{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:C4S4ON7RR3TOHLB7ASXV4DE6NO","short_pith_number":"pith:C4S4ON7R","canonical_record":{"source":{"id":"1609.04077","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-09-14T00:24:30Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"2c43a5a1e4a6e23b547f082703e9e466a9656ce0393a5d2a541206d4ac4a8d61","abstract_canon_sha256":"2e3a879089d499882d0cadd6dd8d041ae9c797e0922a613f0cf26ad96087e1ea"},"schema_version":"1.0"},"canonical_sha256":"1725c737f18ee6e3ac3f04af5e0c9e6b9badf3371e0c21f1b682b7c915fc80dd","source":{"kind":"arxiv","id":"1609.04077","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04077","created_at":"2026-05-18T01:03:40Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04077v2","created_at":"2026-05-18T01:03:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04077","created_at":"2026-05-18T01:03:40Z"},{"alias_kind":"pith_short_12","alias_value":"C4S4ON7RR3TO","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C4S4ON7RR3TOHLB7","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C4S4ON7R","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:C4S4ON7RR3TOHLB7ASXV4DE6NO","target":"record","payload":{"canonical_record":{"source":{"id":"1609.04077","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-09-14T00:24:30Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"2c43a5a1e4a6e23b547f082703e9e466a9656ce0393a5d2a541206d4ac4a8d61","abstract_canon_sha256":"2e3a879089d499882d0cadd6dd8d041ae9c797e0922a613f0cf26ad96087e1ea"},"schema_version":"1.0"},"canonical_sha256":"1725c737f18ee6e3ac3f04af5e0c9e6b9badf3371e0c21f1b682b7c915fc80dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:40.387626Z","signature_b64":"S3YgWqrHMA3UkGrAvR/GbIaBKFz/AHkrkMul9ODL5/SCY6EkF8rK7XmVzxLSzyjVU682K+nfLRhjPwEX1+7oCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1725c737f18ee6e3ac3f04af5e0c9e6b9badf3371e0c21f1b682b7c915fc80dd","last_reissued_at":"2026-05-18T01:03:40.387165Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:40.387165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.04077","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ih6wNCRr8HD9tvzoArqI8pKH8W51AR23Zy4kWUo6CMBi9+kI6RKXSW3TXYyRrhQKJ2YLkzp5tXLTohsveY/pCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:22:17.161006Z"},"content_sha256":"4d51890905ea4fbdd006d2ee5f87b84f243dd4a240ed978bb45f4b4f29267156","schema_version":"1.0","event_id":"sha256:4d51890905ea4fbdd006d2ee5f87b84f243dd4a240ed978bb45f4b4f29267156"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:C4S4ON7RR3TOHLB7ASXV4DE6NO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From skein theory to presentations for Thompson group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.GR","authors_text":"Yunxiang Ren","submitted_at":"2016-09-14T00:24:30Z","abstract_excerpt":"Jones introduced unitary representations of Thompson group $F$ starting from a given subfactor planar algebra, and all unoriented links arise as matrix coefficients of these representations. Moreover, all oriented links arise as matrix coefficients of a subgroup $\\vec{F}$ which is the stabilizer of a certain vector. Later Golan and Sapir determined the subgroup $\\vec{F}$ and showed many interesting properties. In this paper, we investigate into a large class of groups which arises as subgroups of Thompson group $F$ and reveal the relation between the skein theory of the subfactor planar algebr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04077","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T01:03:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7GJgPdCPRIPB9yffcSqorHAt+ojnJ0+v5liy7kynr37VcSawGeG70z67L0kxfvj5GXSpnG1jqV6YXAXpWRzhBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:22:17.161777Z"},"content_sha256":"925188f5d3866bd1756d3f9e193cf4fbcaabc0977fef861d5a8b120d740bc827","schema_version":"1.0","event_id":"sha256:925188f5d3866bd1756d3f9e193cf4fbcaabc0977fef861d5a8b120d740bc827"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C4S4ON7RR3TOHLB7ASXV4DE6NO/bundle.json","state_url":"https://pith.science/pith/C4S4ON7RR3TOHLB7ASXV4DE6NO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C4S4ON7RR3TOHLB7ASXV4DE6NO/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":"2026-05-31T19:22:17Z","links":{"resolver":"https://pith.science/pith/C4S4ON7RR3TOHLB7ASXV4DE6NO","bundle":"https://pith.science/pith/C4S4ON7RR3TOHLB7ASXV4DE6NO/bundle.json","state":"https://pith.science/pith/C4S4ON7RR3TOHLB7ASXV4DE6NO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C4S4ON7RR3TOHLB7ASXV4DE6NO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:C4S4ON7RR3TOHLB7ASXV4DE6NO","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":"2e3a879089d499882d0cadd6dd8d041ae9c797e0922a613f0cf26ad96087e1ea","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-09-14T00:24:30Z","title_canon_sha256":"2c43a5a1e4a6e23b547f082703e9e466a9656ce0393a5d2a541206d4ac4a8d61"},"schema_version":"1.0","source":{"id":"1609.04077","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04077","created_at":"2026-05-18T01:03:40Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04077v2","created_at":"2026-05-18T01:03:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04077","created_at":"2026-05-18T01:03:40Z"},{"alias_kind":"pith_short_12","alias_value":"C4S4ON7RR3TO","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C4S4ON7RR3TOHLB7","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C4S4ON7R","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:925188f5d3866bd1756d3f9e193cf4fbcaabc0977fef861d5a8b120d740bc827","target":"graph","created_at":"2026-05-18T01:03:40Z","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"},"paper":{"abstract_excerpt":"Jones introduced unitary representations of Thompson group $F$ starting from a given subfactor planar algebra, and all unoriented links arise as matrix coefficients of these representations. Moreover, all oriented links arise as matrix coefficients of a subgroup $\\vec{F}$ which is the stabilizer of a certain vector. Later Golan and Sapir determined the subgroup $\\vec{F}$ and showed many interesting properties. In this paper, we investigate into a large class of groups which arises as subgroups of Thompson group $F$ and reveal the relation between the skein theory of the subfactor planar algebr","authors_text":"Yunxiang Ren","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-09-14T00:24:30Z","title":"From skein theory to presentations for Thompson group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04077","kind":"arxiv","version":2},"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":"sha256:4d51890905ea4fbdd006d2ee5f87b84f243dd4a240ed978bb45f4b4f29267156","target":"record","created_at":"2026-05-18T01:03:40Z","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":"2e3a879089d499882d0cadd6dd8d041ae9c797e0922a613f0cf26ad96087e1ea","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-09-14T00:24:30Z","title_canon_sha256":"2c43a5a1e4a6e23b547f082703e9e466a9656ce0393a5d2a541206d4ac4a8d61"},"schema_version":"1.0","source":{"id":"1609.04077","kind":"arxiv","version":2}},"canonical_sha256":"1725c737f18ee6e3ac3f04af5e0c9e6b9badf3371e0c21f1b682b7c915fc80dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1725c737f18ee6e3ac3f04af5e0c9e6b9badf3371e0c21f1b682b7c915fc80dd","first_computed_at":"2026-05-18T01:03:40.387165Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:40.387165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S3YgWqrHMA3UkGrAvR/GbIaBKFz/AHkrkMul9ODL5/SCY6EkF8rK7XmVzxLSzyjVU682K+nfLRhjPwEX1+7oCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:40.387626Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.04077","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d51890905ea4fbdd006d2ee5f87b84f243dd4a240ed978bb45f4b4f29267156","sha256:925188f5d3866bd1756d3f9e193cf4fbcaabc0977fef861d5a8b120d740bc827"],"state_sha256":"71036658a8dd57835da4a1d786650430952203707c14063e5b83abab81d7762a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GOGuSGyRDEuZByG+zC9yazRsWuyH7EpBDPiBs5VRG4ope4tkTQcWYDCcVwzct8KVwhr8SgR/aVyvbKDhZdLqDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T19:22:17.166782Z","bundle_sha256":"33156b175daa71242edf83dc986d166604083fb3117e27ce46f5a7cfed92042a"}}