{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1993:VVEVTTTHIA2DIGYIAIJV3H4U6X","short_pith_number":"pith:VVEVTTTH","canonical_record":{"source":{"id":"hep-th/9305115","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1993-05-24T00:01:00Z","cross_cats_sorted":[],"title_canon_sha256":"7c0b79eb05d49aec2243eac60662be0b2e575bcd89347930738ce60157306cc4","abstract_canon_sha256":"81f23a96d4afeaec3b458a19f55e33c91f903d4f7a2cf8f5165c707da1abc3cd"},"schema_version":"1.0"},"canonical_sha256":"ad4959ce674034341b0802135d9f94f5f392e200883102066b2cffb9499c68ae","source":{"kind":"arxiv","id":"hep-th/9305115","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9305115","created_at":"2026-05-18T04:37:43Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9305115v2","created_at":"2026-05-18T04:37:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9305115","created_at":"2026-05-18T04:37:43Z"},{"alias_kind":"pith_short_12","alias_value":"VVEVTTTHIA2D","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"VVEVTTTHIA2DIGYI","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"VVEVTTTH","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1993:VVEVTTTHIA2DIGYIAIJV3H4U6X","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9305115","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1993-05-24T00:01:00Z","cross_cats_sorted":[],"title_canon_sha256":"7c0b79eb05d49aec2243eac60662be0b2e575bcd89347930738ce60157306cc4","abstract_canon_sha256":"81f23a96d4afeaec3b458a19f55e33c91f903d4f7a2cf8f5165c707da1abc3cd"},"schema_version":"1.0"},"canonical_sha256":"ad4959ce674034341b0802135d9f94f5f392e200883102066b2cffb9499c68ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:37:43.418265Z","signature_b64":"4S9ApOW9uKbHbTy6PZKCy83eaf2JzCnD37PbFTioJhzefFX3k5pOSCrPsnZw8fZXEAkVdlIHY1xm+XR1URWdAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad4959ce674034341b0802135d9f94f5f392e200883102066b2cffb9499c68ae","last_reissued_at":"2026-05-18T04:37:43.417711Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:37:43.417711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9305115","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":"2026-05-18T04:37:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7+E4fnxdLxBdkGVQsPdS9hoGvbV9QtYJvBjstlrKM5uHSljM4RaVkbyeIYFgpuJHVMmkEqCu13n/Bg0ON5ilCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:03:42.702736Z"},"content_sha256":"165d66a00f5fe38dfac70071ea4bbfa6c0c567e43e54f3eb5c3f91861cdb0f5c","schema_version":"1.0","event_id":"sha256:165d66a00f5fe38dfac70071ea4bbfa6c0c567e43e54f3eb5c3f91861cdb0f5c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1993:VVEVTTTHIA2DIGYIAIJV3H4U6X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological closed-string interpretation of Chern-Simons theory","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Vipul Periwal","submitted_at":"1993-05-24T00:01:00Z","abstract_excerpt":"The exact free energy of SU($N$) Chern-Simons theory at level $k$ is expanded in powers of $(N+k)^{-2}.$ This expansion keeps rank-level duality manifest, and simplifies as $k$ becomes large, keeping $N$ fixed (or vice versa)---this is the weak-coupling (strong-coupling) limit. With the standard normalization, the free energy on the three-sphere in this limit is shown to be the generating function of the Euler characteristics of the moduli spaces of surfaces of genus $g,$ providing a string interpretation for the perturbative expansion. A similar expansion is found for the three-torus, with di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9305115","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":"2026-05-18T04:37:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hh9xg3tGl/q81GyrqXTeiXkQrUldUxSZywTsxQih9cJp1a7p58DgNNvotikMdd1gGLgmW6LuY+Qj6KNoVl7lAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:03:42.703136Z"},"content_sha256":"5680c639c598b67101047704ec1ff095f24d476bb0f7848d5582087fe4833982","schema_version":"1.0","event_id":"sha256:5680c639c598b67101047704ec1ff095f24d476bb0f7848d5582087fe4833982"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VVEVTTTHIA2DIGYIAIJV3H4U6X/bundle.json","state_url":"https://pith.science/pith/VVEVTTTHIA2DIGYIAIJV3H4U6X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VVEVTTTHIA2DIGYIAIJV3H4U6X/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":"2026-06-04T15:03:42Z","links":{"resolver":"https://pith.science/pith/VVEVTTTHIA2DIGYIAIJV3H4U6X","bundle":"https://pith.science/pith/VVEVTTTHIA2DIGYIAIJV3H4U6X/bundle.json","state":"https://pith.science/pith/VVEVTTTHIA2DIGYIAIJV3H4U6X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VVEVTTTHIA2DIGYIAIJV3H4U6X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:VVEVTTTHIA2DIGYIAIJV3H4U6X","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":"81f23a96d4afeaec3b458a19f55e33c91f903d4f7a2cf8f5165c707da1abc3cd","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1993-05-24T00:01:00Z","title_canon_sha256":"7c0b79eb05d49aec2243eac60662be0b2e575bcd89347930738ce60157306cc4"},"schema_version":"1.0","source":{"id":"hep-th/9305115","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9305115","created_at":"2026-05-18T04:37:43Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9305115v2","created_at":"2026-05-18T04:37:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9305115","created_at":"2026-05-18T04:37:43Z"},{"alias_kind":"pith_short_12","alias_value":"VVEVTTTHIA2D","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"VVEVTTTHIA2DIGYI","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"VVEVTTTH","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:5680c639c598b67101047704ec1ff095f24d476bb0f7848d5582087fe4833982","target":"graph","created_at":"2026-05-18T04:37:43Z","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 exact free energy of SU($N$) Chern-Simons theory at level $k$ is expanded in powers of $(N+k)^{-2}.$ This expansion keeps rank-level duality manifest, and simplifies as $k$ becomes large, keeping $N$ fixed (or vice versa)---this is the weak-coupling (strong-coupling) limit. With the standard normalization, the free energy on the three-sphere in this limit is shown to be the generating function of the Euler characteristics of the moduli spaces of surfaces of genus $g,$ providing a string interpretation for the perturbative expansion. A similar expansion is found for the three-torus, with di","authors_text":"Vipul Periwal","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1993-05-24T00:01:00Z","title":"Topological closed-string interpretation of Chern-Simons theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9305115","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":"sha256:165d66a00f5fe38dfac70071ea4bbfa6c0c567e43e54f3eb5c3f91861cdb0f5c","target":"record","created_at":"2026-05-18T04:37:43Z","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":"81f23a96d4afeaec3b458a19f55e33c91f903d4f7a2cf8f5165c707da1abc3cd","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1993-05-24T00:01:00Z","title_canon_sha256":"7c0b79eb05d49aec2243eac60662be0b2e575bcd89347930738ce60157306cc4"},"schema_version":"1.0","source":{"id":"hep-th/9305115","kind":"arxiv","version":2}},"canonical_sha256":"ad4959ce674034341b0802135d9f94f5f392e200883102066b2cffb9499c68ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad4959ce674034341b0802135d9f94f5f392e200883102066b2cffb9499c68ae","first_computed_at":"2026-05-18T04:37:43.417711Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:37:43.417711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4S9ApOW9uKbHbTy6PZKCy83eaf2JzCnD37PbFTioJhzefFX3k5pOSCrPsnZw8fZXEAkVdlIHY1xm+XR1URWdAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:37:43.418265Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9305115","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:165d66a00f5fe38dfac70071ea4bbfa6c0c567e43e54f3eb5c3f91861cdb0f5c","sha256:5680c639c598b67101047704ec1ff095f24d476bb0f7848d5582087fe4833982"],"state_sha256":"cf88015515be590c94ff24395c76f970ad0699ee115c2651a20b8a7d6f714b2a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qWFwJjySwY8DkGkEAJapA+cqBxx2BGdu7BP9GXf28x6QYGranjERYBCtSgZiFKZpFifgfvM14p74BlzLP/mWDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T15:03:42.706279Z","bundle_sha256":"55cd92b97d828db61f11923d0b56769039bca54fd86d4dd1945d3f6291aa5533"}}