{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZDMYCO7FJPNDA23G42IXA4PZRO","short_pith_number":"pith:ZDMYCO7F","canonical_record":{"source":{"id":"1711.07122","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-11-20T02:16:42Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"d5561c168280b198a9d0897ceb914227fb2fa647147f47831d27c2cdbb368df5","abstract_canon_sha256":"d481f5df2d7c81c92864a674090569c1e124669d747a4b4a6d1706f50e7142d2"},"schema_version":"1.0"},"canonical_sha256":"c8d9813be54bda306b66e6917071f98ba843e41acd841db568b15ceba3c152d5","source":{"kind":"arxiv","id":"1711.07122","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.07122","created_at":"2026-05-17T23:39:58Z"},{"alias_kind":"arxiv_version","alias_value":"1711.07122v3","created_at":"2026-05-17T23:39:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.07122","created_at":"2026-05-17T23:39:58Z"},{"alias_kind":"pith_short_12","alias_value":"ZDMYCO7FJPND","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZDMYCO7FJPNDA23G","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZDMYCO7F","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZDMYCO7FJPNDA23G42IXA4PZRO","target":"record","payload":{"canonical_record":{"source":{"id":"1711.07122","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-11-20T02:16:42Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"d5561c168280b198a9d0897ceb914227fb2fa647147f47831d27c2cdbb368df5","abstract_canon_sha256":"d481f5df2d7c81c92864a674090569c1e124669d747a4b4a6d1706f50e7142d2"},"schema_version":"1.0"},"canonical_sha256":"c8d9813be54bda306b66e6917071f98ba843e41acd841db568b15ceba3c152d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:58.872344Z","signature_b64":"IbH2WETxA8kr722GkLyaiLVTzF0sNtw++53vbMQdnWlTdCAA2C/u7b+4XRuStkJVvilG6tFzaJG61COL3iHBBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8d9813be54bda306b66e6917071f98ba843e41acd841db568b15ceba3c152d5","last_reissued_at":"2026-05-17T23:39:58.871900Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:58.871900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.07122","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:39:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bysPrdxQiOLF/KkZvrHBh6to9jS9ysVlzpBGUl2cAOis1EyNMnGtG1WdvLeNtNmWTgcEKjBsGm5eXrouoJPmBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:38:49.099625Z"},"content_sha256":"85e4dc7b83c6c36bf070d147e299b42a12ed58bd040e4a192645289906f231eb","schema_version":"1.0","event_id":"sha256:85e4dc7b83c6c36bf070d147e299b42a12ed58bd040e4a192645289906f231eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZDMYCO7FJPNDA23G42IXA4PZRO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some properties of zero-mode wave functions in abelian Chern-Simons theory on the torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"hep-th","authors_text":"Yasuhiro Abe","submitted_at":"2017-11-20T02:16:42Z","abstract_excerpt":"In geometric quantization a zero-mode wave function in abelian Chern-Simons theory on the torus can be defined as $\\Psi [ a, \\bar{a} ] = e^{- \\frac{K(a, \\bar{a})}{2}} f (a)$ where $K(a ,\\bar{a} )$ denotes a K\\\"ahler potential for the zero-mode variable $a \\in \\mathbb{C}$ on the torus. We first review that the holomorphic wave function $f(a)$ can be described in terms of the Jacobi theta functions by imposing gauge invariance on $\\Psi [ a, \\bar{a} ]$ where gauge transformations are induced by doubly periodic translations of $a$. We discuss that $f(a)$ is quantum theoretically characterized by ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07122","kind":"arxiv","version":3},"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":"2026-05-17T23:39:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NIhLKFY3ENh36m7DVNFu69YWygnxobtmWnuxTf6GagNHb58aHw6yFeehfJRz1+WRwx/o7xlcBcJS7Z9YQpwQAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:38:49.100354Z"},"content_sha256":"ad778252d0822ebfaec648c86f2de39384ef0f25c8512a337c59084cc32f21b7","schema_version":"1.0","event_id":"sha256:ad778252d0822ebfaec648c86f2de39384ef0f25c8512a337c59084cc32f21b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZDMYCO7FJPNDA23G42IXA4PZRO/bundle.json","state_url":"https://pith.science/pith/ZDMYCO7FJPNDA23G42IXA4PZRO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZDMYCO7FJPNDA23G42IXA4PZRO/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":"2026-05-26T08:38:49Z","links":{"resolver":"https://pith.science/pith/ZDMYCO7FJPNDA23G42IXA4PZRO","bundle":"https://pith.science/pith/ZDMYCO7FJPNDA23G42IXA4PZRO/bundle.json","state":"https://pith.science/pith/ZDMYCO7FJPNDA23G42IXA4PZRO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZDMYCO7FJPNDA23G42IXA4PZRO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZDMYCO7FJPNDA23G42IXA4PZRO","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":"d481f5df2d7c81c92864a674090569c1e124669d747a4b4a6d1706f50e7142d2","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-11-20T02:16:42Z","title_canon_sha256":"d5561c168280b198a9d0897ceb914227fb2fa647147f47831d27c2cdbb368df5"},"schema_version":"1.0","source":{"id":"1711.07122","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.07122","created_at":"2026-05-17T23:39:58Z"},{"alias_kind":"arxiv_version","alias_value":"1711.07122v3","created_at":"2026-05-17T23:39:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.07122","created_at":"2026-05-17T23:39:58Z"},{"alias_kind":"pith_short_12","alias_value":"ZDMYCO7FJPND","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZDMYCO7FJPNDA23G","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZDMYCO7F","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:ad778252d0822ebfaec648c86f2de39384ef0f25c8512a337c59084cc32f21b7","target":"graph","created_at":"2026-05-17T23:39:58Z","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":"In geometric quantization a zero-mode wave function in abelian Chern-Simons theory on the torus can be defined as $\\Psi [ a, \\bar{a} ] = e^{- \\frac{K(a, \\bar{a})}{2}} f (a)$ where $K(a ,\\bar{a} )$ denotes a K\\\"ahler potential for the zero-mode variable $a \\in \\mathbb{C}$ on the torus. We first review that the holomorphic wave function $f(a)$ can be described in terms of the Jacobi theta functions by imposing gauge invariance on $\\Psi [ a, \\bar{a} ]$ where gauge transformations are induced by doubly periodic translations of $a$. We discuss that $f(a)$ is quantum theoretically characterized by (","authors_text":"Yasuhiro Abe","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-11-20T02:16:42Z","title":"Some properties of zero-mode wave functions in abelian Chern-Simons theory on the torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07122","kind":"arxiv","version":3},"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":"sha256:85e4dc7b83c6c36bf070d147e299b42a12ed58bd040e4a192645289906f231eb","target":"record","created_at":"2026-05-17T23:39:58Z","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":"d481f5df2d7c81c92864a674090569c1e124669d747a4b4a6d1706f50e7142d2","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-11-20T02:16:42Z","title_canon_sha256":"d5561c168280b198a9d0897ceb914227fb2fa647147f47831d27c2cdbb368df5"},"schema_version":"1.0","source":{"id":"1711.07122","kind":"arxiv","version":3}},"canonical_sha256":"c8d9813be54bda306b66e6917071f98ba843e41acd841db568b15ceba3c152d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8d9813be54bda306b66e6917071f98ba843e41acd841db568b15ceba3c152d5","first_computed_at":"2026-05-17T23:39:58.871900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:58.871900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IbH2WETxA8kr722GkLyaiLVTzF0sNtw++53vbMQdnWlTdCAA2C/u7b+4XRuStkJVvilG6tFzaJG61COL3iHBBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:58.872344Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.07122","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85e4dc7b83c6c36bf070d147e299b42a12ed58bd040e4a192645289906f231eb","sha256:ad778252d0822ebfaec648c86f2de39384ef0f25c8512a337c59084cc32f21b7"],"state_sha256":"2df8fb073dda40bf25664764eb68816bc1c5986a62decfadcb9520b9109abce0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZPlbojVZ4+0keJPoXFh3a1TxlTaOJV/hH86zl5I/hbuC7sV1nsggwAJ5FvfID6bFh+4ue8MD5mVr0KyaaH4IDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T08:38:49.103593Z","bundle_sha256":"0e39cacf6a31249b7658c693780679870be884f78331586093dc58c50dde847b"}}