{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:II7UTYQ4KBNURVOIESE3V5ENVH","short_pith_number":"pith:II7UTYQ4","canonical_record":{"source":{"id":"1409.7111","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-24T21:39:28Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"7a7626b25e2e5c45c31bc2348f38d3cb4b91af2a004d56ec281cb90ad9671beb","abstract_canon_sha256":"c6898fc17ea65f301570c5f66052512432bce46f5e95875aef8d44ac4ae4fe9c"},"schema_version":"1.0"},"canonical_sha256":"423f49e21c505b48d5c82489baf48da9f71a657b9a401cf9ff07239974cf0656","source":{"kind":"arxiv","id":"1409.7111","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7111","created_at":"2026-05-18T01:27:15Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7111v1","created_at":"2026-05-18T01:27:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7111","created_at":"2026-05-18T01:27:15Z"},{"alias_kind":"pith_short_12","alias_value":"II7UTYQ4KBNU","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"II7UTYQ4KBNURVOI","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"II7UTYQ4","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:II7UTYQ4KBNURVOIESE3V5ENVH","target":"record","payload":{"canonical_record":{"source":{"id":"1409.7111","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-24T21:39:28Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"7a7626b25e2e5c45c31bc2348f38d3cb4b91af2a004d56ec281cb90ad9671beb","abstract_canon_sha256":"c6898fc17ea65f301570c5f66052512432bce46f5e95875aef8d44ac4ae4fe9c"},"schema_version":"1.0"},"canonical_sha256":"423f49e21c505b48d5c82489baf48da9f71a657b9a401cf9ff07239974cf0656","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:15.303292Z","signature_b64":"jFh8tWjsuozf8l5po5IcnUhyXxsaTJYcJMEmLFeKOKwheCoEEwZtXHzjGqfNrxlUIspyoZYtNkAEQgZEuHMyBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"423f49e21c505b48d5c82489baf48da9f71a657b9a401cf9ff07239974cf0656","last_reissued_at":"2026-05-18T01:27:15.302598Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:15.302598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.7111","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":"2026-05-18T01:27:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oVnZysENfy607cNLxAkoanOETpx7n2k/YHRpRjse38yQqPXkwDk7GIrqYrVInGkIKQiD2EpCR3W68Lq3udGUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T16:20:36.147756Z"},"content_sha256":"cb07d401d15a411157d3cc0a6d36123e46d9482b302ec4321db89208f655f6af","schema_version":"1.0","event_id":"sha256:cb07d401d15a411157d3cc0a6d36123e46d9482b302ec4321db89208f655f6af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:II7UTYQ4KBNURVOIESE3V5ENVH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equivariant oriented cohomology of flag varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AG","authors_text":"Baptiste Calm\\`es, Changlong Zhong, Kirill Zainoulline","submitted_at":"2014-09-24T21:39:28Z","abstract_excerpt":"Given an equivariant oriented cohomology theory $h$, a split reductive group $G$, a maximal torus $T$ in $G$, and a parabolic subgroup $P$ containing $T$, we explain how the $T$-equivariant oriented cohomology ring $h_T(G/P)$ can be identified with the dual of a coalgebra defined using exclusively the root datum of $(G,T)$, a set of simple roots defining $P$ and the formal group law of $h$. In two papers [Push-pull operators on the formal affine Demazure algebra and its dual, arXiv:1312.0019] and [A coproduct structure on the formal affine Demazure algebra, arXiv:1209.1676], we studied the pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7111","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":"2026-05-18T01:27:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jmydzwpVGFWjCFh8UB/OIqYHwcFmaeOnXt7fEWO/TeBNlGAdZ9mbVBFUMDyQZE3aWwWOLtuW4glaPK9/GVg3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T16:20:36.148103Z"},"content_sha256":"68160f3511173ce590e1b8b055f25c046c4fedce466fbe1776d1d5d6790fc118","schema_version":"1.0","event_id":"sha256:68160f3511173ce590e1b8b055f25c046c4fedce466fbe1776d1d5d6790fc118"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/II7UTYQ4KBNURVOIESE3V5ENVH/bundle.json","state_url":"https://pith.science/pith/II7UTYQ4KBNURVOIESE3V5ENVH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/II7UTYQ4KBNURVOIESE3V5ENVH/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":"2026-06-20T16:20:36Z","links":{"resolver":"https://pith.science/pith/II7UTYQ4KBNURVOIESE3V5ENVH","bundle":"https://pith.science/pith/II7UTYQ4KBNURVOIESE3V5ENVH/bundle.json","state":"https://pith.science/pith/II7UTYQ4KBNURVOIESE3V5ENVH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/II7UTYQ4KBNURVOIESE3V5ENVH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:II7UTYQ4KBNURVOIESE3V5ENVH","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":"c6898fc17ea65f301570c5f66052512432bce46f5e95875aef8d44ac4ae4fe9c","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-24T21:39:28Z","title_canon_sha256":"7a7626b25e2e5c45c31bc2348f38d3cb4b91af2a004d56ec281cb90ad9671beb"},"schema_version":"1.0","source":{"id":"1409.7111","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7111","created_at":"2026-05-18T01:27:15Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7111v1","created_at":"2026-05-18T01:27:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7111","created_at":"2026-05-18T01:27:15Z"},{"alias_kind":"pith_short_12","alias_value":"II7UTYQ4KBNU","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"II7UTYQ4KBNURVOI","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"II7UTYQ4","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:68160f3511173ce590e1b8b055f25c046c4fedce466fbe1776d1d5d6790fc118","target":"graph","created_at":"2026-05-18T01:27:15Z","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 an equivariant oriented cohomology theory $h$, a split reductive group $G$, a maximal torus $T$ in $G$, and a parabolic subgroup $P$ containing $T$, we explain how the $T$-equivariant oriented cohomology ring $h_T(G/P)$ can be identified with the dual of a coalgebra defined using exclusively the root datum of $(G,T)$, a set of simple roots defining $P$ and the formal group law of $h$. In two papers [Push-pull operators on the formal affine Demazure algebra and its dual, arXiv:1312.0019] and [A coproduct structure on the formal affine Demazure algebra, arXiv:1209.1676], we studied the pro","authors_text":"Baptiste Calm\\`es, Changlong Zhong, Kirill Zainoulline","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-24T21:39:28Z","title":"Equivariant oriented cohomology of flag varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7111","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:cb07d401d15a411157d3cc0a6d36123e46d9482b302ec4321db89208f655f6af","target":"record","created_at":"2026-05-18T01:27:15Z","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":"c6898fc17ea65f301570c5f66052512432bce46f5e95875aef8d44ac4ae4fe9c","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-24T21:39:28Z","title_canon_sha256":"7a7626b25e2e5c45c31bc2348f38d3cb4b91af2a004d56ec281cb90ad9671beb"},"schema_version":"1.0","source":{"id":"1409.7111","kind":"arxiv","version":1}},"canonical_sha256":"423f49e21c505b48d5c82489baf48da9f71a657b9a401cf9ff07239974cf0656","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"423f49e21c505b48d5c82489baf48da9f71a657b9a401cf9ff07239974cf0656","first_computed_at":"2026-05-18T01:27:15.302598Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:15.302598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jFh8tWjsuozf8l5po5IcnUhyXxsaTJYcJMEmLFeKOKwheCoEEwZtXHzjGqfNrxlUIspyoZYtNkAEQgZEuHMyBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:15.303292Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.7111","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb07d401d15a411157d3cc0a6d36123e46d9482b302ec4321db89208f655f6af","sha256:68160f3511173ce590e1b8b055f25c046c4fedce466fbe1776d1d5d6790fc118"],"state_sha256":"83e586752348ea219b247f058e5b4702a28ad8e534777e6cac59fe51f024a81b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xCoJwuUERGjg0E9q61mmOdK7qjBxeq2Quxy9Us5/uGSnd5ftJ9h6xufbvhS1i+g/orWJS0xng581/zqOTWqCAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T16:20:36.150361Z","bundle_sha256":"6b5a0cc64ad8770f28f54c08ecfb87f5a5a48de396707273ce7c1be2a9a1d0b0"}}