{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:MYKT4FIDMXKEZERIYVLNQQVEWH","short_pith_number":"pith:MYKT4FID","canonical_record":{"source":{"id":"2505.22755","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2025-05-28T18:15:25Z","cross_cats_sorted":["math.LO","math.RA"],"title_canon_sha256":"1117f961f8ca0dd4bf82b19425747617c3309bf2590aef48ae6ca8dd63550edb","abstract_canon_sha256":"2183b3c04183cf63b90e97f1d744b3753f5efe9b22337972cb3acc8f3c195a05"},"schema_version":"1.0"},"canonical_sha256":"66153e150365d44c9228c556d842a4b1ddcfe5b845d881be4b00940ce1eb97ba","source":{"kind":"arxiv","id":"2505.22755","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.22755","created_at":"2026-07-05T11:11:49Z"},{"alias_kind":"arxiv_version","alias_value":"2505.22755v1","created_at":"2026-07-05T11:11:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.22755","created_at":"2026-07-05T11:11:49Z"},{"alias_kind":"pith_short_12","alias_value":"MYKT4FIDMXKE","created_at":"2026-07-05T11:11:49Z"},{"alias_kind":"pith_short_16","alias_value":"MYKT4FIDMXKEZERI","created_at":"2026-07-05T11:11:49Z"},{"alias_kind":"pith_short_8","alias_value":"MYKT4FID","created_at":"2026-07-05T11:11:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:MYKT4FIDMXKEZERIYVLNQQVEWH","target":"record","payload":{"canonical_record":{"source":{"id":"2505.22755","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2025-05-28T18:15:25Z","cross_cats_sorted":["math.LO","math.RA"],"title_canon_sha256":"1117f961f8ca0dd4bf82b19425747617c3309bf2590aef48ae6ca8dd63550edb","abstract_canon_sha256":"2183b3c04183cf63b90e97f1d744b3753f5efe9b22337972cb3acc8f3c195a05"},"schema_version":"1.0"},"canonical_sha256":"66153e150365d44c9228c556d842a4b1ddcfe5b845d881be4b00940ce1eb97ba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:11:49.599846Z","signature_b64":"imHKiyq+jhPBRcvNezKqtKEeeVQJIN5uo65iYteIF4oaUYLzkp7J1vIh9JZSadPadhKDfaRzM8nBTbGTBQwYAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66153e150365d44c9228c556d842a4b1ddcfe5b845d881be4b00940ce1eb97ba","last_reissued_at":"2026-07-05T11:11:49.599311Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:11:49.599311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.22755","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":"2026-07-05T11:11:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cWV/kD+Pp/8maM4Y89f7gA/irvtIhXYhbQHdev54paY9FZb8gBEGMzR4yKCcZGWgnl4JhxPtwNUX5pAVsopxCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T23:53:44.503406Z"},"content_sha256":"4f11b1ce872fe7ffab4659d6cf79ebc48cb4cf78e095fce3537ead02808d83ab","schema_version":"1.0","event_id":"sha256:4f11b1ce872fe7ffab4659d6cf79ebc48cb4cf78e095fce3537ead02808d83ab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:MYKT4FIDMXKEZERIYVLNQQVEWH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A canonical Makanin-Razborov diagram and a pseudo topology for sets of tuples in free groups, semigroups, associative algebras and Lie algebras I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO","math.RA"],"primary_cat":"math.GR","authors_text":"Z. Sela","submitted_at":"2025-05-28T18:15:25Z","abstract_excerpt":"The JSJ decomposition and the Makanin-Razborov diagram were proved to be essential in studying varieties over free groups, semigroups and associative algebras. In this paper we suggest a unified conceptual approach to the applicability of these structures over all these algebraic categories. With a variety over each of these algebraic categories we naturally associate a set of tuples in a free group. Then we show how to associate a Makanin-Razborov diagram with any set of tuples over a free group. Furthermore, in case the MR diagram that is associated with a set of tuples is single ended, we p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22755","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/2505.22755/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":"2026-07-05T11:11:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WGfr9LejO7khtMVuAqklyc2C8b3A5pg2W+NDMz6Dv2jwJjhHBlkQryyb14eXWPKhGYO9rIeFMNiIf+o/SOM7Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T23:53:44.504416Z"},"content_sha256":"71cca3a3961939cffc0372cb77572699c358b17f84cda2ff8934a1e888f236cb","schema_version":"1.0","event_id":"sha256:71cca3a3961939cffc0372cb77572699c358b17f84cda2ff8934a1e888f236cb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MYKT4FIDMXKEZERIYVLNQQVEWH/bundle.json","state_url":"https://pith.science/pith/MYKT4FIDMXKEZERIYVLNQQVEWH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MYKT4FIDMXKEZERIYVLNQQVEWH/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":"2026-08-07T23:53:44Z","links":{"resolver":"https://pith.science/pith/MYKT4FIDMXKEZERIYVLNQQVEWH","bundle":"https://pith.science/pith/MYKT4FIDMXKEZERIYVLNQQVEWH/bundle.json","state":"https://pith.science/pith/MYKT4FIDMXKEZERIYVLNQQVEWH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MYKT4FIDMXKEZERIYVLNQQVEWH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:MYKT4FIDMXKEZERIYVLNQQVEWH","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":"2183b3c04183cf63b90e97f1d744b3753f5efe9b22337972cb3acc8f3c195a05","cross_cats_sorted":["math.LO","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2025-05-28T18:15:25Z","title_canon_sha256":"1117f961f8ca0dd4bf82b19425747617c3309bf2590aef48ae6ca8dd63550edb"},"schema_version":"1.0","source":{"id":"2505.22755","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.22755","created_at":"2026-07-05T11:11:49Z"},{"alias_kind":"arxiv_version","alias_value":"2505.22755v1","created_at":"2026-07-05T11:11:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.22755","created_at":"2026-07-05T11:11:49Z"},{"alias_kind":"pith_short_12","alias_value":"MYKT4FIDMXKE","created_at":"2026-07-05T11:11:49Z"},{"alias_kind":"pith_short_16","alias_value":"MYKT4FIDMXKEZERI","created_at":"2026-07-05T11:11:49Z"},{"alias_kind":"pith_short_8","alias_value":"MYKT4FID","created_at":"2026-07-05T11:11:49Z"}],"graph_snapshots":[{"event_id":"sha256:71cca3a3961939cffc0372cb77572699c358b17f84cda2ff8934a1e888f236cb","target":"graph","created_at":"2026-07-05T11:11:49Z","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/2505.22755/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The JSJ decomposition and the Makanin-Razborov diagram were proved to be essential in studying varieties over free groups, semigroups and associative algebras. In this paper we suggest a unified conceptual approach to the applicability of these structures over all these algebraic categories. With a variety over each of these algebraic categories we naturally associate a set of tuples in a free group. Then we show how to associate a Makanin-Razborov diagram with any set of tuples over a free group. Furthermore, in case the MR diagram that is associated with a set of tuples is single ended, we p","authors_text":"Z. Sela","cross_cats":["math.LO","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2025-05-28T18:15:25Z","title":"A canonical Makanin-Razborov diagram and a pseudo topology for sets of tuples in free groups, semigroups, associative algebras and Lie algebras I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22755","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":"sha256:4f11b1ce872fe7ffab4659d6cf79ebc48cb4cf78e095fce3537ead02808d83ab","target":"record","created_at":"2026-07-05T11:11:49Z","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":"2183b3c04183cf63b90e97f1d744b3753f5efe9b22337972cb3acc8f3c195a05","cross_cats_sorted":["math.LO","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2025-05-28T18:15:25Z","title_canon_sha256":"1117f961f8ca0dd4bf82b19425747617c3309bf2590aef48ae6ca8dd63550edb"},"schema_version":"1.0","source":{"id":"2505.22755","kind":"arxiv","version":1}},"canonical_sha256":"66153e150365d44c9228c556d842a4b1ddcfe5b845d881be4b00940ce1eb97ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66153e150365d44c9228c556d842a4b1ddcfe5b845d881be4b00940ce1eb97ba","first_computed_at":"2026-07-05T11:11:49.599311Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:49.599311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"imHKiyq+jhPBRcvNezKqtKEeeVQJIN5uo65iYteIF4oaUYLzkp7J1vIh9JZSadPadhKDfaRzM8nBTbGTBQwYAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:49.599846Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.22755","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f11b1ce872fe7ffab4659d6cf79ebc48cb4cf78e095fce3537ead02808d83ab","sha256:71cca3a3961939cffc0372cb77572699c358b17f84cda2ff8934a1e888f236cb"],"state_sha256":"ba3dafc18aa484e038636341152cab13e1de8238915a4e0589aca16d84e43ce8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f/TKQA/ldz4eTNGo4X5ZHR3e+k4bsD9Khwn9zuPyLvVZ+6nuDoK5nB9u+VXCNAxKCiwaoepiXQ6h/zd0EJxcBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T23:53:44.512013Z","bundle_sha256":"cee16b7844660755c0fd13092b1276a7cc703328983b28dae8d18709ccb5b16e"}}