{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:VOSI74FARX477XHNTTPTTA5EBR","short_pith_number":"pith:VOSI74FA","canonical_record":{"source":{"id":"0809.0305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2008-09-01T19:52:50Z","cross_cats_sorted":[],"title_canon_sha256":"720d81d6af200ca45d94c3e44db5811ba056273aa0ce17ea00a95f3bf0604c0a","abstract_canon_sha256":"20cd513d395975ee508b550683043389ea2270205673daec6110022d33d14ce1"},"schema_version":"1.0"},"canonical_sha256":"aba48ff0a08df9ffdced9cdf3983a40c6af4f046bfedfcae6387f6db8aeac62c","source":{"kind":"arxiv","id":"0809.0305","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.0305","created_at":"2026-05-18T02:15:35Z"},{"alias_kind":"arxiv_version","alias_value":"0809.0305v2","created_at":"2026-05-18T02:15:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.0305","created_at":"2026-05-18T02:15:35Z"},{"alias_kind":"pith_short_12","alias_value":"VOSI74FARX47","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"VOSI74FARX477XHN","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"VOSI74FA","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:VOSI74FARX477XHNTTPTTA5EBR","target":"record","payload":{"canonical_record":{"source":{"id":"0809.0305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2008-09-01T19:52:50Z","cross_cats_sorted":[],"title_canon_sha256":"720d81d6af200ca45d94c3e44db5811ba056273aa0ce17ea00a95f3bf0604c0a","abstract_canon_sha256":"20cd513d395975ee508b550683043389ea2270205673daec6110022d33d14ce1"},"schema_version":"1.0"},"canonical_sha256":"aba48ff0a08df9ffdced9cdf3983a40c6af4f046bfedfcae6387f6db8aeac62c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:15:35.702357Z","signature_b64":"GJlq57iVHecPd+UBBKzgLPHqmby7KYrhrwBO/PRPQkBuYu+qiFmBB+/+LeezzJx7kdV8yOe4m9e/5RHDDNhpCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aba48ff0a08df9ffdced9cdf3983a40c6af4f046bfedfcae6387f6db8aeac62c","last_reissued_at":"2026-05-18T02:15:35.701651Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:15:35.701651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0809.0305","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":"2026-05-18T02:15:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"utrYzjqS4yUvZo3KuNxSw3U1GNVuv0JicoQFpT5mLsPBiWMZ+gK4rxX30c5l4Ox8Xo4ufZNptQ7Z7HHchp+PBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T17:30:13.107818Z"},"content_sha256":"0f1a26b4f1ce31c69da7d2dedfd3a01507e8d8660b4e356325556daa723598df","schema_version":"1.0","event_id":"sha256:0f1a26b4f1ce31c69da7d2dedfd3a01507e8d8660b4e356325556daa723598df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:VOSI74FARX477XHNTTPTTA5EBR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Branes and Quantization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Edward Witten, Sergei Gukov","submitted_at":"2008-09-01T19:52:50Z","abstract_excerpt":"The problem of quantizing a symplectic manifold (M,\\omega) can be formulated in terms of the A-model of a complexification of M. This leads to an interesting new perspective on quantization. From this point of view, the Hilbert space obtained by quantization of (M,\\omega) is the space of (Bcc,B') strings, where Bcc and B' are two A-branes; B' is an ordinary Lagrangian A-brane, and Bcc is a space-filling coisotropic A-brane. B' is supported on M, and the choice of \\omega is encoded in the choice of Bcc. As an example, we describe from this point of view the representations of the group SL(2,R)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.0305","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:15:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2P/lJ421myGoKAZj4z0uFaDdu4nlwjGlXnM05eX7xH+zR4zMmtGfV6poMowYwAhZ40zJJ+fBw3CAWXOlPXTLCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T17:30:13.108413Z"},"content_sha256":"99c73b49c98bba0bfd540cbac465b2e732c86a2a666cac3bfc7911769f436aae","schema_version":"1.0","event_id":"sha256:99c73b49c98bba0bfd540cbac465b2e732c86a2a666cac3bfc7911769f436aae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VOSI74FARX477XHNTTPTTA5EBR/bundle.json","state_url":"https://pith.science/pith/VOSI74FARX477XHNTTPTTA5EBR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VOSI74FARX477XHNTTPTTA5EBR/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":"2026-05-22T17:30:13Z","links":{"resolver":"https://pith.science/pith/VOSI74FARX477XHNTTPTTA5EBR","bundle":"https://pith.science/pith/VOSI74FARX477XHNTTPTTA5EBR/bundle.json","state":"https://pith.science/pith/VOSI74FARX477XHNTTPTTA5EBR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VOSI74FARX477XHNTTPTTA5EBR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:VOSI74FARX477XHNTTPTTA5EBR","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":"20cd513d395975ee508b550683043389ea2270205673daec6110022d33d14ce1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2008-09-01T19:52:50Z","title_canon_sha256":"720d81d6af200ca45d94c3e44db5811ba056273aa0ce17ea00a95f3bf0604c0a"},"schema_version":"1.0","source":{"id":"0809.0305","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.0305","created_at":"2026-05-18T02:15:35Z"},{"alias_kind":"arxiv_version","alias_value":"0809.0305v2","created_at":"2026-05-18T02:15:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.0305","created_at":"2026-05-18T02:15:35Z"},{"alias_kind":"pith_short_12","alias_value":"VOSI74FARX47","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"VOSI74FARX477XHN","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"VOSI74FA","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:99c73b49c98bba0bfd540cbac465b2e732c86a2a666cac3bfc7911769f436aae","target":"graph","created_at":"2026-05-18T02:15:35Z","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"},"paper":{"abstract_excerpt":"The problem of quantizing a symplectic manifold (M,\\omega) can be formulated in terms of the A-model of a complexification of M. This leads to an interesting new perspective on quantization. From this point of view, the Hilbert space obtained by quantization of (M,\\omega) is the space of (Bcc,B') strings, where Bcc and B' are two A-branes; B' is an ordinary Lagrangian A-brane, and Bcc is a space-filling coisotropic A-brane. B' is supported on M, and the choice of \\omega is encoded in the choice of Bcc. As an example, we describe from this point of view the representations of the group SL(2,R).","authors_text":"Edward Witten, Sergei Gukov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2008-09-01T19:52:50Z","title":"Branes and Quantization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.0305","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":"sha256:0f1a26b4f1ce31c69da7d2dedfd3a01507e8d8660b4e356325556daa723598df","target":"record","created_at":"2026-05-18T02:15:35Z","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":"20cd513d395975ee508b550683043389ea2270205673daec6110022d33d14ce1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2008-09-01T19:52:50Z","title_canon_sha256":"720d81d6af200ca45d94c3e44db5811ba056273aa0ce17ea00a95f3bf0604c0a"},"schema_version":"1.0","source":{"id":"0809.0305","kind":"arxiv","version":2}},"canonical_sha256":"aba48ff0a08df9ffdced9cdf3983a40c6af4f046bfedfcae6387f6db8aeac62c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aba48ff0a08df9ffdced9cdf3983a40c6af4f046bfedfcae6387f6db8aeac62c","first_computed_at":"2026-05-18T02:15:35.701651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:35.701651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GJlq57iVHecPd+UBBKzgLPHqmby7KYrhrwBO/PRPQkBuYu+qiFmBB+/+LeezzJx7kdV8yOe4m9e/5RHDDNhpCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:35.702357Z","signed_message":"canonical_sha256_bytes"},"source_id":"0809.0305","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f1a26b4f1ce31c69da7d2dedfd3a01507e8d8660b4e356325556daa723598df","sha256:99c73b49c98bba0bfd540cbac465b2e732c86a2a666cac3bfc7911769f436aae"],"state_sha256":"bf5244814dbf2613d33adc5effb5e46633c910704b7fadad9e454af854c11a84"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Z5/eArfkgrGg3JNdUWkAhHAVSqbBE5O7SYP8fUidZiw4gGKtFaS6b4kMG310xdwzuwJFf7pWidBNnwaKDk1DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T17:30:13.111766Z","bundle_sha256":"e06ed062a133602450c86f03fbdb3cf454a1816f44be97dfef0562473670021f"}}