{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:RMYK5F44MK42WUUV2Y5G7XOD73","short_pith_number":"pith:RMYK5F44","canonical_record":{"source":{"id":"0912.2160","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.DM","submitted_at":"2009-12-11T06:43:57Z","cross_cats_sorted":[],"title_canon_sha256":"b3c20e8c933d45a8d5d921f0d6ab2c7199911a8a19933698fa6121533c3047d3","abstract_canon_sha256":"86a5f3a8e933fe7e7ad9358bc65f627c6fcae4a9ed33c0eb6dec2ca1fc2c3574"},"schema_version":"1.0"},"canonical_sha256":"8b30ae979c62b9ab5295d63a6fddc3fed15ae8f7b0dbbe99ea76b65497210ceb","source":{"kind":"arxiv","id":"0912.2160","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.2160","created_at":"2026-07-04T17:17:38Z"},{"alias_kind":"arxiv_version","alias_value":"0912.2160v1","created_at":"2026-07-04T17:17:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.2160","created_at":"2026-07-04T17:17:38Z"},{"alias_kind":"pith_short_12","alias_value":"RMYK5F44MK42","created_at":"2026-07-04T17:17:38Z"},{"alias_kind":"pith_short_16","alias_value":"RMYK5F44MK42WUUV","created_at":"2026-07-04T17:17:38Z"},{"alias_kind":"pith_short_8","alias_value":"RMYK5F44","created_at":"2026-07-04T17:17:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:RMYK5F44MK42WUUV2Y5G7XOD73","target":"record","payload":{"canonical_record":{"source":{"id":"0912.2160","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.DM","submitted_at":"2009-12-11T06:43:57Z","cross_cats_sorted":[],"title_canon_sha256":"b3c20e8c933d45a8d5d921f0d6ab2c7199911a8a19933698fa6121533c3047d3","abstract_canon_sha256":"86a5f3a8e933fe7e7ad9358bc65f627c6fcae4a9ed33c0eb6dec2ca1fc2c3574"},"schema_version":"1.0"},"canonical_sha256":"8b30ae979c62b9ab5295d63a6fddc3fed15ae8f7b0dbbe99ea76b65497210ceb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:17:38.362348Z","signature_b64":"Y7Wvdc8tdKlUrL5nWayU43myejSqQ6DWlCb/oJwYRl0DI9L3z5EXKmtzF9HsFXWiIvbtYD39quo3ie0ool0RDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b30ae979c62b9ab5295d63a6fddc3fed15ae8f7b0dbbe99ea76b65497210ceb","last_reissued_at":"2026-07-04T17:17:38.361906Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:17:38.361906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.2160","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":"2026-07-04T17:17:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Db3P4xVrOI0LrpwElbCDg1LqjN4HhuAQIHVwOqcVYjFySzqifWwZjaTX6MEuH4d5RAHVXOVi1HR9ZqoqmBAICg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T00:47:33.779130Z"},"content_sha256":"a1eb82c13e4b0cace31815b3abdc6f4a6b8d99529f1671acc3623cc6c655a7e4","schema_version":"1.0","event_id":"sha256:a1eb82c13e4b0cace31815b3abdc6f4a6b8d99529f1671acc3623cc6c655a7e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:RMYK5F44MK42WUUV2Y5G7XOD73","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matrix Graph Grammars: Transformation of Restrictions","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Pedro Pablo Perez Velasco","submitted_at":"2009-12-11T06:43:57Z","abstract_excerpt":"In the Matrix approach to graph transformation we represent simple digraphs and rules with Boolean matrices and vectors, and the rewriting is expressed using Boolean operations only. In previous works, we developed analysis techniques enabling the study of the applicability of rule sequences, their independence, stated reachability and the minimal digraph able to fire a sequence. In [20], graph constraints and application conditions (so-called restrictions) have been studied in detail. In the present contribution we tackle the problem of translating post-conditions into pre-conditions and vice"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2160","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0912.2160/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T17:17:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kw4cKKzh5T7PDBT3ntmZRDlb4ohnQQts3IgX9ngXajNXyIEqM7WcLLwhL+RJAD4R33YEhzBePP7opMzOdmo2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T00:47:33.779513Z"},"content_sha256":"6d85e519b22e458451c1b77c113be4d751b922d448666484e66f13cff2c1b751","schema_version":"1.0","event_id":"sha256:6d85e519b22e458451c1b77c113be4d751b922d448666484e66f13cff2c1b751"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RMYK5F44MK42WUUV2Y5G7XOD73/bundle.json","state_url":"https://pith.science/pith/RMYK5F44MK42WUUV2Y5G7XOD73/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RMYK5F44MK42WUUV2Y5G7XOD73/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":"2026-07-05T00:47:33Z","links":{"resolver":"https://pith.science/pith/RMYK5F44MK42WUUV2Y5G7XOD73","bundle":"https://pith.science/pith/RMYK5F44MK42WUUV2Y5G7XOD73/bundle.json","state":"https://pith.science/pith/RMYK5F44MK42WUUV2Y5G7XOD73/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RMYK5F44MK42WUUV2Y5G7XOD73/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:RMYK5F44MK42WUUV2Y5G7XOD73","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":"86a5f3a8e933fe7e7ad9358bc65f627c6fcae4a9ed33c0eb6dec2ca1fc2c3574","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.DM","submitted_at":"2009-12-11T06:43:57Z","title_canon_sha256":"b3c20e8c933d45a8d5d921f0d6ab2c7199911a8a19933698fa6121533c3047d3"},"schema_version":"1.0","source":{"id":"0912.2160","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.2160","created_at":"2026-07-04T17:17:38Z"},{"alias_kind":"arxiv_version","alias_value":"0912.2160v1","created_at":"2026-07-04T17:17:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.2160","created_at":"2026-07-04T17:17:38Z"},{"alias_kind":"pith_short_12","alias_value":"RMYK5F44MK42","created_at":"2026-07-04T17:17:38Z"},{"alias_kind":"pith_short_16","alias_value":"RMYK5F44MK42WUUV","created_at":"2026-07-04T17:17:38Z"},{"alias_kind":"pith_short_8","alias_value":"RMYK5F44","created_at":"2026-07-04T17:17:38Z"}],"graph_snapshots":[{"event_id":"sha256:6d85e519b22e458451c1b77c113be4d751b922d448666484e66f13cff2c1b751","target":"graph","created_at":"2026-07-04T17:17:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0912.2160/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the Matrix approach to graph transformation we represent simple digraphs and rules with Boolean matrices and vectors, and the rewriting is expressed using Boolean operations only. In previous works, we developed analysis techniques enabling the study of the applicability of rule sequences, their independence, stated reachability and the minimal digraph able to fire a sequence. In [20], graph constraints and application conditions (so-called restrictions) have been studied in detail. In the present contribution we tackle the problem of translating post-conditions into pre-conditions and vice","authors_text":"Pedro Pablo Perez Velasco","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.DM","submitted_at":"2009-12-11T06:43:57Z","title":"Matrix Graph Grammars: Transformation of Restrictions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2160","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:a1eb82c13e4b0cace31815b3abdc6f4a6b8d99529f1671acc3623cc6c655a7e4","target":"record","created_at":"2026-07-04T17:17:38Z","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":"86a5f3a8e933fe7e7ad9358bc65f627c6fcae4a9ed33c0eb6dec2ca1fc2c3574","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.DM","submitted_at":"2009-12-11T06:43:57Z","title_canon_sha256":"b3c20e8c933d45a8d5d921f0d6ab2c7199911a8a19933698fa6121533c3047d3"},"schema_version":"1.0","source":{"id":"0912.2160","kind":"arxiv","version":1}},"canonical_sha256":"8b30ae979c62b9ab5295d63a6fddc3fed15ae8f7b0dbbe99ea76b65497210ceb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b30ae979c62b9ab5295d63a6fddc3fed15ae8f7b0dbbe99ea76b65497210ceb","first_computed_at":"2026-07-04T17:17:38.361906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:17:38.361906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y7Wvdc8tdKlUrL5nWayU43myejSqQ6DWlCb/oJwYRl0DI9L3z5EXKmtzF9HsFXWiIvbtYD39quo3ie0ool0RDA==","signature_status":"signed_v1","signed_at":"2026-07-04T17:17:38.362348Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.2160","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1eb82c13e4b0cace31815b3abdc6f4a6b8d99529f1671acc3623cc6c655a7e4","sha256:6d85e519b22e458451c1b77c113be4d751b922d448666484e66f13cff2c1b751"],"state_sha256":"106c101b50f20b9abd066c3913ba7ced71cb2f9414e84d483cb6b00eaa5b00ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZlrB4kS3j7D5t0DPgJYkxYi+cRmqbE4PvTcRrZncjHPe6GcFDyqBtyyqcYYvWb1G+qAJu4K2Y8+HLwtUMuBsCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T00:47:33.781501Z","bundle_sha256":"4c785da370418404b690d3106f0db1863a78d20f20283dda4a6c49689a907926"}}