{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:C772ZD3NKB5SWV24E32HNVCKXZ","short_pith_number":"pith:C772ZD3N","canonical_record":{"source":{"id":"1505.03130","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-05-12T19:33:32Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"9a82a27b66e63a98f35b856949ce873a1e8617134fb2b52438de62eea0e034da","abstract_canon_sha256":"bd0d36a33edb494e7e46fc5727ac8fe1c39b86f8b2a0c751106fbe1cbcbbbff6"},"schema_version":"1.0"},"canonical_sha256":"17ffac8f6d507b2b575c26f476d44abe637fd9a028a36a9230cf9480d098ed03","source":{"kind":"arxiv","id":"1505.03130","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03130","created_at":"2026-05-18T02:14:08Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03130v1","created_at":"2026-05-18T02:14:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03130","created_at":"2026-05-18T02:14:08Z"},{"alias_kind":"pith_short_12","alias_value":"C772ZD3NKB5S","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"C772ZD3NKB5SWV24","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"C772ZD3N","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:C772ZD3NKB5SWV24E32HNVCKXZ","target":"record","payload":{"canonical_record":{"source":{"id":"1505.03130","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-05-12T19:33:32Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"9a82a27b66e63a98f35b856949ce873a1e8617134fb2b52438de62eea0e034da","abstract_canon_sha256":"bd0d36a33edb494e7e46fc5727ac8fe1c39b86f8b2a0c751106fbe1cbcbbbff6"},"schema_version":"1.0"},"canonical_sha256":"17ffac8f6d507b2b575c26f476d44abe637fd9a028a36a9230cf9480d098ed03","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:14:08.902017Z","signature_b64":"OCTIHSRkUkJp0BwH2SVzNS5y77wNa9G0u4esowjzJcTaSaCXvRSdGhnXC8h3131c8sqjhaaDFN5JPSKcwGobBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17ffac8f6d507b2b575c26f476d44abe637fd9a028a36a9230cf9480d098ed03","last_reissued_at":"2026-05-18T02:14:08.901343Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:14:08.901343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.03130","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":"2026-05-18T02:14:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Nbu7Da4+zVrrALPDlpp2/uSzJbG1dweLTCVgtNOMzX2p1RrCC8HYUv6N+9y9zjDgh+iO8pcjRRXzyYDEMqEDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:59:38.914450Z"},"content_sha256":"575799e9b8f7931dfc135037c75ee53cf469930d4bd5399fcc3b8041244578dd","schema_version":"1.0","event_id":"sha256:575799e9b8f7931dfc135037c75ee53cf469930d4bd5399fcc3b8041244578dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:C772ZD3NKB5SWV24E32HNVCKXZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytic Torsion, 3d Mirror Symmetry And Supergroup Chern-Simons Theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"hep-th","authors_text":"Victor Mikhaylov","submitted_at":"2015-05-12T19:33:32Z","abstract_excerpt":"We consider topological field theories that compute the Reidemeister-Milnor-Turaev torsion in three dimensions. These are the psl(1|1) and the U(1|1) Chern-Simons theories, coupled to a background complex flat gauge field. We use the 3d mirror symmetry to derive the Meng-Taubes theorem, which relates the torsion and the Seiberg-Witten invariants, for a three-manifold with arbitrary first Betti number. We also present the Hamiltonian quantization of our theories, find the modular transformations of states, and various properties of loop operators. Our results for the U(1|1) theory are in genera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03130","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":""},"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":"2026-05-18T02:14:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RnHih4XRG1MohqTpwLUvAtGSMVJGjSztxFFHeGOcMaKRPj1wI+U9EGPMQEUmW70rZMwBd8YyJTwZEN6yFWxTBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:59:38.914813Z"},"content_sha256":"dc7fc2617f29a7103d322bacbb3f155c449841917bc67346a38d643781247a8e","schema_version":"1.0","event_id":"sha256:dc7fc2617f29a7103d322bacbb3f155c449841917bc67346a38d643781247a8e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C772ZD3NKB5SWV24E32HNVCKXZ/bundle.json","state_url":"https://pith.science/pith/C772ZD3NKB5SWV24E32HNVCKXZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C772ZD3NKB5SWV24E32HNVCKXZ/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":"2026-06-02T16:59:38Z","links":{"resolver":"https://pith.science/pith/C772ZD3NKB5SWV24E32HNVCKXZ","bundle":"https://pith.science/pith/C772ZD3NKB5SWV24E32HNVCKXZ/bundle.json","state":"https://pith.science/pith/C772ZD3NKB5SWV24E32HNVCKXZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C772ZD3NKB5SWV24E32HNVCKXZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:C772ZD3NKB5SWV24E32HNVCKXZ","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":"bd0d36a33edb494e7e46fc5727ac8fe1c39b86f8b2a0c751106fbe1cbcbbbff6","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-05-12T19:33:32Z","title_canon_sha256":"9a82a27b66e63a98f35b856949ce873a1e8617134fb2b52438de62eea0e034da"},"schema_version":"1.0","source":{"id":"1505.03130","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03130","created_at":"2026-05-18T02:14:08Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03130v1","created_at":"2026-05-18T02:14:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03130","created_at":"2026-05-18T02:14:08Z"},{"alias_kind":"pith_short_12","alias_value":"C772ZD3NKB5S","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"C772ZD3NKB5SWV24","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"C772ZD3N","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:dc7fc2617f29a7103d322bacbb3f155c449841917bc67346a38d643781247a8e","target":"graph","created_at":"2026-05-18T02:14:08Z","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":"We consider topological field theories that compute the Reidemeister-Milnor-Turaev torsion in three dimensions. These are the psl(1|1) and the U(1|1) Chern-Simons theories, coupled to a background complex flat gauge field. We use the 3d mirror symmetry to derive the Meng-Taubes theorem, which relates the torsion and the Seiberg-Witten invariants, for a three-manifold with arbitrary first Betti number. We also present the Hamiltonian quantization of our theories, find the modular transformations of states, and various properties of loop operators. Our results for the U(1|1) theory are in genera","authors_text":"Victor Mikhaylov","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-05-12T19:33:32Z","title":"Analytic Torsion, 3d Mirror Symmetry And Supergroup Chern-Simons Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03130","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":"sha256:575799e9b8f7931dfc135037c75ee53cf469930d4bd5399fcc3b8041244578dd","target":"record","created_at":"2026-05-18T02:14:08Z","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":"bd0d36a33edb494e7e46fc5727ac8fe1c39b86f8b2a0c751106fbe1cbcbbbff6","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-05-12T19:33:32Z","title_canon_sha256":"9a82a27b66e63a98f35b856949ce873a1e8617134fb2b52438de62eea0e034da"},"schema_version":"1.0","source":{"id":"1505.03130","kind":"arxiv","version":1}},"canonical_sha256":"17ffac8f6d507b2b575c26f476d44abe637fd9a028a36a9230cf9480d098ed03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17ffac8f6d507b2b575c26f476d44abe637fd9a028a36a9230cf9480d098ed03","first_computed_at":"2026-05-18T02:14:08.901343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:08.901343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OCTIHSRkUkJp0BwH2SVzNS5y77wNa9G0u4esowjzJcTaSaCXvRSdGhnXC8h3131c8sqjhaaDFN5JPSKcwGobBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:08.902017Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.03130","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:575799e9b8f7931dfc135037c75ee53cf469930d4bd5399fcc3b8041244578dd","sha256:dc7fc2617f29a7103d322bacbb3f155c449841917bc67346a38d643781247a8e"],"state_sha256":"b0e25771ec079850b139642aafb6d64f31e0eb45b349629c852a092f35f5e9e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+bjJflwlKWiIrPu2RCYPcZOWp0a3+wQhiEiuiKa2zSt9xcNffq7cHuQZj8hqMMMo4SsOnW8u+hcHDSLpc73SAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T16:59:38.916762Z","bundle_sha256":"e67af423039ac11c92ef510201bcb5b3e618c3fcd35cd062072e9fbaa698aa17"}}