{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:6GJF43GO3YFNASS77UBHN3XESG","short_pith_number":"pith:6GJF43GO","canonical_record":{"source":{"id":"2304.00832","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-04-03T09:20:13Z","cross_cats_sorted":["math.AT","math.SG"],"title_canon_sha256":"ec272a70b3d6655e4939439fb51cc90c600bfa176111de03c14ec7cd63a65703","abstract_canon_sha256":"0a8e2e84128943ee1510977d2488c9fcf171cbd9c735e695baed8cba34c84afd"},"schema_version":"1.0"},"canonical_sha256":"f1925e6ccede0ad04a5ffd0276eee491918a4f360b48bfcce8f390b67443b336","source":{"kind":"arxiv","id":"2304.00832","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.00832","created_at":"2026-07-05T05:57:23Z"},{"alias_kind":"arxiv_version","alias_value":"2304.00832v1","created_at":"2026-07-05T05:57:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.00832","created_at":"2026-07-05T05:57:23Z"},{"alias_kind":"pith_short_12","alias_value":"6GJF43GO3YFN","created_at":"2026-07-05T05:57:23Z"},{"alias_kind":"pith_short_16","alias_value":"6GJF43GO3YFNASS7","created_at":"2026-07-05T05:57:23Z"},{"alias_kind":"pith_short_8","alias_value":"6GJF43GO","created_at":"2026-07-05T05:57:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:6GJF43GO3YFNASS77UBHN3XESG","target":"record","payload":{"canonical_record":{"source":{"id":"2304.00832","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-04-03T09:20:13Z","cross_cats_sorted":["math.AT","math.SG"],"title_canon_sha256":"ec272a70b3d6655e4939439fb51cc90c600bfa176111de03c14ec7cd63a65703","abstract_canon_sha256":"0a8e2e84128943ee1510977d2488c9fcf171cbd9c735e695baed8cba34c84afd"},"schema_version":"1.0"},"canonical_sha256":"f1925e6ccede0ad04a5ffd0276eee491918a4f360b48bfcce8f390b67443b336","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:57:23.258094Z","signature_b64":"eqVJW/gqX9W/x2GSEa4Sw1nh1LQpRO4TZjp3TzTMCepvuNbJX9f6rij8dCP6+DgnFw51jTZ4tXTZnnNtI2L4CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1925e6ccede0ad04a5ffd0276eee491918a4f360b48bfcce8f390b67443b336","last_reissued_at":"2026-07-05T05:57:23.257480Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:57:23.257480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2304.00832","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":"2026-07-05T05:57:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W76gGdLl4+FV44vDS0/+5dLvPWrTILAAcNdPGyWANjlvxct3OHSXJgM+fSBTOdBV5a9zVov27YBWhZxhE0YdDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T08:36:49.718949Z"},"content_sha256":"1ceb0918bec2a820726d9b0214bc929249fba22939b9c0aeb6aa7521abb4d3a3","schema_version":"1.0","event_id":"sha256:1ceb0918bec2a820726d9b0214bc929249fba22939b9c0aeb6aa7521abb4d3a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:6GJF43GO3YFNASS77UBHN3XESG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coherent-Constructible Correspondence for Toric Fibrations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT","math.SG"],"primary_cat":"math.AG","authors_text":"Pyongwon Suh, Yuxuan Hu","submitted_at":"2023-04-03T09:20:13Z","abstract_excerpt":"Let $\\Sigma$ be a fan inside the lattice $\\mathbb{Z}^n$, and $\\mathcal{E}:\\mathbb{Z}^n \\rightarrow \\operatorname{Pic}{S}$ be a map of abelian groups. We introduce the notion of a principal toric fibration $\\mathcal{X}_{\\Sigma, \\mathcal{E}}$ over the base scheme $S$, relativizing the usual toric construction for $\\Sigma$. We show that the category of ind-coherent sheaves on such a fibration is equivalent to the global section of the Kashiwara-Schapira stack twisted by a certain local system of categories with stalk $\\operatorname{Ind}\\operatorname{Coh} S$. It is a simultaneous generalization of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.00832","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/2304.00832/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":"2026-07-05T05:57:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aMiAdC1HNeqtVD/pId2fMLn8uEjZw//LJvT7tvK71r5rPZ6rIFyOxohYjozul4WV0B/VgeMmBFiUCDeLwkzmAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T08:36:49.719851Z"},"content_sha256":"1d5875a4a0ce1a731f366ee27b64588d8c72dabbe82c1afb07746738247e5b38","schema_version":"1.0","event_id":"sha256:1d5875a4a0ce1a731f366ee27b64588d8c72dabbe82c1afb07746738247e5b38"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6GJF43GO3YFNASS77UBHN3XESG/bundle.json","state_url":"https://pith.science/pith/6GJF43GO3YFNASS77UBHN3XESG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6GJF43GO3YFNASS77UBHN3XESG/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":"2026-08-12T08:36:49Z","links":{"resolver":"https://pith.science/pith/6GJF43GO3YFNASS77UBHN3XESG","bundle":"https://pith.science/pith/6GJF43GO3YFNASS77UBHN3XESG/bundle.json","state":"https://pith.science/pith/6GJF43GO3YFNASS77UBHN3XESG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6GJF43GO3YFNASS77UBHN3XESG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:6GJF43GO3YFNASS77UBHN3XESG","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":"0a8e2e84128943ee1510977d2488c9fcf171cbd9c735e695baed8cba34c84afd","cross_cats_sorted":["math.AT","math.SG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-04-03T09:20:13Z","title_canon_sha256":"ec272a70b3d6655e4939439fb51cc90c600bfa176111de03c14ec7cd63a65703"},"schema_version":"1.0","source":{"id":"2304.00832","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.00832","created_at":"2026-07-05T05:57:23Z"},{"alias_kind":"arxiv_version","alias_value":"2304.00832v1","created_at":"2026-07-05T05:57:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.00832","created_at":"2026-07-05T05:57:23Z"},{"alias_kind":"pith_short_12","alias_value":"6GJF43GO3YFN","created_at":"2026-07-05T05:57:23Z"},{"alias_kind":"pith_short_16","alias_value":"6GJF43GO3YFNASS7","created_at":"2026-07-05T05:57:23Z"},{"alias_kind":"pith_short_8","alias_value":"6GJF43GO","created_at":"2026-07-05T05:57:23Z"}],"graph_snapshots":[{"event_id":"sha256:1d5875a4a0ce1a731f366ee27b64588d8c72dabbe82c1afb07746738247e5b38","target":"graph","created_at":"2026-07-05T05:57:23Z","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/2304.00832/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\Sigma$ be a fan inside the lattice $\\mathbb{Z}^n$, and $\\mathcal{E}:\\mathbb{Z}^n \\rightarrow \\operatorname{Pic}{S}$ be a map of abelian groups. We introduce the notion of a principal toric fibration $\\mathcal{X}_{\\Sigma, \\mathcal{E}}$ over the base scheme $S$, relativizing the usual toric construction for $\\Sigma$. We show that the category of ind-coherent sheaves on such a fibration is equivalent to the global section of the Kashiwara-Schapira stack twisted by a certain local system of categories with stalk $\\operatorname{Ind}\\operatorname{Coh} S$. It is a simultaneous generalization of","authors_text":"Pyongwon Suh, Yuxuan Hu","cross_cats":["math.AT","math.SG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-04-03T09:20:13Z","title":"Coherent-Constructible Correspondence for Toric Fibrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.00832","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":"sha256:1ceb0918bec2a820726d9b0214bc929249fba22939b9c0aeb6aa7521abb4d3a3","target":"record","created_at":"2026-07-05T05:57:23Z","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":"0a8e2e84128943ee1510977d2488c9fcf171cbd9c735e695baed8cba34c84afd","cross_cats_sorted":["math.AT","math.SG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-04-03T09:20:13Z","title_canon_sha256":"ec272a70b3d6655e4939439fb51cc90c600bfa176111de03c14ec7cd63a65703"},"schema_version":"1.0","source":{"id":"2304.00832","kind":"arxiv","version":1}},"canonical_sha256":"f1925e6ccede0ad04a5ffd0276eee491918a4f360b48bfcce8f390b67443b336","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1925e6ccede0ad04a5ffd0276eee491918a4f360b48bfcce8f390b67443b336","first_computed_at":"2026-07-05T05:57:23.257480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:57:23.257480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eqVJW/gqX9W/x2GSEa4Sw1nh1LQpRO4TZjp3TzTMCepvuNbJX9f6rij8dCP6+DgnFw51jTZ4tXTZnnNtI2L4CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:57:23.258094Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.00832","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ceb0918bec2a820726d9b0214bc929249fba22939b9c0aeb6aa7521abb4d3a3","sha256:1d5875a4a0ce1a731f366ee27b64588d8c72dabbe82c1afb07746738247e5b38"],"state_sha256":"32dce03a16ac7b1631534c5eaa4bba9dabd65bfac39723cd18e597b9eb1ec164"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F+f7PDJmPO5iuzN2yNqnlohsTIGGUl4zmDBj+Tvx8vw/7vCwSBGXQXHCktxKjdpwOKvh0VaxykdLr0S4xqX5Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T08:36:49.731260Z","bundle_sha256":"e682b433716eb53cdc112d0661d68d0bc96990e8baaf239f619477d7d9831c54"}}