{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:MBOAR7PZ54TNCKMW57OTI2YTTR","short_pith_number":"pith:MBOAR7PZ","canonical_record":{"source":{"id":"2604.08736","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-lat","submitted_at":"2026-04-09T20:00:03Z","cross_cats_sorted":["cond-mat.str-el","hep-th"],"title_canon_sha256":"bcf6a36620625ae298dc78c582d87d63f21464ff515a7f0801c9c6d0c7b45d5b","abstract_canon_sha256":"b83e27c2a5e30ac7b4e03e99258f609a4a9991f1369c5297000a7916a2546934"},"schema_version":"1.0"},"canonical_sha256":"605c08fdf9ef26d12996efdd346b139c6a52e5fc8707ea43f5edb0ebb2fafa23","source":{"kind":"arxiv","id":"2604.08736","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.08736","created_at":"2026-07-02T00:18:28Z"},{"alias_kind":"arxiv_version","alias_value":"2604.08736v3","created_at":"2026-07-02T00:18:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.08736","created_at":"2026-07-02T00:18:28Z"},{"alias_kind":"pith_short_12","alias_value":"MBOAR7PZ54TN","created_at":"2026-07-02T00:18:28Z"},{"alias_kind":"pith_short_16","alias_value":"MBOAR7PZ54TNCKMW","created_at":"2026-07-02T00:18:28Z"},{"alias_kind":"pith_short_8","alias_value":"MBOAR7PZ","created_at":"2026-07-02T00:18:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:MBOAR7PZ54TNCKMW57OTI2YTTR","target":"record","payload":{"canonical_record":{"source":{"id":"2604.08736","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-lat","submitted_at":"2026-04-09T20:00:03Z","cross_cats_sorted":["cond-mat.str-el","hep-th"],"title_canon_sha256":"bcf6a36620625ae298dc78c582d87d63f21464ff515a7f0801c9c6d0c7b45d5b","abstract_canon_sha256":"b83e27c2a5e30ac7b4e03e99258f609a4a9991f1369c5297000a7916a2546934"},"schema_version":"1.0"},"canonical_sha256":"605c08fdf9ef26d12996efdd346b139c6a52e5fc8707ea43f5edb0ebb2fafa23","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T00:18:28.491517Z","signature_b64":"kfLSmj43ceh0l61L+arwpMbEO+QymtYjiAxFa3pfslQHRauyG8xMpBd/RqWnsT8/oepy9om35a/eYs7A0aiIAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"605c08fdf9ef26d12996efdd346b139c6a52e5fc8707ea43f5edb0ebb2fafa23","last_reissued_at":"2026-07-02T00:18:28.490770Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T00:18:28.490770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2604.08736","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":"2026-07-02T00:18:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ExTK7pz7f1eVYTMLAzst1quiRRCs2dJcHYExsigVYGdAEkvuuVJEpw28mwOYK3JC0E1HWXHm+U3qFrU92M4OAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T19:52:57.827077Z"},"content_sha256":"c76dfce2d516b305d0e5299ab2d495ba6c3c1eb50e591b3a2b045d327d26aa65","schema_version":"1.0","event_id":"sha256:c76dfce2d516b305d0e5299ab2d495ba6c3c1eb50e591b3a2b045d327d26aa65"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:MBOAR7PZ54TNCKMW57OTI2YTTR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact SL(2,Z)-Structure of Lattice Maxwell Theory with $\\theta$-term in Modified Villain Formulation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Lattice Maxwell theory with theta term exhibits exact SL(2,Z) duality in the modified Villain formulation.","cross_cats":["cond-mat.str-el","hep-th"],"primary_cat":"hep-lat","authors_text":"Shoto Aoki, Toshinari Takemoto, Yoshio Kikukawa","submitted_at":"2026-04-09T20:00:03Z","abstract_excerpt":"We study the duality of lattice Maxwell theory in the modified Villain formulation, employing an ultra-local action with a theta term. Although this action is known to become non ultra-local through the Poisson resummation formula, we show that this non ultra-locality can be removed by incorporating a non-local transformation procedure into the definition of the S-transformation. As a result, the ultra-local action with a theta term exhibits an exact SL(2,Z)-duality. We further analyze the SL(2,Z)-structure of Wilson and 't Hooft loops, demonstrating that they transform properly up to a nontri"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"As a result, the ultra-local action with a theta term exhibits an exact SL(2,Z)-duality. We further analyze the SL(2,Z)-structure of Wilson and 't Hooft loops, demonstrating that they transform properly up to a nontrivial phase factor arising from the nontrivial self-linking of the loops.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the non-local transformation procedure added to the S-transformation removes non ultra-locality from the Poisson resummation without introducing inconsistencies or changing the physical content of the duality.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The ultra-local modified Villain action for lattice Maxwell theory with theta term has exact SL(2,Z) duality, with Wilson and 't Hooft loops transforming up to a phase from self-linking.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Lattice Maxwell theory with theta term exhibits exact SL(2,Z) duality in the modified Villain formulation.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4289384dbe6ee16cb2eb1dcda5471a9aa4887b32ba070f97c9858af916e1756a"},"source":{"id":"2604.08736","kind":"arxiv","version":3},"verdict":{"id":"d14ba3cf-22b4-4c0f-b3e7-7d188f93a87c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T16:51:09.699932Z","strongest_claim":"As a result, the ultra-local action with a theta term exhibits an exact SL(2,Z)-duality. We further analyze the SL(2,Z)-structure of Wilson and 't Hooft loops, demonstrating that they transform properly up to a nontrivial phase factor arising from the nontrivial self-linking of the loops.","one_line_summary":"The ultra-local modified Villain action for lattice Maxwell theory with theta term has exact SL(2,Z) duality, with Wilson and 't Hooft loops transforming up to a phase from self-linking.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the non-local transformation procedure added to the S-transformation removes non ultra-locality from the Poisson resummation without introducing inconsistencies or changing the physical content of the duality.","pith_extraction_headline":"Lattice Maxwell theory with theta term exhibits exact SL(2,Z) duality in the modified Villain formulation."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.08736/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":"d14ba3cf-22b4-4c0f-b3e7-7d188f93a87c"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-02T00:18:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hVDMhRpSBoGUwPRGQEf78Rn+5TQhRJFF5GDrety4oZ1uPyVfRY+SEEI6zULe12i8agoX9ZVsYM9OsIq9g42oCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T19:52:57.827792Z"},"content_sha256":"3e0b6e7e2cbc600de39c9afa61f267a94a1eae55a965da0ab6fdee05147eb1d2","schema_version":"1.0","event_id":"sha256:3e0b6e7e2cbc600de39c9afa61f267a94a1eae55a965da0ab6fdee05147eb1d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MBOAR7PZ54TNCKMW57OTI2YTTR/bundle.json","state_url":"https://pith.science/pith/MBOAR7PZ54TNCKMW57OTI2YTTR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MBOAR7PZ54TNCKMW57OTI2YTTR/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":"2026-08-03T19:52:57Z","links":{"resolver":"https://pith.science/pith/MBOAR7PZ54TNCKMW57OTI2YTTR","bundle":"https://pith.science/pith/MBOAR7PZ54TNCKMW57OTI2YTTR/bundle.json","state":"https://pith.science/pith/MBOAR7PZ54TNCKMW57OTI2YTTR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MBOAR7PZ54TNCKMW57OTI2YTTR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MBOAR7PZ54TNCKMW57OTI2YTTR","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":"b83e27c2a5e30ac7b4e03e99258f609a4a9991f1369c5297000a7916a2546934","cross_cats_sorted":["cond-mat.str-el","hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-lat","submitted_at":"2026-04-09T20:00:03Z","title_canon_sha256":"bcf6a36620625ae298dc78c582d87d63f21464ff515a7f0801c9c6d0c7b45d5b"},"schema_version":"1.0","source":{"id":"2604.08736","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.08736","created_at":"2026-07-02T00:18:28Z"},{"alias_kind":"arxiv_version","alias_value":"2604.08736v3","created_at":"2026-07-02T00:18:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.08736","created_at":"2026-07-02T00:18:28Z"},{"alias_kind":"pith_short_12","alias_value":"MBOAR7PZ54TN","created_at":"2026-07-02T00:18:28Z"},{"alias_kind":"pith_short_16","alias_value":"MBOAR7PZ54TNCKMW","created_at":"2026-07-02T00:18:28Z"},{"alias_kind":"pith_short_8","alias_value":"MBOAR7PZ","created_at":"2026-07-02T00:18:28Z"}],"graph_snapshots":[{"event_id":"sha256:3e0b6e7e2cbc600de39c9afa61f267a94a1eae55a965da0ab6fdee05147eb1d2","target":"graph","created_at":"2026-07-02T00:18:28Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"As a result, the ultra-local action with a theta term exhibits an exact SL(2,Z)-duality. We further analyze the SL(2,Z)-structure of Wilson and 't Hooft loops, demonstrating that they transform properly up to a nontrivial phase factor arising from the nontrivial self-linking of the loops."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the non-local transformation procedure added to the S-transformation removes non ultra-locality from the Poisson resummation without introducing inconsistencies or changing the physical content of the duality."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"The ultra-local modified Villain action for lattice Maxwell theory with theta term has exact SL(2,Z) duality, with Wilson and 't Hooft loops transforming up to a phase from self-linking."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Lattice Maxwell theory with theta term exhibits exact SL(2,Z) duality in the modified Villain formulation."}],"snapshot_sha256":"4289384dbe6ee16cb2eb1dcda5471a9aa4887b32ba070f97c9858af916e1756a"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2604.08736/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the duality of lattice Maxwell theory in the modified Villain formulation, employing an ultra-local action with a theta term. Although this action is known to become non ultra-local through the Poisson resummation formula, we show that this non ultra-locality can be removed by incorporating a non-local transformation procedure into the definition of the S-transformation. As a result, the ultra-local action with a theta term exhibits an exact SL(2,Z)-duality. We further analyze the SL(2,Z)-structure of Wilson and 't Hooft loops, demonstrating that they transform properly up to a nontri","authors_text":"Shoto Aoki, Toshinari Takemoto, Yoshio Kikukawa","cross_cats":["cond-mat.str-el","hep-th"],"headline":"Lattice Maxwell theory with theta term exhibits exact SL(2,Z) duality in the modified Villain formulation.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-lat","submitted_at":"2026-04-09T20:00:03Z","title":"Exact SL(2,Z)-Structure of Lattice Maxwell Theory with $\\theta$-term in Modified Villain Formulation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.08736","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-10T16:51:09.699932Z","id":"d14ba3cf-22b4-4c0f-b3e7-7d188f93a87c","model_set":{"reader":"grok-4.3"},"one_line_summary":"The ultra-local modified Villain action for lattice Maxwell theory with theta term has exact SL(2,Z) duality, with Wilson and 't Hooft loops transforming up to a phase from self-linking.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Lattice Maxwell theory with theta term exhibits exact SL(2,Z) duality in the modified Villain formulation.","strongest_claim":"As a result, the ultra-local action with a theta term exhibits an exact SL(2,Z)-duality. We further analyze the SL(2,Z)-structure of Wilson and 't Hooft loops, demonstrating that they transform properly up to a nontrivial phase factor arising from the nontrivial self-linking of the loops.","weakest_assumption":"That the non-local transformation procedure added to the S-transformation removes non ultra-locality from the Poisson resummation without introducing inconsistencies or changing the physical content of the duality."}},"verdict_id":"d14ba3cf-22b4-4c0f-b3e7-7d188f93a87c"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c76dfce2d516b305d0e5299ab2d495ba6c3c1eb50e591b3a2b045d327d26aa65","target":"record","created_at":"2026-07-02T00:18:28Z","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":"b83e27c2a5e30ac7b4e03e99258f609a4a9991f1369c5297000a7916a2546934","cross_cats_sorted":["cond-mat.str-el","hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-lat","submitted_at":"2026-04-09T20:00:03Z","title_canon_sha256":"bcf6a36620625ae298dc78c582d87d63f21464ff515a7f0801c9c6d0c7b45d5b"},"schema_version":"1.0","source":{"id":"2604.08736","kind":"arxiv","version":3}},"canonical_sha256":"605c08fdf9ef26d12996efdd346b139c6a52e5fc8707ea43f5edb0ebb2fafa23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"605c08fdf9ef26d12996efdd346b139c6a52e5fc8707ea43f5edb0ebb2fafa23","first_computed_at":"2026-07-02T00:18:28.490770Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T00:18:28.490770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kfLSmj43ceh0l61L+arwpMbEO+QymtYjiAxFa3pfslQHRauyG8xMpBd/RqWnsT8/oepy9om35a/eYs7A0aiIAg==","signature_status":"signed_v1","signed_at":"2026-07-02T00:18:28.491517Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.08736","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c76dfce2d516b305d0e5299ab2d495ba6c3c1eb50e591b3a2b045d327d26aa65","sha256:3e0b6e7e2cbc600de39c9afa61f267a94a1eae55a965da0ab6fdee05147eb1d2"],"state_sha256":"991d03941029d9c1de2306fabe036686d6e9ef499bbba8309d8d4b6297f159e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6tww3fMxABIiotaQO7+yIAgy3J+d5PmNTcrOlWdGufoXSlDVnrpyDSVq12aAOeBum8FAdcfKYRNDweRXMPu8Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T19:52:57.833316Z","bundle_sha256":"3135ea424e03c15689d34025e8b8fe47d63bd3247db3df13e64b669d081eb238"}}