{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:OYGDEFGG6MY5YR77OACPY4SMDE","short_pith_number":"pith:OYGDEFGG","canonical_record":{"source":{"id":"2607.06189","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AG","submitted_at":"2026-07-07T12:11:49Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"2cc33d336306255fd8b02645d292901700d923e71d78d9f2e87bd9b4311f1681","abstract_canon_sha256":"64d0d9316d21b4aa548160901a2fa9774b69cd15f5568b32afc8129282567c21"},"schema_version":"1.0"},"canonical_sha256":"760c3214c6f331dc47ff7004fc724c191b5629f00447ecd83a10e7075a0cb895","source":{"kind":"arxiv","id":"2607.06189","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.06189","created_at":"2026-07-08T01:19:17Z"},{"alias_kind":"arxiv_version","alias_value":"2607.06189v1","created_at":"2026-07-08T01:19:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06189","created_at":"2026-07-08T01:19:17Z"},{"alias_kind":"pith_short_12","alias_value":"OYGDEFGG6MY5","created_at":"2026-07-08T01:19:17Z"},{"alias_kind":"pith_short_16","alias_value":"OYGDEFGG6MY5YR77","created_at":"2026-07-08T01:19:17Z"},{"alias_kind":"pith_short_8","alias_value":"OYGDEFGG","created_at":"2026-07-08T01:19:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:OYGDEFGG6MY5YR77OACPY4SMDE","target":"record","payload":{"canonical_record":{"source":{"id":"2607.06189","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AG","submitted_at":"2026-07-07T12:11:49Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"2cc33d336306255fd8b02645d292901700d923e71d78d9f2e87bd9b4311f1681","abstract_canon_sha256":"64d0d9316d21b4aa548160901a2fa9774b69cd15f5568b32afc8129282567c21"},"schema_version":"1.0"},"canonical_sha256":"760c3214c6f331dc47ff7004fc724c191b5629f00447ecd83a10e7075a0cb895","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-08T01:19:17.026711Z","signature_b64":"3b43uVD07QYsD1xcoJXwGoaFadOnEcC+3O4ANwQA54zk0G6NrgB6nuO8nWjCU8Tsb2ToE61NFItvfBDbKeSqBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"760c3214c6f331dc47ff7004fc724c191b5629f00447ecd83a10e7075a0cb895","last_reissued_at":"2026-07-08T01:19:17.026187Z","signature_status":"signed_v1","first_computed_at":"2026-07-08T01:19:17.026187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.06189","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":"2026-07-08T01:19:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FIhcXv6tX7334wkB4QvAW5tGVtveDzOXSZv3xtj/1e0vgE44MaPpOmWfdfTfmKvd9p64DKVyivrCw1qikkv0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T09:44:21.435624Z"},"content_sha256":"7ba98957e6b9ca1bb7296877591374cb3698a8acee01ada70c12f31085085bc6","schema_version":"1.0","event_id":"sha256:7ba98957e6b9ca1bb7296877591374cb3698a8acee01ada70c12f31085085bc6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:OYGDEFGG6MY5YR77OACPY4SMDE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Motivic quasimap wall-crossing for Grassmannians","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.AG","authors_text":"Siddarth Kannan, Terry Dekun Song","submitted_at":"2026-07-07T12:11:49Z","abstract_excerpt":"We prove a wall-crossing formula for the Euler characteristics, considered as virtual mixed Hodge structures, of moduli spaces of $\\varepsilon$-stable quasimaps to the Grassmannian $\\mathbb{G}(r, N)$. For each $\\varepsilon > 0$, we define a $\\mathbb{Q}$-algebra automorphism of the ring of symmetric functions which takes the generating function for the $\\mathbb{S}_n$-equivariant Euler characteristics of the moduli spaces of stable maps $\\overline{\\mathcal{M}}_{g, n}(\\mathbb{G}(r, N), d)$ to the corresponding generating function for Toda's moduli spaces of $\\varepsilon$-stable quasimaps $\\overli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06189","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.06189/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":"2026-07-08T01:19:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1kUwVWsNvTgArK8ql3Squ/mDwRjHhq5XZTzMB1QjiN8UsMvL0HijT5s0Zar4PbxI/rktI5bPBfHoNQfWhMkeCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T09:44:21.436192Z"},"content_sha256":"5130857bf0674dea55a1d5b86b7b5a8c27e48b39ca05bd7ed601aa7ee1c498b9","schema_version":"1.0","event_id":"sha256:5130857bf0674dea55a1d5b86b7b5a8c27e48b39ca05bd7ed601aa7ee1c498b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OYGDEFGG6MY5YR77OACPY4SMDE/bundle.json","state_url":"https://pith.science/pith/OYGDEFGG6MY5YR77OACPY4SMDE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OYGDEFGG6MY5YR77OACPY4SMDE/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":"2026-08-12T09:44:21Z","links":{"resolver":"https://pith.science/pith/OYGDEFGG6MY5YR77OACPY4SMDE","bundle":"https://pith.science/pith/OYGDEFGG6MY5YR77OACPY4SMDE/bundle.json","state":"https://pith.science/pith/OYGDEFGG6MY5YR77OACPY4SMDE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OYGDEFGG6MY5YR77OACPY4SMDE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:OYGDEFGG6MY5YR77OACPY4SMDE","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":"64d0d9316d21b4aa548160901a2fa9774b69cd15f5568b32afc8129282567c21","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AG","submitted_at":"2026-07-07T12:11:49Z","title_canon_sha256":"2cc33d336306255fd8b02645d292901700d923e71d78d9f2e87bd9b4311f1681"},"schema_version":"1.0","source":{"id":"2607.06189","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.06189","created_at":"2026-07-08T01:19:17Z"},{"alias_kind":"arxiv_version","alias_value":"2607.06189v1","created_at":"2026-07-08T01:19:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06189","created_at":"2026-07-08T01:19:17Z"},{"alias_kind":"pith_short_12","alias_value":"OYGDEFGG6MY5","created_at":"2026-07-08T01:19:17Z"},{"alias_kind":"pith_short_16","alias_value":"OYGDEFGG6MY5YR77","created_at":"2026-07-08T01:19:17Z"},{"alias_kind":"pith_short_8","alias_value":"OYGDEFGG","created_at":"2026-07-08T01:19:17Z"}],"graph_snapshots":[{"event_id":"sha256:5130857bf0674dea55a1d5b86b7b5a8c27e48b39ca05bd7ed601aa7ee1c498b9","target":"graph","created_at":"2026-07-08T01:19:17Z","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/2607.06189/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a wall-crossing formula for the Euler characteristics, considered as virtual mixed Hodge structures, of moduli spaces of $\\varepsilon$-stable quasimaps to the Grassmannian $\\mathbb{G}(r, N)$. For each $\\varepsilon > 0$, we define a $\\mathbb{Q}$-algebra automorphism of the ring of symmetric functions which takes the generating function for the $\\mathbb{S}_n$-equivariant Euler characteristics of the moduli spaces of stable maps $\\overline{\\mathcal{M}}_{g, n}(\\mathbb{G}(r, N), d)$ to the corresponding generating function for Toda's moduli spaces of $\\varepsilon$-stable quasimaps $\\overli","authors_text":"Siddarth Kannan, Terry Dekun Song","cross_cats":["math-ph","math.CO","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AG","submitted_at":"2026-07-07T12:11:49Z","title":"Motivic quasimap wall-crossing for Grassmannians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06189","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":"sha256:7ba98957e6b9ca1bb7296877591374cb3698a8acee01ada70c12f31085085bc6","target":"record","created_at":"2026-07-08T01:19:17Z","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":"64d0d9316d21b4aa548160901a2fa9774b69cd15f5568b32afc8129282567c21","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AG","submitted_at":"2026-07-07T12:11:49Z","title_canon_sha256":"2cc33d336306255fd8b02645d292901700d923e71d78d9f2e87bd9b4311f1681"},"schema_version":"1.0","source":{"id":"2607.06189","kind":"arxiv","version":1}},"canonical_sha256":"760c3214c6f331dc47ff7004fc724c191b5629f00447ecd83a10e7075a0cb895","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"760c3214c6f331dc47ff7004fc724c191b5629f00447ecd83a10e7075a0cb895","first_computed_at":"2026-07-08T01:19:17.026187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-08T01:19:17.026187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3b43uVD07QYsD1xcoJXwGoaFadOnEcC+3O4ANwQA54zk0G6NrgB6nuO8nWjCU8Tsb2ToE61NFItvfBDbKeSqBw==","signature_status":"signed_v1","signed_at":"2026-07-08T01:19:17.026711Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.06189","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ba98957e6b9ca1bb7296877591374cb3698a8acee01ada70c12f31085085bc6","sha256:5130857bf0674dea55a1d5b86b7b5a8c27e48b39ca05bd7ed601aa7ee1c498b9"],"state_sha256":"7e7669d611b079e921210e7092dc39b07afa4f45081d4dc0feba8f4d158cfa19"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s/piiZaEmWht8eabUtHvo8PmMv+JmUU6nh0id2Q2Hj+aRKPZH3IdQNlURDFZ2RAWE2pNzDwmlgbsbg8eCDVJAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T09:44:21.442124Z","bundle_sha256":"8b6464917e7d49af04276790f77001c70304e4444e7d2ff2267b77aa6fe7f849"}}