{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:5KLKKYSINHQZTOTQX5RP5LK4IQ","short_pith_number":"pith:5KLKKYSI","canonical_record":{"source":{"id":"2508.18248","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-08-25T17:39:44Z","cross_cats_sorted":["hep-th","math.QA"],"title_canon_sha256":"6a493b7f978a159409662e717bfd6dd0fc831b8d6559ba9c3a6ca1c99a1ee682","abstract_canon_sha256":"9fd7a58d450f34ea24facb3f42b4db3aacaf4251d35b0195e1edb707f31f9cd3"},"schema_version":"1.0"},"canonical_sha256":"ea96a5624869e199ba70bf62fead5c443b98916cd45c1de360fb2d7c01c5fb6f","source":{"kind":"arxiv","id":"2508.18248","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.18248","created_at":"2026-07-05T11:58:56Z"},{"alias_kind":"arxiv_version","alias_value":"2508.18248v1","created_at":"2026-07-05T11:58:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.18248","created_at":"2026-07-05T11:58:56Z"},{"alias_kind":"pith_short_12","alias_value":"5KLKKYSINHQZ","created_at":"2026-07-05T11:58:56Z"},{"alias_kind":"pith_short_16","alias_value":"5KLKKYSINHQZTOTQ","created_at":"2026-07-05T11:58:56Z"},{"alias_kind":"pith_short_8","alias_value":"5KLKKYSI","created_at":"2026-07-05T11:58:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:5KLKKYSINHQZTOTQX5RP5LK4IQ","target":"record","payload":{"canonical_record":{"source":{"id":"2508.18248","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-08-25T17:39:44Z","cross_cats_sorted":["hep-th","math.QA"],"title_canon_sha256":"6a493b7f978a159409662e717bfd6dd0fc831b8d6559ba9c3a6ca1c99a1ee682","abstract_canon_sha256":"9fd7a58d450f34ea24facb3f42b4db3aacaf4251d35b0195e1edb707f31f9cd3"},"schema_version":"1.0"},"canonical_sha256":"ea96a5624869e199ba70bf62fead5c443b98916cd45c1de360fb2d7c01c5fb6f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:58:56.246220Z","signature_b64":"ycJ9Ntr+t1oy7xR3XPQffXvFMu3l9EwajTcAPkJvUtuhRscsba9ws1s2XKkOIRzdpEQsTuNakFDbva2jlMJvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea96a5624869e199ba70bf62fead5c443b98916cd45c1de360fb2d7c01c5fb6f","last_reissued_at":"2026-07-05T11:58:56.245737Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:58:56.245737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.18248","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":"2026-07-05T11:58:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gxezliqKc71qfAAMpz0Wd8U63mUgRm9r62IapzVoqElTBQh0H2vx+FlNpHlPVO0KjpyiwolbO3PxWeYCsyasAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T10:34:43.368953Z"},"content_sha256":"d433afcae72c9c3d3fecca7dbb3431917accab0101e6f2b6ffd41d5ceaf7fe5b","schema_version":"1.0","event_id":"sha256:d433afcae72c9c3d3fecca7dbb3431917accab0101e6f2b6ffd41d5ceaf7fe5b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:5KLKKYSINHQZTOTQX5RP5LK4IQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inverse Hamiltonian reduction for affine W-algebras in type A","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.QA"],"primary_cat":"math.RT","authors_text":"Dylan Butson, Sujay Nair","submitted_at":"2025-08-25T17:39:44Z","abstract_excerpt":"We give a geometric proof of inverse Hamiltonian reduction for all affine W-algebras in type A at generic level, a certain embedding of the affine W-algebra corresponding to an arbitrary nilpotent in $\\mathfrak{gl}_N$ into that corresponding to a larger nilpotent with respect to the closure order on orbits, tensored with an auxiliary algebra of free fields. We proceed by constructing strict chiral quantizations of equivariant Slodowy slices, sheaves of $\\hbar$-adic vertex algebras on the arc spaces of the slices, and then localizing them on quasi-Darboux open sets. We also provide a generaliza"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.18248","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/2508.18248/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":"2026-07-05T11:58:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZLMdfgktAg409iw2JuYBy7V4Ci32sFaK484mNJGZavk56BbxO5T/oVfEfF91Gvp7VS1X1dKA2ijCoCTaGVTJAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T10:34:43.369696Z"},"content_sha256":"ada7f7d4554be707ac73f472e655aef4ccf872f611ab4e2515a1855413114c31","schema_version":"1.0","event_id":"sha256:ada7f7d4554be707ac73f472e655aef4ccf872f611ab4e2515a1855413114c31"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5KLKKYSINHQZTOTQX5RP5LK4IQ/bundle.json","state_url":"https://pith.science/pith/5KLKKYSINHQZTOTQX5RP5LK4IQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5KLKKYSINHQZTOTQX5RP5LK4IQ/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":"2026-08-21T10:34:43Z","links":{"resolver":"https://pith.science/pith/5KLKKYSINHQZTOTQX5RP5LK4IQ","bundle":"https://pith.science/pith/5KLKKYSINHQZTOTQX5RP5LK4IQ/bundle.json","state":"https://pith.science/pith/5KLKKYSINHQZTOTQX5RP5LK4IQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5KLKKYSINHQZTOTQX5RP5LK4IQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:5KLKKYSINHQZTOTQX5RP5LK4IQ","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":"9fd7a58d450f34ea24facb3f42b4db3aacaf4251d35b0195e1edb707f31f9cd3","cross_cats_sorted":["hep-th","math.QA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-08-25T17:39:44Z","title_canon_sha256":"6a493b7f978a159409662e717bfd6dd0fc831b8d6559ba9c3a6ca1c99a1ee682"},"schema_version":"1.0","source":{"id":"2508.18248","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.18248","created_at":"2026-07-05T11:58:56Z"},{"alias_kind":"arxiv_version","alias_value":"2508.18248v1","created_at":"2026-07-05T11:58:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.18248","created_at":"2026-07-05T11:58:56Z"},{"alias_kind":"pith_short_12","alias_value":"5KLKKYSINHQZ","created_at":"2026-07-05T11:58:56Z"},{"alias_kind":"pith_short_16","alias_value":"5KLKKYSINHQZTOTQ","created_at":"2026-07-05T11:58:56Z"},{"alias_kind":"pith_short_8","alias_value":"5KLKKYSI","created_at":"2026-07-05T11:58:56Z"}],"graph_snapshots":[{"event_id":"sha256:ada7f7d4554be707ac73f472e655aef4ccf872f611ab4e2515a1855413114c31","target":"graph","created_at":"2026-07-05T11:58:56Z","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/2508.18248/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a geometric proof of inverse Hamiltonian reduction for all affine W-algebras in type A at generic level, a certain embedding of the affine W-algebra corresponding to an arbitrary nilpotent in $\\mathfrak{gl}_N$ into that corresponding to a larger nilpotent with respect to the closure order on orbits, tensored with an auxiliary algebra of free fields. We proceed by constructing strict chiral quantizations of equivariant Slodowy slices, sheaves of $\\hbar$-adic vertex algebras on the arc spaces of the slices, and then localizing them on quasi-Darboux open sets. We also provide a generaliza","authors_text":"Dylan Butson, Sujay Nair","cross_cats":["hep-th","math.QA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-08-25T17:39:44Z","title":"Inverse Hamiltonian reduction for affine W-algebras in type A"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.18248","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:d433afcae72c9c3d3fecca7dbb3431917accab0101e6f2b6ffd41d5ceaf7fe5b","target":"record","created_at":"2026-07-05T11:58:56Z","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":"9fd7a58d450f34ea24facb3f42b4db3aacaf4251d35b0195e1edb707f31f9cd3","cross_cats_sorted":["hep-th","math.QA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-08-25T17:39:44Z","title_canon_sha256":"6a493b7f978a159409662e717bfd6dd0fc831b8d6559ba9c3a6ca1c99a1ee682"},"schema_version":"1.0","source":{"id":"2508.18248","kind":"arxiv","version":1}},"canonical_sha256":"ea96a5624869e199ba70bf62fead5c443b98916cd45c1de360fb2d7c01c5fb6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea96a5624869e199ba70bf62fead5c443b98916cd45c1de360fb2d7c01c5fb6f","first_computed_at":"2026-07-05T11:58:56.245737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:58:56.245737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ycJ9Ntr+t1oy7xR3XPQffXvFMu3l9EwajTcAPkJvUtuhRscsba9ws1s2XKkOIRzdpEQsTuNakFDbva2jlMJvBA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:58:56.246220Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.18248","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d433afcae72c9c3d3fecca7dbb3431917accab0101e6f2b6ffd41d5ceaf7fe5b","sha256:ada7f7d4554be707ac73f472e655aef4ccf872f611ab4e2515a1855413114c31"],"state_sha256":"50880362777017c78be3e2a88f46a78c6ea2ec74c80a8a08ce16afcc7c0606f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HPuBEvDEQzPG5BqBYP+Rex8iQAHejxcGN5f91J4EEYNOXo8t3eTPU8mEZoWSskcr0Slgz05x5SBjwg3UtBhvAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T10:34:43.375930Z","bundle_sha256":"e6969d2752b37a24780b77d1e2019d0ef328209de835cfc2f0ba7789e17b7836"}}