{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:KI326CCJ53X54UVEMGV6D3Z2DP","short_pith_number":"pith:KI326CCJ","schema_version":"1.0","canonical_sha256":"5237af0849eeefde52a461abe1ef3a1be0788873250cbc2ff7b0f7152198b0de","source":{"kind":"arxiv","id":"2109.13501","version":1},"attestation_state":"computed","paper":{"title":"On The Faithfulness of the extension of Lawrence-Krammer representation of the group of conjugating automorphisms C_3","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Mohamad N. Nasser, Mohammad N. Abdulrahim","submitted_at":"2021-09-28T05:44:48Z","abstract_excerpt":"Let $C_n$ be the group of conjugating automorphisms. We study the representation $\\rho$ of $C_n$, an extension of Lawrence-Krammer representation of the braid group $B_n$, defined by Valerij G. Bardakov. As Bardakov proved that the representation $\\rho$ is unfaithful for $n \\geq 5$, the cases $n=3,4$ remain open. In our work, we make attempts towards the faithfulness of $\\rho$ in the case $n=3$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2109.13501","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RT","submitted_at":"2021-09-28T05:44:48Z","cross_cats_sorted":[],"title_canon_sha256":"1c8c3146c50893298519144cd668e09b46ffbb5f0980e88aeb1946f2ec2a0404","abstract_canon_sha256":"82b3cf357836aea3eee5e994493320dc55911719485bcea1cbd8d72f2240a707"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:18:03.438382Z","signature_b64":"hAKFOzsflanefp832C9qJ53prlSMlRI7xfN9NwAzg8LZ1RoA61Cr4vWz6OmvAv3+Lkrzc0xXqUquAeO4B0imBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5237af0849eeefde52a461abe1ef3a1be0788873250cbc2ff7b0f7152198b0de","last_reissued_at":"2026-07-05T03:18:03.437909Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:18:03.437909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On The Faithfulness of the extension of Lawrence-Krammer representation of the group of conjugating automorphisms C_3","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Mohamad N. Nasser, Mohammad N. Abdulrahim","submitted_at":"2021-09-28T05:44:48Z","abstract_excerpt":"Let $C_n$ be the group of conjugating automorphisms. We study the representation $\\rho$ of $C_n$, an extension of Lawrence-Krammer representation of the braid group $B_n$, defined by Valerij G. Bardakov. As Bardakov proved that the representation $\\rho$ is unfaithful for $n \\geq 5$, the cases $n=3,4$ remain open. In our work, we make attempts towards the faithfulness of $\\rho$ in the case $n=3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.13501","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/2109.13501/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2109.13501","created_at":"2026-07-05T03:18:03.437966+00:00"},{"alias_kind":"arxiv_version","alias_value":"2109.13501v1","created_at":"2026-07-05T03:18:03.437966+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.13501","created_at":"2026-07-05T03:18:03.437966+00:00"},{"alias_kind":"pith_short_12","alias_value":"KI326CCJ53X5","created_at":"2026-07-05T03:18:03.437966+00:00"},{"alias_kind":"pith_short_16","alias_value":"KI326CCJ53X54UVE","created_at":"2026-07-05T03:18:03.437966+00:00"},{"alias_kind":"pith_short_8","alias_value":"KI326CCJ","created_at":"2026-07-05T03:18:03.437966+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KI326CCJ53X54UVEMGV6D3Z2DP","json":"https://pith.science/pith/KI326CCJ53X54UVEMGV6D3Z2DP.json","graph_json":"https://pith.science/api/pith-number/KI326CCJ53X54UVEMGV6D3Z2DP/graph.json","events_json":"https://pith.science/api/pith-number/KI326CCJ53X54UVEMGV6D3Z2DP/events.json","paper":"https://pith.science/paper/KI326CCJ"},"agent_actions":{"view_html":"https://pith.science/pith/KI326CCJ53X54UVEMGV6D3Z2DP","download_json":"https://pith.science/pith/KI326CCJ53X54UVEMGV6D3Z2DP.json","view_paper":"https://pith.science/paper/KI326CCJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2109.13501&json=true","fetch_graph":"https://pith.science/api/pith-number/KI326CCJ53X54UVEMGV6D3Z2DP/graph.json","fetch_events":"https://pith.science/api/pith-number/KI326CCJ53X54UVEMGV6D3Z2DP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KI326CCJ53X54UVEMGV6D3Z2DP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KI326CCJ53X54UVEMGV6D3Z2DP/action/storage_attestation","attest_author":"https://pith.science/pith/KI326CCJ53X54UVEMGV6D3Z2DP/action/author_attestation","sign_citation":"https://pith.science/pith/KI326CCJ53X54UVEMGV6D3Z2DP/action/citation_signature","submit_replication":"https://pith.science/pith/KI326CCJ53X54UVEMGV6D3Z2DP/action/replication_record"}},"created_at":"2026-07-05T03:18:03.437966+00:00","updated_at":"2026-07-05T03:18:03.437966+00:00"}