{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:JFR3FFNZGTWHREXUHEJURDJ43H","short_pith_number":"pith:JFR3FFNZ","canonical_record":{"source":{"id":"2601.07057","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2026-01-11T20:39:00Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"711d7ea659d345447732ce8341facba0bfd53ec36fdcf7fd489b6e29eb15e303","abstract_canon_sha256":"0c9cfd19a3f67a466361c7328eef682816e0fe3b0c350427ab400b71bfc08eba"},"schema_version":"1.0"},"canonical_sha256":"4963b295b934ec7892f43913488d3cd9ecd095b053ec3025e335ffb073218e42","source":{"kind":"arxiv","id":"2601.07057","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.07057","created_at":"2026-07-28T01:22:27Z"},{"alias_kind":"arxiv_version","alias_value":"2601.07057v3","created_at":"2026-07-28T01:22:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.07057","created_at":"2026-07-28T01:22:27Z"},{"alias_kind":"pith_short_12","alias_value":"JFR3FFNZGTWH","created_at":"2026-07-28T01:22:27Z"},{"alias_kind":"pith_short_16","alias_value":"JFR3FFNZGTWHREXU","created_at":"2026-07-28T01:22:27Z"},{"alias_kind":"pith_short_8","alias_value":"JFR3FFNZ","created_at":"2026-07-28T01:22:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:JFR3FFNZGTWHREXUHEJURDJ43H","target":"record","payload":{"canonical_record":{"source":{"id":"2601.07057","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2026-01-11T20:39:00Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"711d7ea659d345447732ce8341facba0bfd53ec36fdcf7fd489b6e29eb15e303","abstract_canon_sha256":"0c9cfd19a3f67a466361c7328eef682816e0fe3b0c350427ab400b71bfc08eba"},"schema_version":"1.0"},"canonical_sha256":"4963b295b934ec7892f43913488d3cd9ecd095b053ec3025e335ffb073218e42","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T01:22:27.439589Z","signature_b64":"8+ehcO1kHHzDdYWWTwzHsn4lIjQx1gx6bIBHPR9PCVTab1X7d29zVAiFm73B9/ZzvJ5X+nuq5weyb89rLD/VCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4963b295b934ec7892f43913488d3cd9ecd095b053ec3025e335ffb073218e42","last_reissued_at":"2026-07-28T01:22:27.438680Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T01:22:27.438680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2601.07057","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-28T01:22:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EFNvWF1PsFNpmPz9r5jRq0BxZoVQHHP08vbPQUld+PweO7eE/Dpi3X4LrXVZaIO9zpebuRrlJx2FH6TWWiRyAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T15:48:54.940755Z"},"content_sha256":"b316be82854f2a165cdd8a70acb9389cba7fab5de01f5c6cdd34f4f64bc0dc69","schema_version":"1.0","event_id":"sha256:b316be82854f2a165cdd8a70acb9389cba7fab5de01f5c6cdd34f4f64bc0dc69"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:JFR3FFNZGTWHREXUHEJURDJ43H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Idempotents and Powers of Ideals in Quandle Rings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RA","authors_text":"Mohamed Elhamdadi, Valeriy Bardakov","submitted_at":"2026-01-11T20:39:00Z","abstract_excerpt":"This article addresses two central problems in the theory of quandle rings. First, motivated by Conjecture 3.10 in Internat. J. Math. 34 (2023), no. 3, Paper No. 2350011: for a semi-latin quandle $X$, every nonzero idempotent in the integral quandle ring $\\mathbb{Z}[X]$ necessarily corresponds to an element of $X$, we investigate idempotents in quandle rings of semi-latin quandles. Precisely, we prove that if the ground ring is an integral domain with unity, then the quandle ring of Core($\\mathbb{Z}$) admits only trivial idempotents. Second, powers of augmentation ideals in quandle rings have "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.07057","kind":"arxiv","version":3},"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/2601.07057/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":"2026-07-28T01:22:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kHIaPCvR/dTr0C9NRu8aQJQVyThJGglfjcA5cvi/KeD50RD3WNBisk5PCNl/yIW/zQXeRbrnN+AmO0pDyk6BDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T15:48:54.941734Z"},"content_sha256":"bc9a0f3d79f4ad9f3513c73cc2b34955b2c647045a8d948d788701c3d8f5d512","schema_version":"1.0","event_id":"sha256:bc9a0f3d79f4ad9f3513c73cc2b34955b2c647045a8d948d788701c3d8f5d512"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JFR3FFNZGTWHREXUHEJURDJ43H/bundle.json","state_url":"https://pith.science/pith/JFR3FFNZGTWHREXUHEJURDJ43H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JFR3FFNZGTWHREXUHEJURDJ43H/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":"2026-08-18T15:48:54Z","links":{"resolver":"https://pith.science/pith/JFR3FFNZGTWHREXUHEJURDJ43H","bundle":"https://pith.science/pith/JFR3FFNZGTWHREXUHEJURDJ43H/bundle.json","state":"https://pith.science/pith/JFR3FFNZGTWHREXUHEJURDJ43H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JFR3FFNZGTWHREXUHEJURDJ43H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:JFR3FFNZGTWHREXUHEJURDJ43H","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":"0c9cfd19a3f67a466361c7328eef682816e0fe3b0c350427ab400b71bfc08eba","cross_cats_sorted":["math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2026-01-11T20:39:00Z","title_canon_sha256":"711d7ea659d345447732ce8341facba0bfd53ec36fdcf7fd489b6e29eb15e303"},"schema_version":"1.0","source":{"id":"2601.07057","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.07057","created_at":"2026-07-28T01:22:27Z"},{"alias_kind":"arxiv_version","alias_value":"2601.07057v3","created_at":"2026-07-28T01:22:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.07057","created_at":"2026-07-28T01:22:27Z"},{"alias_kind":"pith_short_12","alias_value":"JFR3FFNZGTWH","created_at":"2026-07-28T01:22:27Z"},{"alias_kind":"pith_short_16","alias_value":"JFR3FFNZGTWHREXU","created_at":"2026-07-28T01:22:27Z"},{"alias_kind":"pith_short_8","alias_value":"JFR3FFNZ","created_at":"2026-07-28T01:22:27Z"}],"graph_snapshots":[{"event_id":"sha256:bc9a0f3d79f4ad9f3513c73cc2b34955b2c647045a8d948d788701c3d8f5d512","target":"graph","created_at":"2026-07-28T01:22:27Z","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/2601.07057/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This article addresses two central problems in the theory of quandle rings. First, motivated by Conjecture 3.10 in Internat. J. Math. 34 (2023), no. 3, Paper No. 2350011: for a semi-latin quandle $X$, every nonzero idempotent in the integral quandle ring $\\mathbb{Z}[X]$ necessarily corresponds to an element of $X$, we investigate idempotents in quandle rings of semi-latin quandles. Precisely, we prove that if the ground ring is an integral domain with unity, then the quandle ring of Core($\\mathbb{Z}$) admits only trivial idempotents. Second, powers of augmentation ideals in quandle rings have ","authors_text":"Mohamed Elhamdadi, Valeriy Bardakov","cross_cats":["math.GR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2026-01-11T20:39:00Z","title":"Idempotents and Powers of Ideals in Quandle Rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.07057","kind":"arxiv","version":3},"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:b316be82854f2a165cdd8a70acb9389cba7fab5de01f5c6cdd34f4f64bc0dc69","target":"record","created_at":"2026-07-28T01:22:27Z","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":"0c9cfd19a3f67a466361c7328eef682816e0fe3b0c350427ab400b71bfc08eba","cross_cats_sorted":["math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2026-01-11T20:39:00Z","title_canon_sha256":"711d7ea659d345447732ce8341facba0bfd53ec36fdcf7fd489b6e29eb15e303"},"schema_version":"1.0","source":{"id":"2601.07057","kind":"arxiv","version":3}},"canonical_sha256":"4963b295b934ec7892f43913488d3cd9ecd095b053ec3025e335ffb073218e42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4963b295b934ec7892f43913488d3cd9ecd095b053ec3025e335ffb073218e42","first_computed_at":"2026-07-28T01:22:27.438680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-28T01:22:27.438680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8+ehcO1kHHzDdYWWTwzHsn4lIjQx1gx6bIBHPR9PCVTab1X7d29zVAiFm73B9/ZzvJ5X+nuq5weyb89rLD/VCA==","signature_status":"signed_v1","signed_at":"2026-07-28T01:22:27.439589Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.07057","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b316be82854f2a165cdd8a70acb9389cba7fab5de01f5c6cdd34f4f64bc0dc69","sha256:bc9a0f3d79f4ad9f3513c73cc2b34955b2c647045a8d948d788701c3d8f5d512"],"state_sha256":"756e4d51a0e5b0598036e74405cfe5dabe981234b741ca0dcfbe23a91bd90467"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KyGNgf0/1tWhjfi2qPpjcjB2B2CXOUCVvHbVNtpOEQ8/5Oce0TCBlwa+jAFOs1Zxj604rgqYf/IDspYvHeATAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T15:48:54.950850Z","bundle_sha256":"44b6556403fa07e6450a8655db98dd2579f3ceb0bb69b47b338d9b475f9738bf"}}