{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LNWBDKVKTGKJVOZNQR6CDLF6UU","short_pith_number":"pith:LNWBDKVK","canonical_record":{"source":{"id":"1610.04414","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-14T11:49:10Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"bd36d78f6feb1c5e1c4e81792675fa505675b36b96e38cbb0c8e38b6b40280d2","abstract_canon_sha256":"1f27a4f7dd67e562905425619aa270ae4b84780d46cca5c3ae18e5c53451f0f8"},"schema_version":"1.0"},"canonical_sha256":"5b6c11aaaa99949abb2d847c21acbea501566d98df2891951e80171c29de5086","source":{"kind":"arxiv","id":"1610.04414","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04414","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04414v1","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04414","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"pith_short_12","alias_value":"LNWBDKVKTGKJ","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LNWBDKVKTGKJVOZN","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LNWBDKVK","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LNWBDKVKTGKJVOZNQR6CDLF6UU","target":"record","payload":{"canonical_record":{"source":{"id":"1610.04414","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-14T11:49:10Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"bd36d78f6feb1c5e1c4e81792675fa505675b36b96e38cbb0c8e38b6b40280d2","abstract_canon_sha256":"1f27a4f7dd67e562905425619aa270ae4b84780d46cca5c3ae18e5c53451f0f8"},"schema_version":"1.0"},"canonical_sha256":"5b6c11aaaa99949abb2d847c21acbea501566d98df2891951e80171c29de5086","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:57.106129Z","signature_b64":"p3wzACL7umlNH4q4CNOiueQmow6DtjbiJmLEyk6il+P006hDmFz3Aayt1OMk1aPknhaW0QyWMcEbxaQJIPv+Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b6c11aaaa99949abb2d847c21acbea501566d98df2891951e80171c29de5086","last_reissued_at":"2026-05-18T00:20:57.105653Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:57.105653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.04414","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":"2026-05-18T00:20:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/84tHBHu7oAnbYSN1su3Lm4Kgp+tTsKatPcH74mwbzeMy7eb5YB3qsfvtXN5UGIzerkQeO2lEsevehP1ElnkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:51:46.418031Z"},"content_sha256":"d9dd05b54d06427431f0e70e39a165ba617a33b445972a65f2949c8a4a5f2866","schema_version":"1.0","event_id":"sha256:d9dd05b54d06427431f0e70e39a165ba617a33b445972a65f2949c8a4a5f2866"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LNWBDKVKTGKJVOZNQR6CDLF6UU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On high-dimensional representations of knot groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GT","authors_text":"Michael Heusener, Stefan Friedl","submitted_at":"2016-10-14T11:49:10Z","abstract_excerpt":"Given a hyperbolic knot $K$ and any $n\\geq 2$ the abelian representations and the holonomy representation each give rise to an $(n-1)$-dimensional component in the $\\operatorname{SL}(n,\\Bbb{C})$-character variety. A component of the $\\operatorname{SL}(n,\\Bbb{C})$-character variety of dimension $\\geq n$ is called high-dimensional.\n  It was proved by Cooper and Long that there exist hyperbolic knots with high-dimensional components in the $\\operatorname{SL}(2,\\Bbb{C})$-character variety. We show that given any non-trivial knot $K$ and sufficiently large $n$ the $\\operatorname{SL}(n,\\Bbb{C})$-cha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04414","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":""},"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":"2026-05-18T00:20:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k8IjS+2N1v+aEai32nMXHiw9kbh4rsGvypEFnRnjxswCh0Ebks1YzU0ffSrchoIdcctfW5VOZa2wQuANZ4GfDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:51:46.418679Z"},"content_sha256":"3b1131f96f3a97fc95fda2c77f646d8800d9a72c6281395fcb6a51e610a9df19","schema_version":"1.0","event_id":"sha256:3b1131f96f3a97fc95fda2c77f646d8800d9a72c6281395fcb6a51e610a9df19"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LNWBDKVKTGKJVOZNQR6CDLF6UU/bundle.json","state_url":"https://pith.science/pith/LNWBDKVKTGKJVOZNQR6CDLF6UU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LNWBDKVKTGKJVOZNQR6CDLF6UU/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":"2026-05-29T15:51:46Z","links":{"resolver":"https://pith.science/pith/LNWBDKVKTGKJVOZNQR6CDLF6UU","bundle":"https://pith.science/pith/LNWBDKVKTGKJVOZNQR6CDLF6UU/bundle.json","state":"https://pith.science/pith/LNWBDKVKTGKJVOZNQR6CDLF6UU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LNWBDKVKTGKJVOZNQR6CDLF6UU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LNWBDKVKTGKJVOZNQR6CDLF6UU","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":"1f27a4f7dd67e562905425619aa270ae4b84780d46cca5c3ae18e5c53451f0f8","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-14T11:49:10Z","title_canon_sha256":"bd36d78f6feb1c5e1c4e81792675fa505675b36b96e38cbb0c8e38b6b40280d2"},"schema_version":"1.0","source":{"id":"1610.04414","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04414","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04414v1","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04414","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"pith_short_12","alias_value":"LNWBDKVKTGKJ","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LNWBDKVKTGKJVOZN","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LNWBDKVK","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:3b1131f96f3a97fc95fda2c77f646d8800d9a72c6281395fcb6a51e610a9df19","target":"graph","created_at":"2026-05-18T00:20:57Z","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":"Given a hyperbolic knot $K$ and any $n\\geq 2$ the abelian representations and the holonomy representation each give rise to an $(n-1)$-dimensional component in the $\\operatorname{SL}(n,\\Bbb{C})$-character variety. A component of the $\\operatorname{SL}(n,\\Bbb{C})$-character variety of dimension $\\geq n$ is called high-dimensional.\n  It was proved by Cooper and Long that there exist hyperbolic knots with high-dimensional components in the $\\operatorname{SL}(2,\\Bbb{C})$-character variety. We show that given any non-trivial knot $K$ and sufficiently large $n$ the $\\operatorname{SL}(n,\\Bbb{C})$-cha","authors_text":"Michael Heusener, Stefan Friedl","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-14T11:49:10Z","title":"On high-dimensional representations of knot groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04414","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:d9dd05b54d06427431f0e70e39a165ba617a33b445972a65f2949c8a4a5f2866","target":"record","created_at":"2026-05-18T00:20:57Z","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":"1f27a4f7dd67e562905425619aa270ae4b84780d46cca5c3ae18e5c53451f0f8","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-14T11:49:10Z","title_canon_sha256":"bd36d78f6feb1c5e1c4e81792675fa505675b36b96e38cbb0c8e38b6b40280d2"},"schema_version":"1.0","source":{"id":"1610.04414","kind":"arxiv","version":1}},"canonical_sha256":"5b6c11aaaa99949abb2d847c21acbea501566d98df2891951e80171c29de5086","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b6c11aaaa99949abb2d847c21acbea501566d98df2891951e80171c29de5086","first_computed_at":"2026-05-18T00:20:57.105653Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:57.105653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p3wzACL7umlNH4q4CNOiueQmow6DtjbiJmLEyk6il+P006hDmFz3Aayt1OMk1aPknhaW0QyWMcEbxaQJIPv+Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:57.106129Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.04414","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9dd05b54d06427431f0e70e39a165ba617a33b445972a65f2949c8a4a5f2866","sha256:3b1131f96f3a97fc95fda2c77f646d8800d9a72c6281395fcb6a51e610a9df19"],"state_sha256":"052a52ff9e7b7c0b99ca5daab27056262ee1b395779871553e267ca5f19fe240"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UX+iBFEDqVOSeXaPT2+IA4/mERQOX7FoscoBCuxh641H0Ogo401pxU+TrYGpg/N00s8o65+b1bn5JH97fTw3AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T15:51:46.421964Z","bundle_sha256":"0081dea7d8316c4d8317471f570348a67f916c56b662631e428795988512318a"}}