{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:43KYJWUJYHVTCJRANFTJ4R753B","short_pith_number":"pith:43KYJWUJ","canonical_record":{"source":{"id":"1606.06015","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-06-20T08:46:54Z","cross_cats_sorted":["math-ph","math.GT","math.MP"],"title_canon_sha256":"6d62aa2f52e7167ab270ef7b8af7d7a06847a18ecffb2714e19879685af88fd4","abstract_canon_sha256":"952bed05656103c8581384c2e9ab7c28ce915824b27c2c80c78a96c5d95b693e"},"schema_version":"1.0"},"canonical_sha256":"e6d584da89c1eb31262069669e47fdd87f77487e680267cb5c12aa9a483934b9","source":{"kind":"arxiv","id":"1606.06015","version":8},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.06015","created_at":"2026-05-18T00:32:21Z"},{"alias_kind":"arxiv_version","alias_value":"1606.06015v8","created_at":"2026-05-18T00:32:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06015","created_at":"2026-05-18T00:32:21Z"},{"alias_kind":"pith_short_12","alias_value":"43KYJWUJYHVT","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"43KYJWUJYHVTCJRA","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"43KYJWUJ","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:43KYJWUJYHVTCJRANFTJ4R753B","target":"record","payload":{"canonical_record":{"source":{"id":"1606.06015","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-06-20T08:46:54Z","cross_cats_sorted":["math-ph","math.GT","math.MP"],"title_canon_sha256":"6d62aa2f52e7167ab270ef7b8af7d7a06847a18ecffb2714e19879685af88fd4","abstract_canon_sha256":"952bed05656103c8581384c2e9ab7c28ce915824b27c2c80c78a96c5d95b693e"},"schema_version":"1.0"},"canonical_sha256":"e6d584da89c1eb31262069669e47fdd87f77487e680267cb5c12aa9a483934b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:21.330234Z","signature_b64":"nKM0gBEvlhiL/Fn7ULGakZood9jexiNPREKZAUZ+QRIWfdYyeMaQ6JdAQSu74poGNOxlYGsjBTLO9ttwGiwECA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6d584da89c1eb31262069669e47fdd87f77487e680267cb5c12aa9a483934b9","last_reissued_at":"2026-05-18T00:32:21.329582Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:21.329582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.06015","source_version":8,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S1rbWBxlbCj7fvTGAQ2TFE4TKB3vlOkdxgN3gT9ySYT3Ixpxcc0TMN/4GvGBakoxunNIq8UsK25KsqB63+lKAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T16:15:15.598046Z"},"content_sha256":"f33dab975470d054b0ff4c43d78ff870f7a122b87ab6cc7e0f65618ce266cbca","schema_version":"1.0","event_id":"sha256:f33dab975470d054b0ff4c43d78ff870f7a122b87ab6cc7e0f65618ce266cbca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:43KYJWUJYHVTCJRANFTJ4R753B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Factorization of differential expansion for antiparallel double-braid knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.GT","math.MP"],"primary_cat":"hep-th","authors_text":"A.Morozov","submitted_at":"2016-06-20T08:46:54Z","abstract_excerpt":"Continuing the quest for exclusive Racah matrices, which are needed for evaluation of colored arborescent-knot polynomials in Chern-Simons theory, we suggest to extract them from a new kind of a double-evolution -- that of the antiparallel double-braids, which is a simple two-parametric family of two-bridge knots, generalizing the one-parametric family of twist knots. In the case of rectangular representations $R=[r^s]$ we found an evidence that the corresponding differential expansion miraculously factorizes and can be obtained from that for the twist knots. This reduces the problem of rectan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06015","kind":"arxiv","version":8},"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":"2026-05-18T00:32:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P2KAWeeJsWpjpUX/+Ymsm/ainPeMTyC4KfZLEMjRE/lE+B0JQiCiHiQ9J8rulnM3g/IpqSgWKtaXTuektBs8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T16:15:15.598406Z"},"content_sha256":"709407e93471a855d4d5732d887d221314ca83b6f4dfb60f0eee2cd28abf2d7e","schema_version":"1.0","event_id":"sha256:709407e93471a855d4d5732d887d221314ca83b6f4dfb60f0eee2cd28abf2d7e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/43KYJWUJYHVTCJRANFTJ4R753B/bundle.json","state_url":"https://pith.science/pith/43KYJWUJYHVTCJRANFTJ4R753B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/43KYJWUJYHVTCJRANFTJ4R753B/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":"2026-08-11T16:15:15Z","links":{"resolver":"https://pith.science/pith/43KYJWUJYHVTCJRANFTJ4R753B","bundle":"https://pith.science/pith/43KYJWUJYHVTCJRANFTJ4R753B/bundle.json","state":"https://pith.science/pith/43KYJWUJYHVTCJRANFTJ4R753B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/43KYJWUJYHVTCJRANFTJ4R753B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:43KYJWUJYHVTCJRANFTJ4R753B","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":"952bed05656103c8581384c2e9ab7c28ce915824b27c2c80c78a96c5d95b693e","cross_cats_sorted":["math-ph","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-06-20T08:46:54Z","title_canon_sha256":"6d62aa2f52e7167ab270ef7b8af7d7a06847a18ecffb2714e19879685af88fd4"},"schema_version":"1.0","source":{"id":"1606.06015","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.06015","created_at":"2026-05-18T00:32:21Z"},{"alias_kind":"arxiv_version","alias_value":"1606.06015v8","created_at":"2026-05-18T00:32:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06015","created_at":"2026-05-18T00:32:21Z"},{"alias_kind":"pith_short_12","alias_value":"43KYJWUJYHVT","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"43KYJWUJYHVTCJRA","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"43KYJWUJ","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:709407e93471a855d4d5732d887d221314ca83b6f4dfb60f0eee2cd28abf2d7e","target":"graph","created_at":"2026-05-18T00:32:21Z","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":"Continuing the quest for exclusive Racah matrices, which are needed for evaluation of colored arborescent-knot polynomials in Chern-Simons theory, we suggest to extract them from a new kind of a double-evolution -- that of the antiparallel double-braids, which is a simple two-parametric family of two-bridge knots, generalizing the one-parametric family of twist knots. In the case of rectangular representations $R=[r^s]$ we found an evidence that the corresponding differential expansion miraculously factorizes and can be obtained from that for the twist knots. This reduces the problem of rectan","authors_text":"A.Morozov","cross_cats":["math-ph","math.GT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-06-20T08:46:54Z","title":"Factorization of differential expansion for antiparallel double-braid knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06015","kind":"arxiv","version":8},"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:f33dab975470d054b0ff4c43d78ff870f7a122b87ab6cc7e0f65618ce266cbca","target":"record","created_at":"2026-05-18T00:32:21Z","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":"952bed05656103c8581384c2e9ab7c28ce915824b27c2c80c78a96c5d95b693e","cross_cats_sorted":["math-ph","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-06-20T08:46:54Z","title_canon_sha256":"6d62aa2f52e7167ab270ef7b8af7d7a06847a18ecffb2714e19879685af88fd4"},"schema_version":"1.0","source":{"id":"1606.06015","kind":"arxiv","version":8}},"canonical_sha256":"e6d584da89c1eb31262069669e47fdd87f77487e680267cb5c12aa9a483934b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6d584da89c1eb31262069669e47fdd87f77487e680267cb5c12aa9a483934b9","first_computed_at":"2026-05-18T00:32:21.329582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:21.329582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nKM0gBEvlhiL/Fn7ULGakZood9jexiNPREKZAUZ+QRIWfdYyeMaQ6JdAQSu74poGNOxlYGsjBTLO9ttwGiwECA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:21.330234Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.06015","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f33dab975470d054b0ff4c43d78ff870f7a122b87ab6cc7e0f65618ce266cbca","sha256:709407e93471a855d4d5732d887d221314ca83b6f4dfb60f0eee2cd28abf2d7e"],"state_sha256":"b5291163638171614c3c7b8f0136269b6f8f4c4d9938ed2c0a9ac19786204edb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l0JNm41yxiVmWp+4uR+DHmXAuGoeAv6TRgOnxrM4dsKQlxXWfXjKDVaxy5v+FTK/R8hoLEB6cmh8GfQToJV+BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T16:15:15.602295Z","bundle_sha256":"28175189c150b559c73632b8520260d0b87f77cc814daf2334bd8cf41a75e803"}}