz2ENaMj6ho6uYEZtvyIsHN59QRQkOkFpK5ccuqgyf5KxbKFnEKhuzQ3DOUQ/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T20:06:13.074932Z"},"content_sha256":"eda4e86c40d0edf6b5c0e2d47ec0a437b5391787f1bfe8a2163d153756a37b6b","schema_version":"1.0","event_id":"sha256:eda4e86c40d0edf6b5c0e2d47ec0a437b5391787f1bfe8a2163d153756a37b6b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CGKUVD5LU53Z2BSQKTZUBQJBLW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial invariants by linear algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Saddek Bensalem, Steven de Oliveira, Virgile Prevosto","submitted_at":"2016-11-23T10:25:54Z","abstract_excerpt":"We present in this paper a new technique for generating polynomial invariants, divided in two independent parts : a procedure that reduces polynomial assignments composed loops analysis to linear loops under certain hypotheses and a procedure for generating inductive invariants for linear loops. Both of these techniques have a polynomial complexity for a bounded number of variables and we guarantee the completeness of the technique for a bounded degree which we successfully implemented for C programs verification."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07726","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":"2026-05-18T00:56:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qYoYXrX/m/0lXONeiRYTfdPsh5EkP6ixIB1v33QMYr+/dosuDrKnE8Ks67Oip7ZWW9+B57lWCb5fb6oAaSOEDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T20:06:13.075291Z"},"content_sha256":"d0800c61835f51168137c192c430372902f9b666afe7c22266824175070ab624","schema_version":"1.0","event_id":"sha256:d0800c61835f51168137c192c430372902f9b666afe7c22266824175070ab624"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CGKUVD5LU53Z2BSQKTZUBQJBLW/bundle.json","state_url":"https://pith.science/pith/CGKUVD5LU53Z2BSQKTZUBQJBLW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CGKUVD5LU53Z2BSQKTZUBQJBLW/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":"2026-05-20T20:06:13Z","links":{"resolver":"https://pith.science/pith/CGKUVD5LU53Z2BSQKTZUBQJBLW","bundle":"https://pith.science/pith/CGKUVD5LU53Z2BSQKTZUBQJBLW/bundle.json","state":"https://pith.science/pith/CGKUVD5LU53Z2BSQKTZUBQJBLW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CGKUVD5LU53Z2BSQKTZUBQJBLW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CGKUVD5LU53Z2BSQKTZUBQJBLW","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":"e52467009742a0bc2842eb090470d03d1c4dd93177b463c546a50fc9139e1001","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-11-23T10:25:54Z","title_canon_sha256":"c9c448a7fb5aa956768e2e6a3a41203f3ed6d0cffa11ec7a5babd00bc66d61b3"},"schema_version":"1.0","source":{"id":"1611.07726","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07726","created_at":"2026-05-18T00:56:59Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07726v1","created_at":"2026-05-18T00:56:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07726","created_at":"2026-05-18T00:56:59Z"},{"alias_kind":"pith_short_12","alias_value":"CGKUVD5LU53Z","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CGKUVD5LU53Z2BSQ","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CGKUVD5L","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:d0800c61835f51168137c192c430372902f9b666afe7c22266824175070ab624","target":"graph","created_at":"2026-05-18T00:56:59Z","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 present in this paper a new technique for generating polynomial invariants, divided in two independent parts : a procedure that reduces polynomial assignments composed loops analysis to linear loops under certain hypotheses and a procedure for generating inductive invariants for linear loops. Both of these techniques have a polynomial complexity for a bounded number of variables and we guarantee the completeness of the technique for a bounded degree which we successfully implemented for C programs verification.","authors_text":"Saddek Bensalem, Steven de Oliveira, Virgile Prevosto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-11-23T10:25:54Z","title":"Polynomial invariants by linear algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07726","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:eda4e86c40d0edf6b5c0e2d47ec0a437b5391787f1bfe8a2163d153756a37b6b","target":"record","created_at":"2026-05-18T00:56:59Z","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":"e52467009742a0bc2842eb090470d03d1c4dd93177b463c546a50fc9139e1001","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-11-23T10:25:54Z","title_canon_sha256":"c9c448a7fb5aa956768e2e6a3a41203f3ed6d0cffa11ec7a5babd00bc66d61b3"},"schema_version":"1.0","source":{"id":"1611.07726","kind":"arxiv","version":1}},"canonical_sha256":"11954a8faba7779d065054f340c1215d98143e1d631f47ab495aff9c1ce615c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11954a8faba7779d065054f340c1215d98143e1d631f47ab495aff9c1ce615c6","first_computed_at":"2026-05-18T00:56:59.989192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:59.989192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GkVksBm0Z0k6IfIWscWn/faUQp9R7Ddtk3f+5spzx30006M9u1oc91jpW1KB+npltC7kMcQw4K9pVhZ9pI8dDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:59.989772Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.07726","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eda4e86c40d0edf6b5c0e2d47ec0a437b5391787f1bfe8a2163d153756a37b6b","sha256:d0800c61835f51168137c192c430372902f9b666afe7c22266824175070ab624"],"state_sha256":"bd6f0d5e0dbd557d9722f0f718c8c000d77b6cd64cbbcfb3daf386c5de60182b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+3Ic16lONg1SdeQoo/AwAurRqLLIW0V/Yg8rXyjz8yNfhoTWcpEwKrKmt0qXwkLV3o9B8STTMZEHnPAqMvRvAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T20:06:13.077917Z","bundle_sha256":"bee658399b7b8272fc40bbc99eebef2ef9d61a38486ff4613b902b5800580d5f"}}