{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:BF7SU7ULBCKBLOMF3BZMEY2W6D","short_pith_number":"pith:BF7SU7UL","canonical_record":{"source":{"id":"2506.06219","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-06-06T16:27:25Z","cross_cats_sorted":["math-ph","math.GT","math.MP","math.QA"],"title_canon_sha256":"f3a000b5eb853e3342796fc776089e7ad5c8b94a744a986b20e10a03f31cd9f1","abstract_canon_sha256":"361507527aa7d407126f0dd21dbf22c551a56670d88a5ae034f951f90b011e80"},"schema_version":"1.0"},"canonical_sha256":"097f2a7e8b089415b985d872c26356f0cd4139d17f9955de20cb5b55296fb913","source":{"kind":"arxiv","id":"2506.06219","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.06219","created_at":"2026-07-05T12:01:23Z"},{"alias_kind":"arxiv_version","alias_value":"2506.06219v1","created_at":"2026-07-05T12:01:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.06219","created_at":"2026-07-05T12:01:23Z"},{"alias_kind":"pith_short_12","alias_value":"BF7SU7ULBCKB","created_at":"2026-07-05T12:01:23Z"},{"alias_kind":"pith_short_16","alias_value":"BF7SU7ULBCKBLOMF","created_at":"2026-07-05T12:01:23Z"},{"alias_kind":"pith_short_8","alias_value":"BF7SU7UL","created_at":"2026-07-05T12:01:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:BF7SU7ULBCKBLOMF3BZMEY2W6D","target":"record","payload":{"canonical_record":{"source":{"id":"2506.06219","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-06-06T16:27:25Z","cross_cats_sorted":["math-ph","math.GT","math.MP","math.QA"],"title_canon_sha256":"f3a000b5eb853e3342796fc776089e7ad5c8b94a744a986b20e10a03f31cd9f1","abstract_canon_sha256":"361507527aa7d407126f0dd21dbf22c551a56670d88a5ae034f951f90b011e80"},"schema_version":"1.0"},"canonical_sha256":"097f2a7e8b089415b985d872c26356f0cd4139d17f9955de20cb5b55296fb913","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:01:23.256118Z","signature_b64":"OltTAXxqGumYC68EZAJFDKvKyHmPPtvyBgTUV5f+AdHv+5peYyTc5zBO83xS3jJNlztvbuBJabE4Dmzxc78eDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"097f2a7e8b089415b985d872c26356f0cd4139d17f9955de20cb5b55296fb913","last_reissued_at":"2026-07-05T12:01:23.255590Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:01:23.255590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.06219","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":"2026-07-05T12:01:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8+gP0Ab1z2kvKxXQv8OK80+m/VXhdhCmfmxmL1GUcd3ZZ3kWrwTfs93DGiVjvNTJSoXj8Q/IdvtTcTEfo2/aDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:40:31.349267Z"},"content_sha256":"906b816deecd6084ec6a1f75cb51c0932dafa07e260954e7c4cd89fdcd7cdae5","schema_version":"1.0","event_id":"sha256:906b816deecd6084ec6a1f75cb51c0932dafa07e260954e7c4cd89fdcd7cdae5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:BF7SU7ULBCKBLOMF3BZMEY2W6D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Torus knots in adjoint representation and Vogel's universality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.GT","math.MP","math.QA"],"primary_cat":"hep-th","authors_text":"Andrei Mironov, Liudmila Bishler","submitted_at":"2025-06-06T16:27:25Z","abstract_excerpt":"Vogel's universality gives a unified description of the adjoint sector of representation theory for simple Lie algebras in terms of three parameters $\\alpha,\\beta,\\gamma$, which are homogeneous coordinates of Vogel's plane. It is associated with representation theory within the framework of Chern-Simons theory only, and gives rise to universal knot invariants. We extend the list of these latter further, and explain how to deal with the adjoint invariants for the torus knots $T[m,n]$ considering the case of $T[4,n]$ with odd $n$ in detail."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.06219","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/2506.06219/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":"2026-07-05T12:01:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yphMBpp/W9iVcpZ59foXHQenv0n8fIgNbpryjIBmKiv3crzDhyZXbsKROgyN8UQnX7/Uqmo1q/RbGqVSt52+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:40:31.349868Z"},"content_sha256":"bc86c116fecd10f8d0548daebf6b5331a1ae3b2a34a91242f4e44a02629a7d02","schema_version":"1.0","event_id":"sha256:bc86c116fecd10f8d0548daebf6b5331a1ae3b2a34a91242f4e44a02629a7d02"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BF7SU7ULBCKBLOMF3BZMEY2W6D/bundle.json","state_url":"https://pith.science/pith/BF7SU7ULBCKBLOMF3BZMEY2W6D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BF7SU7ULBCKBLOMF3BZMEY2W6D/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":"2026-08-09T03:40:31Z","links":{"resolver":"https://pith.science/pith/BF7SU7ULBCKBLOMF3BZMEY2W6D","bundle":"https://pith.science/pith/BF7SU7ULBCKBLOMF3BZMEY2W6D/bundle.json","state":"https://pith.science/pith/BF7SU7ULBCKBLOMF3BZMEY2W6D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BF7SU7ULBCKBLOMF3BZMEY2W6D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BF7SU7ULBCKBLOMF3BZMEY2W6D","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":"361507527aa7d407126f0dd21dbf22c551a56670d88a5ae034f951f90b011e80","cross_cats_sorted":["math-ph","math.GT","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-06-06T16:27:25Z","title_canon_sha256":"f3a000b5eb853e3342796fc776089e7ad5c8b94a744a986b20e10a03f31cd9f1"},"schema_version":"1.0","source":{"id":"2506.06219","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.06219","created_at":"2026-07-05T12:01:23Z"},{"alias_kind":"arxiv_version","alias_value":"2506.06219v1","created_at":"2026-07-05T12:01:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.06219","created_at":"2026-07-05T12:01:23Z"},{"alias_kind":"pith_short_12","alias_value":"BF7SU7ULBCKB","created_at":"2026-07-05T12:01:23Z"},{"alias_kind":"pith_short_16","alias_value":"BF7SU7ULBCKBLOMF","created_at":"2026-07-05T12:01:23Z"},{"alias_kind":"pith_short_8","alias_value":"BF7SU7UL","created_at":"2026-07-05T12:01:23Z"}],"graph_snapshots":[{"event_id":"sha256:bc86c116fecd10f8d0548daebf6b5331a1ae3b2a34a91242f4e44a02629a7d02","target":"graph","created_at":"2026-07-05T12:01:23Z","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/2506.06219/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Vogel's universality gives a unified description of the adjoint sector of representation theory for simple Lie algebras in terms of three parameters $\\alpha,\\beta,\\gamma$, which are homogeneous coordinates of Vogel's plane. It is associated with representation theory within the framework of Chern-Simons theory only, and gives rise to universal knot invariants. We extend the list of these latter further, and explain how to deal with the adjoint invariants for the torus knots $T[m,n]$ considering the case of $T[4,n]$ with odd $n$ in detail.","authors_text":"Andrei Mironov, Liudmila Bishler","cross_cats":["math-ph","math.GT","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-06-06T16:27:25Z","title":"Torus knots in adjoint representation and Vogel's universality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.06219","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":"sha256:906b816deecd6084ec6a1f75cb51c0932dafa07e260954e7c4cd89fdcd7cdae5","target":"record","created_at":"2026-07-05T12:01:23Z","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":"361507527aa7d407126f0dd21dbf22c551a56670d88a5ae034f951f90b011e80","cross_cats_sorted":["math-ph","math.GT","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-06-06T16:27:25Z","title_canon_sha256":"f3a000b5eb853e3342796fc776089e7ad5c8b94a744a986b20e10a03f31cd9f1"},"schema_version":"1.0","source":{"id":"2506.06219","kind":"arxiv","version":1}},"canonical_sha256":"097f2a7e8b089415b985d872c26356f0cd4139d17f9955de20cb5b55296fb913","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"097f2a7e8b089415b985d872c26356f0cd4139d17f9955de20cb5b55296fb913","first_computed_at":"2026-07-05T12:01:23.255590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:01:23.255590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OltTAXxqGumYC68EZAJFDKvKyHmPPtvyBgTUV5f+AdHv+5peYyTc5zBO83xS3jJNlztvbuBJabE4Dmzxc78eDg==","signature_status":"signed_v1","signed_at":"2026-07-05T12:01:23.256118Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.06219","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:906b816deecd6084ec6a1f75cb51c0932dafa07e260954e7c4cd89fdcd7cdae5","sha256:bc86c116fecd10f8d0548daebf6b5331a1ae3b2a34a91242f4e44a02629a7d02"],"state_sha256":"d93d26d67dd1a7c537663ecc75938b41c19cef956bc332c83c375f671c7e2467"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b5l6f93jC1/GIkUnZ+AGmth0P6sGZSztBrKc1pc/As891PrwXO9kSppzH9b4PRJ1L1VW5f+c+BaHzvbyuS9VBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T03:40:31.354034Z","bundle_sha256":"9bfc552441eadaaab03ff3040595333e198a463e41489260ec3d3cb4a4737037"}}