{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:XQ7V7VJJP5WBIM2CQF6CDW6ATN","short_pith_number":"pith:XQ7V7VJJ","canonical_record":{"source":{"id":"2607.16045","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2026-07-17T15:16:58Z","cross_cats_sorted":[],"title_canon_sha256":"a1c7d8d2bebe81f64eb5f90df132f7b016ea05a339883c829a9f8a8838eb4be5","abstract_canon_sha256":"2abf67f0a40c5da74d9373c2edb651139bdff33bb8862964f89d1bd8560a8e85"},"schema_version":"1.0"},"canonical_sha256":"bc3f5fd5297f6c143342817c21dbc09b7e7cb7a2c7558255cd88df8eb5f799bb","source":{"kind":"arxiv","id":"2607.16045","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16045","created_at":"2026-07-20T02:19:27Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16045v1","created_at":"2026-07-20T02:19:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16045","created_at":"2026-07-20T02:19:27Z"},{"alias_kind":"pith_short_12","alias_value":"XQ7V7VJJP5WB","created_at":"2026-07-20T02:19:27Z"},{"alias_kind":"pith_short_16","alias_value":"XQ7V7VJJP5WBIM2C","created_at":"2026-07-20T02:19:27Z"},{"alias_kind":"pith_short_8","alias_value":"XQ7V7VJJ","created_at":"2026-07-20T02:19:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:XQ7V7VJJP5WBIM2CQF6CDW6ATN","target":"record","payload":{"canonical_record":{"source":{"id":"2607.16045","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2026-07-17T15:16:58Z","cross_cats_sorted":[],"title_canon_sha256":"a1c7d8d2bebe81f64eb5f90df132f7b016ea05a339883c829a9f8a8838eb4be5","abstract_canon_sha256":"2abf67f0a40c5da74d9373c2edb651139bdff33bb8862964f89d1bd8560a8e85"},"schema_version":"1.0"},"canonical_sha256":"bc3f5fd5297f6c143342817c21dbc09b7e7cb7a2c7558255cd88df8eb5f799bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-20T02:19:27.961660Z","signature_b64":"ibYj9Kzd9r28Dgj7ZA/qtCPDOLIv9J1WKkuRERvhFmNS+s0FPwB8ANRpfHLfe8MDSG75eqrcSIkDhtAHfq+fCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc3f5fd5297f6c143342817c21dbc09b7e7cb7a2c7558255cd88df8eb5f799bb","last_reissued_at":"2026-07-20T02:19:27.960755Z","signature_status":"signed_v1","first_computed_at":"2026-07-20T02:19:27.960755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.16045","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":"2026-07-20T02:19:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JxDJ+OQUw4Afa+eQBsE8l4AXS/KBp+rHh88K4EjH14u9du1f9mBWC+HlztMlwKrdC8I8HFZOTkQMDard5zILAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T06:18:25.137989Z"},"content_sha256":"4cb3838b331e42501876fcbcdacba5c6f090419539f8f36bb848dd17d5113ea1","schema_version":"1.0","event_id":"sha256:4cb3838b331e42501876fcbcdacba5c6f090419539f8f36bb848dd17d5113ea1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:XQ7V7VJJP5WBIM2CQF6CDW6ATN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Set-theoretic solutions of the Yang-Baxter equation from inverse braces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Francesco Catino, Marzia Mazzotta, Susanna Tieni","submitted_at":"2026-07-17T15:16:58Z","abstract_excerpt":"We introduce the algebraic structure of an inverse brace, namely, a triple $(S,+,\\circ)$ such that both $(S,+)$ and $(S,\\circ)$ are inverse semigroups and the following identity holds $a\\circ(b+c)=a\\circ b-a+a\\circ c$, for all $ a, b, c \\in S$, where $-a$ denotes the inverse of $a \\in S$, with respect to $+$. In particular, every weak brace is an inverse brace. We investigate the fundamental properties of inverse braces and analyze the relationship between additive and multiplicative idempotents, characterizing the condition under which an inverse brace is a weak brace. Our main results concer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16045","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/2607.16045/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":"2026-07-20T02:19:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J9WTIcYTu5e4vtLM8JRojffwatG5T10/LJs91FZSRHi6O/h4wuwmbEKIbYmSlm5xpx3JES2A7U5j3eMIRSMoCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T06:18:25.138397Z"},"content_sha256":"81d2c36802a5fb620e2057c4ae41c1295f20dbbf6c3c3ab7bec854d7190da6df","schema_version":"1.0","event_id":"sha256:81d2c36802a5fb620e2057c4ae41c1295f20dbbf6c3c3ab7bec854d7190da6df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XQ7V7VJJP5WBIM2CQF6CDW6ATN/bundle.json","state_url":"https://pith.science/pith/XQ7V7VJJP5WBIM2CQF6CDW6ATN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XQ7V7VJJP5WBIM2CQF6CDW6ATN/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":"2026-08-13T06:18:25Z","links":{"resolver":"https://pith.science/pith/XQ7V7VJJP5WBIM2CQF6CDW6ATN","bundle":"https://pith.science/pith/XQ7V7VJJP5WBIM2CQF6CDW6ATN/bundle.json","state":"https://pith.science/pith/XQ7V7VJJP5WBIM2CQF6CDW6ATN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XQ7V7VJJP5WBIM2CQF6CDW6ATN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XQ7V7VJJP5WBIM2CQF6CDW6ATN","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":"2abf67f0a40c5da74d9373c2edb651139bdff33bb8862964f89d1bd8560a8e85","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2026-07-17T15:16:58Z","title_canon_sha256":"a1c7d8d2bebe81f64eb5f90df132f7b016ea05a339883c829a9f8a8838eb4be5"},"schema_version":"1.0","source":{"id":"2607.16045","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16045","created_at":"2026-07-20T02:19:27Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16045v1","created_at":"2026-07-20T02:19:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16045","created_at":"2026-07-20T02:19:27Z"},{"alias_kind":"pith_short_12","alias_value":"XQ7V7VJJP5WB","created_at":"2026-07-20T02:19:27Z"},{"alias_kind":"pith_short_16","alias_value":"XQ7V7VJJP5WBIM2C","created_at":"2026-07-20T02:19:27Z"},{"alias_kind":"pith_short_8","alias_value":"XQ7V7VJJ","created_at":"2026-07-20T02:19:27Z"}],"graph_snapshots":[{"event_id":"sha256:81d2c36802a5fb620e2057c4ae41c1295f20dbbf6c3c3ab7bec854d7190da6df","target":"graph","created_at":"2026-07-20T02:19:27Z","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/2607.16045/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the algebraic structure of an inverse brace, namely, a triple $(S,+,\\circ)$ such that both $(S,+)$ and $(S,\\circ)$ are inverse semigroups and the following identity holds $a\\circ(b+c)=a\\circ b-a+a\\circ c$, for all $ a, b, c \\in S$, where $-a$ denotes the inverse of $a \\in S$, with respect to $+$. In particular, every weak brace is an inverse brace. We investigate the fundamental properties of inverse braces and analyze the relationship between additive and multiplicative idempotents, characterizing the condition under which an inverse brace is a weak brace. Our main results concer","authors_text":"Francesco Catino, Marzia Mazzotta, Susanna Tieni","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2026-07-17T15:16:58Z","title":"Set-theoretic solutions of the Yang-Baxter equation from inverse braces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16045","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":"sha256:4cb3838b331e42501876fcbcdacba5c6f090419539f8f36bb848dd17d5113ea1","target":"record","created_at":"2026-07-20T02:19:27Z","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":"2abf67f0a40c5da74d9373c2edb651139bdff33bb8862964f89d1bd8560a8e85","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2026-07-17T15:16:58Z","title_canon_sha256":"a1c7d8d2bebe81f64eb5f90df132f7b016ea05a339883c829a9f8a8838eb4be5"},"schema_version":"1.0","source":{"id":"2607.16045","kind":"arxiv","version":1}},"canonical_sha256":"bc3f5fd5297f6c143342817c21dbc09b7e7cb7a2c7558255cd88df8eb5f799bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc3f5fd5297f6c143342817c21dbc09b7e7cb7a2c7558255cd88df8eb5f799bb","first_computed_at":"2026-07-20T02:19:27.960755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-20T02:19:27.960755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ibYj9Kzd9r28Dgj7ZA/qtCPDOLIv9J1WKkuRERvhFmNS+s0FPwB8ANRpfHLfe8MDSG75eqrcSIkDhtAHfq+fCQ==","signature_status":"signed_v1","signed_at":"2026-07-20T02:19:27.961660Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.16045","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cb3838b331e42501876fcbcdacba5c6f090419539f8f36bb848dd17d5113ea1","sha256:81d2c36802a5fb620e2057c4ae41c1295f20dbbf6c3c3ab7bec854d7190da6df"],"state_sha256":"531f07c2f631905f5cce7e954435e99c779437a379007f90b7457a4be3a32555"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZmPRLycTsEnQwTUBIGgH4xYmBLvu9MK55aYDreNFPCwhnhz+3Uj/zWcbZDEOEuvTzPZiQQ128bQgVcyJtg3dAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T06:18:25.141195Z","bundle_sha256":"27af695dd40dd68f91cf5beaa12adf211c951ba1bb2364473d34a0bd7373636e"}}