{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:XJNKNPBDYKNHUKTDPCLFPX5DTG","short_pith_number":"pith:XJNKNPBD","schema_version":"1.0","canonical_sha256":"ba5aa6bc23c29a7a2a63789657dfa399bc672a6cab3699ed9d052efd2ba337d7","source":{"kind":"arxiv","id":"1607.04503","version":2},"attestation_state":"computed","paper":{"title":"Formal gluing along non-linear flags","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Benjamin Hennion, Gabriele Vezzosi, Mauro Porta","submitted_at":"2016-07-15T13:30:31Z","abstract_excerpt":"In this paper we prove formal glueing along an arbitrary closed substack $Z$ of an arbitrary Artin stack $X$ (locally of finite type over a field $k$), for the stacks of (almost) perfect complexes , and of $G$-bundles on $X$ (for $G$ a smooth affine algebraic $k$-group scheme). By iterating this result, we get a decomposition of these stacks along an arbitrary nonlinear flag of closed substacks in $X$. By taking points over the base field, we deduce from this both a formal glueing, and a flag-related decomposition formula for the corresponding symmetric monoidal derived $\\infty$-categories of "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1607.04503","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-15T13:30:31Z","cross_cats_sorted":[],"title_canon_sha256":"1a6df41cad1872fadbe91baebcadf01922a0eba839fdf69cfa479b7ef279d0ae","abstract_canon_sha256":"139e38e04062ece6b17901b0b8b451d661e3fba7465a80ff4fb44eae5270f7c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:12.471272Z","signature_b64":"3bw2JGUDeAIoNDhJhcI5iyWCR4sskKSjo4QuGLyCO9kPAau91ZIH44QbmUfzphB0QijcsfKt/4x/akZj20nbDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba5aa6bc23c29a7a2a63789657dfa399bc672a6cab3699ed9d052efd2ba337d7","last_reissued_at":"2026-05-18T01:02:12.470671Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:12.470671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Formal gluing along non-linear flags","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Benjamin Hennion, Gabriele Vezzosi, Mauro Porta","submitted_at":"2016-07-15T13:30:31Z","abstract_excerpt":"In this paper we prove formal glueing along an arbitrary closed substack $Z$ of an arbitrary Artin stack $X$ (locally of finite type over a field $k$), for the stacks of (almost) perfect complexes , and of $G$-bundles on $X$ (for $G$ a smooth affine algebraic $k$-group scheme). By iterating this result, we get a decomposition of these stacks along an arbitrary nonlinear flag of closed substacks in $X$. By taking points over the base field, we deduce from this both a formal glueing, and a flag-related decomposition formula for the corresponding symmetric monoidal derived $\\infty$-categories of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04503","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1607.04503","created_at":"2026-05-18T01:02:12.470756+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.04503v2","created_at":"2026-05-18T01:02:12.470756+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04503","created_at":"2026-05-18T01:02:12.470756+00:00"},{"alias_kind":"pith_short_12","alias_value":"XJNKNPBDYKNH","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XJNKNPBDYKNHUKTD","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XJNKNPBD","created_at":"2026-05-18T12:30:51.357362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XJNKNPBDYKNHUKTDPCLFPX5DTG","json":"https://pith.science/pith/XJNKNPBDYKNHUKTDPCLFPX5DTG.json","graph_json":"https://pith.science/api/pith-number/XJNKNPBDYKNHUKTDPCLFPX5DTG/graph.json","events_json":"https://pith.science/api/pith-number/XJNKNPBDYKNHUKTDPCLFPX5DTG/events.json","paper":"https://pith.science/paper/XJNKNPBD"},"agent_actions":{"view_html":"https://pith.science/pith/XJNKNPBDYKNHUKTDPCLFPX5DTG","download_json":"https://pith.science/pith/XJNKNPBDYKNHUKTDPCLFPX5DTG.json","view_paper":"https://pith.science/paper/XJNKNPBD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.04503&json=true","fetch_graph":"https://pith.science/api/pith-number/XJNKNPBDYKNHUKTDPCLFPX5DTG/graph.json","fetch_events":"https://pith.science/api/pith-number/XJNKNPBDYKNHUKTDPCLFPX5DTG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XJNKNPBDYKNHUKTDPCLFPX5DTG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XJNKNPBDYKNHUKTDPCLFPX5DTG/action/storage_attestation","attest_author":"https://pith.science/pith/XJNKNPBDYKNHUKTDPCLFPX5DTG/action/author_attestation","sign_citation":"https://pith.science/pith/XJNKNPBDYKNHUKTDPCLFPX5DTG/action/citation_signature","submit_replication":"https://pith.science/pith/XJNKNPBDYKNHUKTDPCLFPX5DTG/action/replication_record"}},"created_at":"2026-05-18T01:02:12.470756+00:00","updated_at":"2026-05-18T01:02:12.470756+00:00"}