{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:MWVKAWMLUM7KPXCWIJ6ETATY6N","short_pith_number":"pith:MWVKAWML","canonical_record":{"source":{"id":"1905.01523","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-05-04T16:58:21Z","cross_cats_sorted":["hep-th","math.AG","math.MP","math.RT"],"title_canon_sha256":"7f85c696c19728a7c3b00bdb31e6ba879ba89b2aa7dd56e4355515fd9a050d6e","abstract_canon_sha256":"71d8bea6217e1c3389556e2d84ecf233db826356851ce72e7d403e09a636b20a"},"schema_version":"1.0"},"canonical_sha256":"65aaa0598ba33ea7dc56427c498278f35eff9dcd0d7a0f8aba16390cbc45c78a","source":{"kind":"arxiv","id":"1905.01523","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.01523","created_at":"2026-05-17T23:46:58Z"},{"alias_kind":"arxiv_version","alias_value":"1905.01523v1","created_at":"2026-05-17T23:46:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01523","created_at":"2026-05-17T23:46:58Z"},{"alias_kind":"pith_short_12","alias_value":"MWVKAWMLUM7K","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"MWVKAWMLUM7KPXCW","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"MWVKAWML","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:MWVKAWMLUM7KPXCWIJ6ETATY6N","target":"record","payload":{"canonical_record":{"source":{"id":"1905.01523","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-05-04T16:58:21Z","cross_cats_sorted":["hep-th","math.AG","math.MP","math.RT"],"title_canon_sha256":"7f85c696c19728a7c3b00bdb31e6ba879ba89b2aa7dd56e4355515fd9a050d6e","abstract_canon_sha256":"71d8bea6217e1c3389556e2d84ecf233db826356851ce72e7d403e09a636b20a"},"schema_version":"1.0"},"canonical_sha256":"65aaa0598ba33ea7dc56427c498278f35eff9dcd0d7a0f8aba16390cbc45c78a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:58.325687Z","signature_b64":"tJ4MZJEfLb5feNnJ3/pxbX+b/Qw+BYorzL7hWums+sPwQKy4u1oO8IfxhIF1f8iOThSUS13EciC7uynDDkiiBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65aaa0598ba33ea7dc56427c498278f35eff9dcd0d7a0f8aba16390cbc45c78a","last_reissued_at":"2026-05-17T23:46:58.325108Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:58.325108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.01523","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":"2026-05-17T23:46:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zchFC1EsT86GCGTB33bT3dxTW93NQq8E6/o134HmDtZqNV/zC4TF6P0tiTko1lgJUqfpDW1e89yE1W7QMzywBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:55:50.589432Z"},"content_sha256":"823b695c608552dbfe3a60c690ff6b68b1a0cd0e5353c122ef930a6eb620c279","schema_version":"1.0","event_id":"sha256:823b695c608552dbfe3a60c690ff6b68b1a0cd0e5353c122ef930a6eb620c279"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:MWVKAWMLUM7KPXCWIJ6ETATY6N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The 2-leg vertex in K-theoretic DT theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AG","math.MP","math.RT"],"primary_cat":"math-ph","authors_text":"A. Okounkov, A. Osinenko, Ya. Kononov","submitted_at":"2019-05-04T16:58:21Z","abstract_excerpt":"K-theoretic Donaldson-Thomas counts of curves in toric and many related threefolds can be computed in terms of a certain canonical 3-valent tensor, the K-theoretic equivariant vertex. In this paper we derive a formula for the vertex in the case when two out of three entries are nontrivial. We also discuss some applications of this result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01523","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":"2026-05-17T23:46:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ok81QMjA9DaUMxiFIrCzeBBpL6NobjG++0qW2mCuWz6DmU/3Pvn4LjB6sfpGvUAgKBl4yWGS6Dd1bW6vKqCKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:55:50.590289Z"},"content_sha256":"14846cee6879b9ae660d644c82787ee017c6a3509eac7e3ea882b91682898caa","schema_version":"1.0","event_id":"sha256:14846cee6879b9ae660d644c82787ee017c6a3509eac7e3ea882b91682898caa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MWVKAWMLUM7KPXCWIJ6ETATY6N/bundle.json","state_url":"https://pith.science/pith/MWVKAWMLUM7KPXCWIJ6ETATY6N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MWVKAWMLUM7KPXCWIJ6ETATY6N/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":"2026-05-27T13:55:50Z","links":{"resolver":"https://pith.science/pith/MWVKAWMLUM7KPXCWIJ6ETATY6N","bundle":"https://pith.science/pith/MWVKAWMLUM7KPXCWIJ6ETATY6N/bundle.json","state":"https://pith.science/pith/MWVKAWMLUM7KPXCWIJ6ETATY6N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MWVKAWMLUM7KPXCWIJ6ETATY6N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MWVKAWMLUM7KPXCWIJ6ETATY6N","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":"71d8bea6217e1c3389556e2d84ecf233db826356851ce72e7d403e09a636b20a","cross_cats_sorted":["hep-th","math.AG","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-05-04T16:58:21Z","title_canon_sha256":"7f85c696c19728a7c3b00bdb31e6ba879ba89b2aa7dd56e4355515fd9a050d6e"},"schema_version":"1.0","source":{"id":"1905.01523","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.01523","created_at":"2026-05-17T23:46:58Z"},{"alias_kind":"arxiv_version","alias_value":"1905.01523v1","created_at":"2026-05-17T23:46:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01523","created_at":"2026-05-17T23:46:58Z"},{"alias_kind":"pith_short_12","alias_value":"MWVKAWMLUM7K","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"MWVKAWMLUM7KPXCW","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"MWVKAWML","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:14846cee6879b9ae660d644c82787ee017c6a3509eac7e3ea882b91682898caa","target":"graph","created_at":"2026-05-17T23:46:58Z","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":"K-theoretic Donaldson-Thomas counts of curves in toric and many related threefolds can be computed in terms of a certain canonical 3-valent tensor, the K-theoretic equivariant vertex. In this paper we derive a formula for the vertex in the case when two out of three entries are nontrivial. We also discuss some applications of this result.","authors_text":"A. Okounkov, A. Osinenko, Ya. Kononov","cross_cats":["hep-th","math.AG","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-05-04T16:58:21Z","title":"The 2-leg vertex in K-theoretic DT theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01523","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":"sha256:823b695c608552dbfe3a60c690ff6b68b1a0cd0e5353c122ef930a6eb620c279","target":"record","created_at":"2026-05-17T23:46:58Z","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":"71d8bea6217e1c3389556e2d84ecf233db826356851ce72e7d403e09a636b20a","cross_cats_sorted":["hep-th","math.AG","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-05-04T16:58:21Z","title_canon_sha256":"7f85c696c19728a7c3b00bdb31e6ba879ba89b2aa7dd56e4355515fd9a050d6e"},"schema_version":"1.0","source":{"id":"1905.01523","kind":"arxiv","version":1}},"canonical_sha256":"65aaa0598ba33ea7dc56427c498278f35eff9dcd0d7a0f8aba16390cbc45c78a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65aaa0598ba33ea7dc56427c498278f35eff9dcd0d7a0f8aba16390cbc45c78a","first_computed_at":"2026-05-17T23:46:58.325108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:58.325108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tJ4MZJEfLb5feNnJ3/pxbX+b/Qw+BYorzL7hWums+sPwQKy4u1oO8IfxhIF1f8iOThSUS13EciC7uynDDkiiBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:58.325687Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.01523","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:823b695c608552dbfe3a60c690ff6b68b1a0cd0e5353c122ef930a6eb620c279","sha256:14846cee6879b9ae660d644c82787ee017c6a3509eac7e3ea882b91682898caa"],"state_sha256":"cf4dfb3d359dbc58364f92d934d0e7d5627271bd71003ab0af3331e319a3b4d0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2L7WBf78xKzWr+4IgVhcicd7WOyxk1y50u621ORQpY3efjm1roD/64wZU4aVrDhGSbxsdX7FoJkPCatBjNzjAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T13:55:50.593977Z","bundle_sha256":"a42af7dbf793681f82a146ccf465d310d3dafe4e34233bfeef6408fa3eed3c73"}}