{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:RSMPVYGIEIKFBE3DQPZHBF3XDT","short_pith_number":"pith:RSMPVYGI","canonical_record":{"source":{"id":"1412.3323","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-12-10T14:45:04Z","cross_cats_sorted":[],"title_canon_sha256":"f187a7f5fa6228db9600ed76a389ee4f51be7a5555c8d198d79e22b3f661d978","abstract_canon_sha256":"e91c11bcc666cc91d04370d37ca0e7ad133771300688674de0f77563f270057e"},"schema_version":"1.0"},"canonical_sha256":"8c98fae0c8221450936383f27097771cda8598650dcfa83172a5469cb4ae3360","source":{"kind":"arxiv","id":"1412.3323","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3323","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3323v2","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3323","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"RSMPVYGIEIKF","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RSMPVYGIEIKFBE3D","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RSMPVYGI","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:RSMPVYGIEIKFBE3DQPZHBF3XDT","target":"record","payload":{"canonical_record":{"source":{"id":"1412.3323","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-12-10T14:45:04Z","cross_cats_sorted":[],"title_canon_sha256":"f187a7f5fa6228db9600ed76a389ee4f51be7a5555c8d198d79e22b3f661d978","abstract_canon_sha256":"e91c11bcc666cc91d04370d37ca0e7ad133771300688674de0f77563f270057e"},"schema_version":"1.0"},"canonical_sha256":"8c98fae0c8221450936383f27097771cda8598650dcfa83172a5469cb4ae3360","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:13.430860Z","signature_b64":"o3yOSrNQsWO4ZutMWtd9AW86qLtFhtJToMeWiVnsWg0oILClsxZpe56N3RjMy0yKs6IvC8QYZ2AdfCENF7E9Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c98fae0c8221450936383f27097771cda8598650dcfa83172a5469cb4ae3360","last_reissued_at":"2026-05-18T02:18:13.430504Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:13.430504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.3323","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":"2026-05-18T02:18:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3sy+e3hQif9NsU+9g/kg84joSRMQS6aRnNfD+eWH8tvtoWVa7UD551t+ki2cWGMlY9bSoZAfjlSdgAqArwnbDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:48:26.254154Z"},"content_sha256":"48d0140f4f31e1e22f11d0de13d08c20f113b20941cc9fcd2cc563bd73a1028c","schema_version":"1.0","event_id":"sha256:48d0140f4f31e1e22f11d0de13d08c20f113b20941cc9fcd2cc563bd73a1028c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:RSMPVYGIEIKFBE3DQPZHBF3XDT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Divergence and q-divergence in depth 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Anna Lachowska, Anton Alekseev, Elise Raphael","submitted_at":"2014-12-10T14:45:04Z","abstract_excerpt":"The Kashiwara-Vergne Lie algebra $\\mathfrak{krv}$ encodes symmetries of the Kashiwara-Vergne problem on the properties of the Campbell-Hausdorff series. It is conjectures that $\\mathfrak{krv} \\cong \\mathbb{K}t \\oplus \\mathfrak{grt}_1$, where $t$ is a generator of degree 1 and $\\mathfrak{grt}_1$ is the Grothendieck-Teichm\\\"uller Lie algebra. In the paper, we prove this conjecture in depth 2. The main tools in the proof are the divergence cocycle and the representation theory of the dihedral group $D_{12}$. Our calculation is similar to the calculation by Zagier of the graded dimensions of the d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3323","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":"2026-05-18T02:18:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4t5accHcRxYm5ySLlKX1ueaUZKhp8IPseGNdiJGNQxNXAqvzA2NOOwLCrqcCl3K3ctYWT0hgxYNvvZvbbeVqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:48:26.254524Z"},"content_sha256":"30e2d9d6505508d0ab2309f32a098a6ae8f368d382c59c42332587dec7486452","schema_version":"1.0","event_id":"sha256:30e2d9d6505508d0ab2309f32a098a6ae8f368d382c59c42332587dec7486452"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RSMPVYGIEIKFBE3DQPZHBF3XDT/bundle.json","state_url":"https://pith.science/pith/RSMPVYGIEIKFBE3DQPZHBF3XDT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RSMPVYGIEIKFBE3DQPZHBF3XDT/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":"2026-06-07T20:48:26Z","links":{"resolver":"https://pith.science/pith/RSMPVYGIEIKFBE3DQPZHBF3XDT","bundle":"https://pith.science/pith/RSMPVYGIEIKFBE3DQPZHBF3XDT/bundle.json","state":"https://pith.science/pith/RSMPVYGIEIKFBE3DQPZHBF3XDT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RSMPVYGIEIKFBE3DQPZHBF3XDT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RSMPVYGIEIKFBE3DQPZHBF3XDT","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":"e91c11bcc666cc91d04370d37ca0e7ad133771300688674de0f77563f270057e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-12-10T14:45:04Z","title_canon_sha256":"f187a7f5fa6228db9600ed76a389ee4f51be7a5555c8d198d79e22b3f661d978"},"schema_version":"1.0","source":{"id":"1412.3323","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3323","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3323v2","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3323","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"RSMPVYGIEIKF","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RSMPVYGIEIKFBE3D","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RSMPVYGI","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:30e2d9d6505508d0ab2309f32a098a6ae8f368d382c59c42332587dec7486452","target":"graph","created_at":"2026-05-18T02:18:13Z","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":"The Kashiwara-Vergne Lie algebra $\\mathfrak{krv}$ encodes symmetries of the Kashiwara-Vergne problem on the properties of the Campbell-Hausdorff series. It is conjectures that $\\mathfrak{krv} \\cong \\mathbb{K}t \\oplus \\mathfrak{grt}_1$, where $t$ is a generator of degree 1 and $\\mathfrak{grt}_1$ is the Grothendieck-Teichm\\\"uller Lie algebra. In the paper, we prove this conjecture in depth 2. The main tools in the proof are the divergence cocycle and the representation theory of the dihedral group $D_{12}$. Our calculation is similar to the calculation by Zagier of the graded dimensions of the d","authors_text":"Anna Lachowska, Anton Alekseev, Elise Raphael","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-12-10T14:45:04Z","title":"Divergence and q-divergence in depth 2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3323","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":"sha256:48d0140f4f31e1e22f11d0de13d08c20f113b20941cc9fcd2cc563bd73a1028c","target":"record","created_at":"2026-05-18T02:18:13Z","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":"e91c11bcc666cc91d04370d37ca0e7ad133771300688674de0f77563f270057e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-12-10T14:45:04Z","title_canon_sha256":"f187a7f5fa6228db9600ed76a389ee4f51be7a5555c8d198d79e22b3f661d978"},"schema_version":"1.0","source":{"id":"1412.3323","kind":"arxiv","version":2}},"canonical_sha256":"8c98fae0c8221450936383f27097771cda8598650dcfa83172a5469cb4ae3360","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c98fae0c8221450936383f27097771cda8598650dcfa83172a5469cb4ae3360","first_computed_at":"2026-05-18T02:18:13.430504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:13.430504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o3yOSrNQsWO4ZutMWtd9AW86qLtFhtJToMeWiVnsWg0oILClsxZpe56N3RjMy0yKs6IvC8QYZ2AdfCENF7E9Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:13.430860Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3323","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48d0140f4f31e1e22f11d0de13d08c20f113b20941cc9fcd2cc563bd73a1028c","sha256:30e2d9d6505508d0ab2309f32a098a6ae8f368d382c59c42332587dec7486452"],"state_sha256":"48155c21c4c1c0afaafeef4fa44c7047e60f191598144619d8059ee9a90c036a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"thd+hHF3XXyf8M583suusT0vrzlwyehxkJe+yKwbzFIBFkcSOAzvxNZbXFu/cSlNaAfke1pf+nD2yAclNzVAAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T20:48:26.258003Z","bundle_sha256":"ec42a1afd145831145a3e641937198726167dd033d14efc976489beed75f8876"}}