{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:32JBNNTZYZKKO7QFB5WA2JNNBI","short_pith_number":"pith:32JBNNTZ","schema_version":"1.0","canonical_sha256":"de9216b679c654a77e050f6c0d25ad0a2478e6955550b0ecb4ebb3f320d56ebd","source":{"kind":"arxiv","id":"1908.08231","version":1},"attestation_state":"computed","paper":{"title":"The Kauffman bracket skein module of the handlebody of genus 2 via braids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ioannis Diamantis","submitted_at":"2019-08-22T07:16:23Z","abstract_excerpt":"In this paper we present two new bases, $B^{\\prime}_{H_2}$ and $\\mathcal{B}_{H_2}$, for the Kauffman bracket skein module of the handlebody of genus 2 $H_2$, KBSM($H_2$). We start from the well-known Przytycki-basis of KBSM($H_2$), $B_{H_2}$, and using the technique of parting we present elements in $B_{H_2}$ in open braid form. We define an ordering relation on an augmented set $L$ consisting of monomials of all different \"loopings\" in $H_2$, that contains the sets $B_{H_2}$, $B^{\\prime}_{H_2}$ and $\\mathcal{B}_{H_2}$ as proper subsets. Using the Kauffman bracket skein relation we relate $B_{"},"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":"1908.08231","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-08-22T07:16:23Z","cross_cats_sorted":[],"title_canon_sha256":"661e13d90fc8ef5cdb22ea60c0f2fe4454acfe35ba3c5ff7ef42b8ea4d9595ce","abstract_canon_sha256":"6cc35fe217317cfad9f0adb84ae5e2b38a4c6ee5ccd391008d09a84b6c4aca9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:59:10.783619Z","signature_b64":"Jqy1A7Zf9EG9pSaB0XDpQ69LxPVN0O2tjE6nzigmPv4B0mgcE/etsFdLuCxLUhmp0JvX7ceBTXhRshir+9LSDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de9216b679c654a77e050f6c0d25ad0a2478e6955550b0ecb4ebb3f320d56ebd","last_reissued_at":"2026-07-04T23:59:10.783123Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:59:10.783123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Kauffman bracket skein module of the handlebody of genus 2 via braids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ioannis Diamantis","submitted_at":"2019-08-22T07:16:23Z","abstract_excerpt":"In this paper we present two new bases, $B^{\\prime}_{H_2}$ and $\\mathcal{B}_{H_2}$, for the Kauffman bracket skein module of the handlebody of genus 2 $H_2$, KBSM($H_2$). We start from the well-known Przytycki-basis of KBSM($H_2$), $B_{H_2}$, and using the technique of parting we present elements in $B_{H_2}$ in open braid form. We define an ordering relation on an augmented set $L$ consisting of monomials of all different \"loopings\" in $H_2$, that contains the sets $B_{H_2}$, $B^{\\prime}_{H_2}$ and $\\mathcal{B}_{H_2}$ as proper subsets. Using the Kauffman bracket skein relation we relate $B_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08231","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/1908.08231/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":"1908.08231","created_at":"2026-07-04T23:59:10.783181+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.08231v1","created_at":"2026-07-04T23:59:10.783181+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08231","created_at":"2026-07-04T23:59:10.783181+00:00"},{"alias_kind":"pith_short_12","alias_value":"32JBNNTZYZKK","created_at":"2026-07-04T23:59:10.783181+00:00"},{"alias_kind":"pith_short_16","alias_value":"32JBNNTZYZKKO7QF","created_at":"2026-07-04T23:59:10.783181+00:00"},{"alias_kind":"pith_short_8","alias_value":"32JBNNTZ","created_at":"2026-07-04T23:59:10.783181+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/32JBNNTZYZKKO7QFB5WA2JNNBI","json":"https://pith.science/pith/32JBNNTZYZKKO7QFB5WA2JNNBI.json","graph_json":"https://pith.science/api/pith-number/32JBNNTZYZKKO7QFB5WA2JNNBI/graph.json","events_json":"https://pith.science/api/pith-number/32JBNNTZYZKKO7QFB5WA2JNNBI/events.json","paper":"https://pith.science/paper/32JBNNTZ"},"agent_actions":{"view_html":"https://pith.science/pith/32JBNNTZYZKKO7QFB5WA2JNNBI","download_json":"https://pith.science/pith/32JBNNTZYZKKO7QFB5WA2JNNBI.json","view_paper":"https://pith.science/paper/32JBNNTZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.08231&json=true","fetch_graph":"https://pith.science/api/pith-number/32JBNNTZYZKKO7QFB5WA2JNNBI/graph.json","fetch_events":"https://pith.science/api/pith-number/32JBNNTZYZKKO7QFB5WA2JNNBI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/32JBNNTZYZKKO7QFB5WA2JNNBI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/32JBNNTZYZKKO7QFB5WA2JNNBI/action/storage_attestation","attest_author":"https://pith.science/pith/32JBNNTZYZKKO7QFB5WA2JNNBI/action/author_attestation","sign_citation":"https://pith.science/pith/32JBNNTZYZKKO7QFB5WA2JNNBI/action/citation_signature","submit_replication":"https://pith.science/pith/32JBNNTZYZKKO7QFB5WA2JNNBI/action/replication_record"}},"created_at":"2026-07-04T23:59:10.783181+00:00","updated_at":"2026-07-04T23:59:10.783181+00:00"}