{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:G4LC2C6U54OFED4BICFYKSRYQX","short_pith_number":"pith:G4LC2C6U","canonical_record":{"source":{"id":"2506.04191","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RA","submitted_at":"2025-06-04T17:38:18Z","cross_cats_sorted":[],"title_canon_sha256":"558b0b3eddfe26c02530b2dfbee1e20a1fcb5e0d311e341b6723c00469c90ed2","abstract_canon_sha256":"693d482d7dc60c9571df898e0f25d3fcd504448cf751110c6391950f08653a98"},"schema_version":"1.0"},"canonical_sha256":"37162d0bd4ef1c520f81408b854a3885dbea8c3ece032387faa77e969819856e","source":{"kind":"arxiv","id":"2506.04191","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.04191","created_at":"2026-07-05T11:15:58Z"},{"alias_kind":"arxiv_version","alias_value":"2506.04191v1","created_at":"2026-07-05T11:15:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.04191","created_at":"2026-07-05T11:15:58Z"},{"alias_kind":"pith_short_12","alias_value":"G4LC2C6U54OF","created_at":"2026-07-05T11:15:58Z"},{"alias_kind":"pith_short_16","alias_value":"G4LC2C6U54OFED4B","created_at":"2026-07-05T11:15:58Z"},{"alias_kind":"pith_short_8","alias_value":"G4LC2C6U","created_at":"2026-07-05T11:15:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:G4LC2C6U54OFED4BICFYKSRYQX","target":"record","payload":{"canonical_record":{"source":{"id":"2506.04191","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RA","submitted_at":"2025-06-04T17:38:18Z","cross_cats_sorted":[],"title_canon_sha256":"558b0b3eddfe26c02530b2dfbee1e20a1fcb5e0d311e341b6723c00469c90ed2","abstract_canon_sha256":"693d482d7dc60c9571df898e0f25d3fcd504448cf751110c6391950f08653a98"},"schema_version":"1.0"},"canonical_sha256":"37162d0bd4ef1c520f81408b854a3885dbea8c3ece032387faa77e969819856e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:15:58.699969Z","signature_b64":"X7Vh99oh6cmL3Ir/kZkRGGf/+nRONn7bxg84URRwhIFopnJNWzM/WBVXDVyQN5Lix29Jm0W1cTtGvk6vPg73DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37162d0bd4ef1c520f81408b854a3885dbea8c3ece032387faa77e969819856e","last_reissued_at":"2026-07-05T11:15:58.699489Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:15:58.699489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.04191","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":"2026-07-05T11:15:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JUdhWYw6B+TGui1IC3mLQdZbUuxDDRducjUOyJ1KcGeRAd1EqN3Q5BYGGY8BgslLRveISghnjcEe1qh4bIDfDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T13:40:31.213882Z"},"content_sha256":"f50f6f8107bfe35d60bedc7c943bafc48b392416db5a3bb1d4b7bb57e8e2b8ed","schema_version":"1.0","event_id":"sha256:f50f6f8107bfe35d60bedc7c943bafc48b392416db5a3bb1d4b7bb57e8e2b8ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:G4LC2C6U54OFED4BICFYKSRYQX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Associative triple trisystems and standard embeddings","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Guillermo Vera de Salas, Ra\\'ul Felipe","submitted_at":"2025-06-04T17:38:18Z","abstract_excerpt":"Building on the established theories of Jordan triple disystems and Leibniz triple systems, we introduce and develop the theory of associative triple trisystems, filling a significant gap in the existing framework. We establish the classical relationships between associative, Jordan, and Lie triple systems within the context of trisystems. We present a significant example by equipping the space of matrices with a non-trivial associative dialgebra structure. We conclude defining the concept of di-endomorphisms of any module, which enables the construction of the standard embedding for any assoc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04191","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/2506.04191/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":"2026-07-05T11:15:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F/CXKxQwoo5vJ/QDZXD8KQGjofiLtR6Z78fzrZcvUSDXW03kiSs7ezme6A1n07ufoQ33bbyKntEwDxZt2/gIDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T13:40:31.214880Z"},"content_sha256":"21c9fc8aadba419055274e441a5d3ae389c5cf56e97210402f1345c83565e835","schema_version":"1.0","event_id":"sha256:21c9fc8aadba419055274e441a5d3ae389c5cf56e97210402f1345c83565e835"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G4LC2C6U54OFED4BICFYKSRYQX/bundle.json","state_url":"https://pith.science/pith/G4LC2C6U54OFED4BICFYKSRYQX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G4LC2C6U54OFED4BICFYKSRYQX/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":"2026-08-08T13:40:31Z","links":{"resolver":"https://pith.science/pith/G4LC2C6U54OFED4BICFYKSRYQX","bundle":"https://pith.science/pith/G4LC2C6U54OFED4BICFYKSRYQX/bundle.json","state":"https://pith.science/pith/G4LC2C6U54OFED4BICFYKSRYQX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G4LC2C6U54OFED4BICFYKSRYQX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:G4LC2C6U54OFED4BICFYKSRYQX","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":"693d482d7dc60c9571df898e0f25d3fcd504448cf751110c6391950f08653a98","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RA","submitted_at":"2025-06-04T17:38:18Z","title_canon_sha256":"558b0b3eddfe26c02530b2dfbee1e20a1fcb5e0d311e341b6723c00469c90ed2"},"schema_version":"1.0","source":{"id":"2506.04191","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.04191","created_at":"2026-07-05T11:15:58Z"},{"alias_kind":"arxiv_version","alias_value":"2506.04191v1","created_at":"2026-07-05T11:15:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.04191","created_at":"2026-07-05T11:15:58Z"},{"alias_kind":"pith_short_12","alias_value":"G4LC2C6U54OF","created_at":"2026-07-05T11:15:58Z"},{"alias_kind":"pith_short_16","alias_value":"G4LC2C6U54OFED4B","created_at":"2026-07-05T11:15:58Z"},{"alias_kind":"pith_short_8","alias_value":"G4LC2C6U","created_at":"2026-07-05T11:15:58Z"}],"graph_snapshots":[{"event_id":"sha256:21c9fc8aadba419055274e441a5d3ae389c5cf56e97210402f1345c83565e835","target":"graph","created_at":"2026-07-05T11:15:58Z","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/2506.04191/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Building on the established theories of Jordan triple disystems and Leibniz triple systems, we introduce and develop the theory of associative triple trisystems, filling a significant gap in the existing framework. We establish the classical relationships between associative, Jordan, and Lie triple systems within the context of trisystems. We present a significant example by equipping the space of matrices with a non-trivial associative dialgebra structure. We conclude defining the concept of di-endomorphisms of any module, which enables the construction of the standard embedding for any assoc","authors_text":"Guillermo Vera de Salas, Ra\\'ul Felipe","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RA","submitted_at":"2025-06-04T17:38:18Z","title":"Associative triple trisystems and standard embeddings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04191","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:f50f6f8107bfe35d60bedc7c943bafc48b392416db5a3bb1d4b7bb57e8e2b8ed","target":"record","created_at":"2026-07-05T11:15:58Z","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":"693d482d7dc60c9571df898e0f25d3fcd504448cf751110c6391950f08653a98","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RA","submitted_at":"2025-06-04T17:38:18Z","title_canon_sha256":"558b0b3eddfe26c02530b2dfbee1e20a1fcb5e0d311e341b6723c00469c90ed2"},"schema_version":"1.0","source":{"id":"2506.04191","kind":"arxiv","version":1}},"canonical_sha256":"37162d0bd4ef1c520f81408b854a3885dbea8c3ece032387faa77e969819856e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37162d0bd4ef1c520f81408b854a3885dbea8c3ece032387faa77e969819856e","first_computed_at":"2026-07-05T11:15:58.699489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:15:58.699489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X7Vh99oh6cmL3Ir/kZkRGGf/+nRONn7bxg84URRwhIFopnJNWzM/WBVXDVyQN5Lix29Jm0W1cTtGvk6vPg73DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:15:58.699969Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.04191","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f50f6f8107bfe35d60bedc7c943bafc48b392416db5a3bb1d4b7bb57e8e2b8ed","sha256:21c9fc8aadba419055274e441a5d3ae389c5cf56e97210402f1345c83565e835"],"state_sha256":"c7e4bb87ff9bd4bb727a735d0a78e09b25278ae7f05c8dc6b3328b29af4a6a72"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KfFn+dw1N363r67luD1hIGq7WRhW7R6ZrQn/taYJWJ599eXNTWSKHfsCw8QKK4vD8Rz/zn0mSswQVo5PgGL8BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T13:40:31.223386Z","bundle_sha256":"13aad31a6e6d1a18c735b2619f57296b93e64c1e4d99abe387083fc08431e8c6"}}