{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:UMYNUW4CAJODTOM4CWDL5N5LKI","short_pith_number":"pith:UMYNUW4C","canonical_record":{"source":{"id":"1403.6218","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-25T03:04:43Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"61981e8e7d91ce7323b6312be60973a43170b48c0e0de58f2f638c066e5f4bfc","abstract_canon_sha256":"c441110db5cc0889ec8b02de64de00ad0b6c7b73e6aa173d9d499fd3317bf74a"},"schema_version":"1.0"},"canonical_sha256":"a330da5b82025c39b99c1586beb7ab522e08922f69c4c09aa394f5c937c526ba","source":{"kind":"arxiv","id":"1403.6218","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6218","created_at":"2026-07-05T01:25:50Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6218v3","created_at":"2026-07-05T01:25:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6218","created_at":"2026-07-05T01:25:50Z"},{"alias_kind":"pith_short_12","alias_value":"UMYNUW4CAJOD","created_at":"2026-07-05T01:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"UMYNUW4CAJODTOM4","created_at":"2026-07-05T01:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"UMYNUW4C","created_at":"2026-07-05T01:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:UMYNUW4CAJODTOM4CWDL5N5LKI","target":"record","payload":{"canonical_record":{"source":{"id":"1403.6218","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-25T03:04:43Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"61981e8e7d91ce7323b6312be60973a43170b48c0e0de58f2f638c066e5f4bfc","abstract_canon_sha256":"c441110db5cc0889ec8b02de64de00ad0b6c7b73e6aa173d9d499fd3317bf74a"},"schema_version":"1.0"},"canonical_sha256":"a330da5b82025c39b99c1586beb7ab522e08922f69c4c09aa394f5c937c526ba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:25:50.578861Z","signature_b64":"8ZuyA4bDdLV1sGSwmQsBkgInmQat+qhH4vaP2ZXHJljJ6+gUikA1oMtl32xZaYwRn9rJrf1xVBbcNm4nDClnBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a330da5b82025c39b99c1586beb7ab522e08922f69c4c09aa394f5c937c526ba","last_reissued_at":"2026-07-05T01:25:50.578426Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:25:50.578426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.6218","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:25:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rUkhOqGbfWb0jWj4OMrHRaZXR3EVy+Ta/I7SpKxZ8r3jHDy5bf9wdInB+AA6YZ3Bbzj3HhvijY8X3PHsVH82CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T13:17:39.127144Z"},"content_sha256":"1e7296cd46be894673bbe31919303ecec749410f33d340117d55722ec8749f8d","schema_version":"1.0","event_id":"sha256:1e7296cd46be894673bbe31919303ecec749410f33d340117d55722ec8749f8d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:UMYNUW4CAJODTOM4CWDL5N5LKI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equivariant Quantum Cohomology of the Grassmannian via the Rim Hook Rule","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Anna Bertiger, Elizabeth Mili\\'cevi\\'c, Kaisa Taipale","submitted_at":"2014-03-25T03:04:43Z","abstract_excerpt":"A driving question in (quantum) cohomology of flag varieties is to find non-recursive, positive combinatorial formulas for expressing the product of two classes in a particularly nice basis, called the Schubert basis. Bertram, Ciocan-Fontanine and Fulton provided a way to compute quantum products of Schubert classes in the Grassmannian of k-planes in complex n-space by doing classical multiplication and then applying a combinatorial rim hook rule which yields the quantum parameter. In this paper, we provide a generalization of this rim hook rule to the setting in which there is also an action "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6218","kind":"arxiv","version":3},"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/1403.6218/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":"2026-07-05T01:25:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"doqdBKRjNQdAda0hioiX9dRNFS+g2ALzIFWsQgtpmLTvVmbnj7OWI4hcmbtnN1ojotTNNSK+RsG5C5RncMCbAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T13:17:39.127662Z"},"content_sha256":"d6334807bce6a6eca7a8c57cd49fd5a1f7c2c8ecd2191763bf7d11a828906362","schema_version":"1.0","event_id":"sha256:d6334807bce6a6eca7a8c57cd49fd5a1f7c2c8ecd2191763bf7d11a828906362"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UMYNUW4CAJODTOM4CWDL5N5LKI/bundle.json","state_url":"https://pith.science/pith/UMYNUW4CAJODTOM4CWDL5N5LKI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UMYNUW4CAJODTOM4CWDL5N5LKI/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":"2026-08-04T13:17:39Z","links":{"resolver":"https://pith.science/pith/UMYNUW4CAJODTOM4CWDL5N5LKI","bundle":"https://pith.science/pith/UMYNUW4CAJODTOM4CWDL5N5LKI/bundle.json","state":"https://pith.science/pith/UMYNUW4CAJODTOM4CWDL5N5LKI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UMYNUW4CAJODTOM4CWDL5N5LKI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UMYNUW4CAJODTOM4CWDL5N5LKI","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":"c441110db5cc0889ec8b02de64de00ad0b6c7b73e6aa173d9d499fd3317bf74a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-25T03:04:43Z","title_canon_sha256":"61981e8e7d91ce7323b6312be60973a43170b48c0e0de58f2f638c066e5f4bfc"},"schema_version":"1.0","source":{"id":"1403.6218","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6218","created_at":"2026-07-05T01:25:50Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6218v3","created_at":"2026-07-05T01:25:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6218","created_at":"2026-07-05T01:25:50Z"},{"alias_kind":"pith_short_12","alias_value":"UMYNUW4CAJOD","created_at":"2026-07-05T01:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"UMYNUW4CAJODTOM4","created_at":"2026-07-05T01:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"UMYNUW4C","created_at":"2026-07-05T01:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:d6334807bce6a6eca7a8c57cd49fd5a1f7c2c8ecd2191763bf7d11a828906362","target":"graph","created_at":"2026-07-05T01:25:50Z","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/1403.6218/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A driving question in (quantum) cohomology of flag varieties is to find non-recursive, positive combinatorial formulas for expressing the product of two classes in a particularly nice basis, called the Schubert basis. Bertram, Ciocan-Fontanine and Fulton provided a way to compute quantum products of Schubert classes in the Grassmannian of k-planes in complex n-space by doing classical multiplication and then applying a combinatorial rim hook rule which yields the quantum parameter. In this paper, we provide a generalization of this rim hook rule to the setting in which there is also an action ","authors_text":"Anna Bertiger, Elizabeth Mili\\'cevi\\'c, Kaisa Taipale","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-25T03:04:43Z","title":"Equivariant Quantum Cohomology of the Grassmannian via the Rim Hook Rule"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6218","kind":"arxiv","version":3},"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":"sha256:1e7296cd46be894673bbe31919303ecec749410f33d340117d55722ec8749f8d","target":"record","created_at":"2026-07-05T01:25:50Z","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":"c441110db5cc0889ec8b02de64de00ad0b6c7b73e6aa173d9d499fd3317bf74a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-25T03:04:43Z","title_canon_sha256":"61981e8e7d91ce7323b6312be60973a43170b48c0e0de58f2f638c066e5f4bfc"},"schema_version":"1.0","source":{"id":"1403.6218","kind":"arxiv","version":3}},"canonical_sha256":"a330da5b82025c39b99c1586beb7ab522e08922f69c4c09aa394f5c937c526ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a330da5b82025c39b99c1586beb7ab522e08922f69c4c09aa394f5c937c526ba","first_computed_at":"2026-07-05T01:25:50.578426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:25:50.578426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8ZuyA4bDdLV1sGSwmQsBkgInmQat+qhH4vaP2ZXHJljJ6+gUikA1oMtl32xZaYwRn9rJrf1xVBbcNm4nDClnBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:25:50.578861Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.6218","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e7296cd46be894673bbe31919303ecec749410f33d340117d55722ec8749f8d","sha256:d6334807bce6a6eca7a8c57cd49fd5a1f7c2c8ecd2191763bf7d11a828906362"],"state_sha256":"333fe1682dbd58715556781ce7903e73d91524e5b394599736523f34a28b7f8e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9bseO4M5CIWN0by3uVvu33KAGYUVckvFafd4ZoOtWJngwXl/DyW2oFry8zYQULMtnHWa9RONWVYEDS/wLQqwAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T13:17:39.131380Z","bundle_sha256":"15cbdb3be561060dc63609212d6d8dd194fd8993f080bf1f36cdc3d20a4b05f8"}}