{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:UUHOLK6GTQULHEPUK4GBE3OMCC","short_pith_number":"pith:UUHOLK6G","canonical_record":{"source":{"id":"2107.12251","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-07-26T14:55:29Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"2e25904ae30ee54be616dd82e772425beebf6b5462e9de589c7ef85bca303846","abstract_canon_sha256":"56d010734125837afebaec01c78d7b180a67f5098f887aff1c4169f5bec9a08b"},"schema_version":"1.0"},"canonical_sha256":"a50ee5abc69c28b391f4570c126dcc108f7efbda30248b6003b636b0ca9895a8","source":{"kind":"arxiv","id":"2107.12251","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.12251","created_at":"2026-07-05T03:04:27Z"},{"alias_kind":"arxiv_version","alias_value":"2107.12251v2","created_at":"2026-07-05T03:04:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.12251","created_at":"2026-07-05T03:04:27Z"},{"alias_kind":"pith_short_12","alias_value":"UUHOLK6GTQUL","created_at":"2026-07-05T03:04:27Z"},{"alias_kind":"pith_short_16","alias_value":"UUHOLK6GTQULHEPU","created_at":"2026-07-05T03:04:27Z"},{"alias_kind":"pith_short_8","alias_value":"UUHOLK6G","created_at":"2026-07-05T03:04:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:UUHOLK6GTQULHEPUK4GBE3OMCC","target":"record","payload":{"canonical_record":{"source":{"id":"2107.12251","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-07-26T14:55:29Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"2e25904ae30ee54be616dd82e772425beebf6b5462e9de589c7ef85bca303846","abstract_canon_sha256":"56d010734125837afebaec01c78d7b180a67f5098f887aff1c4169f5bec9a08b"},"schema_version":"1.0"},"canonical_sha256":"a50ee5abc69c28b391f4570c126dcc108f7efbda30248b6003b636b0ca9895a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:04:27.620756Z","signature_b64":"QZg74AjDSx4rrHe4G5OtSXxut8jNl5seX0KhFfERq16ciBzctWsmpYcHMgxbROVS60TrfQ5z9x+hEpSupDu4DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a50ee5abc69c28b391f4570c126dcc108f7efbda30248b6003b636b0ca9895a8","last_reissued_at":"2026-07-05T03:04:27.620369Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:04:27.620369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2107.12251","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:04:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JaxDZJk+vp8jQjWZC9WTZNXMsYQpuLPKTiJJvF0upx+PzKTSxjFKs5aVqJ8fiF7D1YkdOuzrER4LZLB2Q1ZMBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T14:35:53.747945Z"},"content_sha256":"952201de2d20ba442fb97a729aee96466a1142db89ba861f886526bfd17e1731","schema_version":"1.0","event_id":"sha256:952201de2d20ba442fb97a729aee96466a1142db89ba861f886526bfd17e1731"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:UUHOLK6GTQULHEPUK4GBE3OMCC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Probing Quantization Via Branes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"hep-th","authors_text":"Davide Gaiotto, Edward Witten","submitted_at":"2021-07-26T14:55:29Z","abstract_excerpt":"We re-examine quantization via branes with the goal of understanding its relation to geometric quantization. If a symplectic manifold $M$ can be quantized in geometric quantization using a polarization ${\\mathcal P}$, and in brane quantization using a complexification $Y$, then the two quantizations agree if ${\\mathcal P}$ can be analytically continued to a holomorphic polarization of $Y$. We also show, roughly, that the automorphism group of $M$ that is realized as a group of symmetries in brane quantization of $M$ is the group of symplectomorphisms of $M$ that can be analytically continued t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.12251","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2107.12251/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":"2026-07-05T03:04:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vb+5yB35n6JvZ670ZYRSeQxd6Jlk7JAjtmBa+WNPlDnPFZGf6gP+ML7G6MXHmHidM7PTxjF2aWJEhhJqoX1aAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T14:35:53.748463Z"},"content_sha256":"dffa089fc48c3d8f76571dc8de4f4e794a6132d858ceb5d2ff4a08c1452f58f7","schema_version":"1.0","event_id":"sha256:dffa089fc48c3d8f76571dc8de4f4e794a6132d858ceb5d2ff4a08c1452f58f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UUHOLK6GTQULHEPUK4GBE3OMCC/bundle.json","state_url":"https://pith.science/pith/UUHOLK6GTQULHEPUK4GBE3OMCC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UUHOLK6GTQULHEPUK4GBE3OMCC/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":"2026-08-14T14:35:53Z","links":{"resolver":"https://pith.science/pith/UUHOLK6GTQULHEPUK4GBE3OMCC","bundle":"https://pith.science/pith/UUHOLK6GTQULHEPUK4GBE3OMCC/bundle.json","state":"https://pith.science/pith/UUHOLK6GTQULHEPUK4GBE3OMCC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UUHOLK6GTQULHEPUK4GBE3OMCC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:UUHOLK6GTQULHEPUK4GBE3OMCC","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":"56d010734125837afebaec01c78d7b180a67f5098f887aff1c4169f5bec9a08b","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-07-26T14:55:29Z","title_canon_sha256":"2e25904ae30ee54be616dd82e772425beebf6b5462e9de589c7ef85bca303846"},"schema_version":"1.0","source":{"id":"2107.12251","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.12251","created_at":"2026-07-05T03:04:27Z"},{"alias_kind":"arxiv_version","alias_value":"2107.12251v2","created_at":"2026-07-05T03:04:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.12251","created_at":"2026-07-05T03:04:27Z"},{"alias_kind":"pith_short_12","alias_value":"UUHOLK6GTQUL","created_at":"2026-07-05T03:04:27Z"},{"alias_kind":"pith_short_16","alias_value":"UUHOLK6GTQULHEPU","created_at":"2026-07-05T03:04:27Z"},{"alias_kind":"pith_short_8","alias_value":"UUHOLK6G","created_at":"2026-07-05T03:04:27Z"}],"graph_snapshots":[{"event_id":"sha256:dffa089fc48c3d8f76571dc8de4f4e794a6132d858ceb5d2ff4a08c1452f58f7","target":"graph","created_at":"2026-07-05T03:04:27Z","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/2107.12251/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We re-examine quantization via branes with the goal of understanding its relation to geometric quantization. If a symplectic manifold $M$ can be quantized in geometric quantization using a polarization ${\\mathcal P}$, and in brane quantization using a complexification $Y$, then the two quantizations agree if ${\\mathcal P}$ can be analytically continued to a holomorphic polarization of $Y$. We also show, roughly, that the automorphism group of $M$ that is realized as a group of symmetries in brane quantization of $M$ is the group of symplectomorphisms of $M$ that can be analytically continued t","authors_text":"Davide Gaiotto, Edward Witten","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-07-26T14:55:29Z","title":"Probing Quantization Via Branes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.12251","kind":"arxiv","version":2},"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":"sha256:952201de2d20ba442fb97a729aee96466a1142db89ba861f886526bfd17e1731","target":"record","created_at":"2026-07-05T03:04:27Z","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":"56d010734125837afebaec01c78d7b180a67f5098f887aff1c4169f5bec9a08b","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-07-26T14:55:29Z","title_canon_sha256":"2e25904ae30ee54be616dd82e772425beebf6b5462e9de589c7ef85bca303846"},"schema_version":"1.0","source":{"id":"2107.12251","kind":"arxiv","version":2}},"canonical_sha256":"a50ee5abc69c28b391f4570c126dcc108f7efbda30248b6003b636b0ca9895a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a50ee5abc69c28b391f4570c126dcc108f7efbda30248b6003b636b0ca9895a8","first_computed_at":"2026-07-05T03:04:27.620369Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:04:27.620369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QZg74AjDSx4rrHe4G5OtSXxut8jNl5seX0KhFfERq16ciBzctWsmpYcHMgxbROVS60TrfQ5z9x+hEpSupDu4DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:04:27.620756Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.12251","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:952201de2d20ba442fb97a729aee96466a1142db89ba861f886526bfd17e1731","sha256:dffa089fc48c3d8f76571dc8de4f4e794a6132d858ceb5d2ff4a08c1452f58f7"],"state_sha256":"1f8dbc907ac4f7598f2e410e272142ef41b66d5a4d96488094fb897a46163eb1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"41PUznOYATVel0C18nWgNHWs0x5QXkSHavxNUnU58lNnzofygQnQvuybZtAGLdS0Q8rdMgtRgtx74fIvIHMJDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T14:35:53.752812Z","bundle_sha256":"adb53f0098f067e7579b4706fe205ae66bcd7b71aa0c88a0db1647f11a0cbf96"}}