{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:MC7UOKIU2KL2XYD5UD73AZI22D","short_pith_number":"pith:MC7UOKIU","canonical_record":{"source":{"id":"2604.20959","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-04-22T18:00:04Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"2a880e57349b911954ad0b25dd181c61eb1b85e509039f1f635f69134f35cef1","abstract_canon_sha256":"260ff2c36e7a3898bd9475cd64df946230c0512ecf0beb360342c98f00923606"},"schema_version":"1.0"},"canonical_sha256":"60bf472914d297abe07da0ffb0651ad0d57b6690a77836f8a39aef726943175b","source":{"kind":"arxiv","id":"2604.20959","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.20959","created_at":"2026-05-21T01:05:19Z"},{"alias_kind":"arxiv_version","alias_value":"2604.20959v2","created_at":"2026-05-21T01:05:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.20959","created_at":"2026-05-21T01:05:19Z"},{"alias_kind":"pith_short_12","alias_value":"MC7UOKIU2KL2","created_at":"2026-05-21T01:05:19Z"},{"alias_kind":"pith_short_16","alias_value":"MC7UOKIU2KL2XYD5","created_at":"2026-05-21T01:05:19Z"},{"alias_kind":"pith_short_8","alias_value":"MC7UOKIU","created_at":"2026-05-21T01:05:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:MC7UOKIU2KL2XYD5UD73AZI22D","target":"record","payload":{"canonical_record":{"source":{"id":"2604.20959","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-04-22T18:00:04Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"2a880e57349b911954ad0b25dd181c61eb1b85e509039f1f635f69134f35cef1","abstract_canon_sha256":"260ff2c36e7a3898bd9475cd64df946230c0512ecf0beb360342c98f00923606"},"schema_version":"1.0"},"canonical_sha256":"60bf472914d297abe07da0ffb0651ad0d57b6690a77836f8a39aef726943175b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:05:19.348936Z","signature_b64":"WYUW5a+TyuqOB4cev9kqk0J1/CBKkSx040HlYU1tdmAE4kDUbOBwNCBikxJtD15ioYQXt/zP9SBDpXNFcRkJCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60bf472914d297abe07da0ffb0651ad0d57b6690a77836f8a39aef726943175b","last_reissued_at":"2026-05-21T01:05:19.348472Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:05:19.348472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2604.20959","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":"2026-05-21T01:05:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Q3JYlTrtQAvt7ErPxOpvbwiS/6yTPjQyxiKnVFCY0cV7JMYxSaxhTQJC4Xm7QsHIDPFPcEZ6FlGCPg+xFdjBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:31:47.587615Z"},"content_sha256":"944f71cec217424b4b0800fa7b4df48844168e9d94c4e19b475154eb49bacdf0","schema_version":"1.0","event_id":"sha256:944f71cec217424b4b0800fa7b4df48844168e9d94c4e19b475154eb49bacdf0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:MC7UOKIU2KL2XYD5UD73AZI22D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Twisted traces and quantization of moduli stacks of 3d $\\mathcal{N}=4$ Chern-Simons-matter theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Sphere partition functions of 3d N=4 Chern-Simons-matter theories equal sums of twisted traces on tensor products of Verma modules over quantized moduli spaces of vacua.","cross_cats":["math.AG","math.RT"],"primary_cat":"hep-th","authors_text":"Leonardo Santilli","submitted_at":"2026-04-22T18:00:04Z","abstract_excerpt":"We conjecture, and show in a plethora of examples, that the sphere partition function of 3d $\\mathcal{N}=4$ Chern-Simons-matter theories equals a sum of twisted traces on tensor products of Verma modules over the quantization of the moduli spaces of vacua. This extends a conjecture of Gaiotto-Okazaki to Chern-Simons-matter theories. We also show that the partition function of every Abelian gauge theory with higher charges has such twisted trace decomposition, and uncover new Abelian dualities between theories with and without Chern-Simons couplings."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The sphere partition function of 3d N=4 Chern-Simons-matter theories equals a sum of twisted traces on tensor products of Verma modules over the quantization of the moduli spaces of vacua.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the quantization of the moduli spaces of vacua is well-defined for the theories under consideration and that the twisted traces on the corresponding Verma modules reproduce the physical partition function.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Sphere partition functions of 3d N=4 Chern-Simons-matter theories are conjectured to equal sums of twisted traces on Verma modules over quantized moduli stacks of vacua.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Sphere partition functions of 3d N=4 Chern-Simons-matter theories equal sums of twisted traces on tensor products of Verma modules over quantized moduli spaces of vacua.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a60cb13b19d58f464b414d749738165092f983691140bf49dd48bebda0797db0"},"source":{"id":"2604.20959","kind":"arxiv","version":2},"verdict":{"id":"7d19ef24-25d8-4893-972e-282680173823","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T23:24:38.963613Z","strongest_claim":"The sphere partition function of 3d N=4 Chern-Simons-matter theories equals a sum of twisted traces on tensor products of Verma modules over the quantization of the moduli spaces of vacua.","one_line_summary":"Sphere partition functions of 3d N=4 Chern-Simons-matter theories are conjectured to equal sums of twisted traces on Verma modules over quantized moduli stacks of vacua.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the quantization of the moduli spaces of vacua is well-defined for the theories under consideration and that the twisted traces on the corresponding Verma modules reproduce the physical partition function.","pith_extraction_headline":"Sphere partition functions of 3d N=4 Chern-Simons-matter theories equal sums of twisted traces on tensor products of Verma modules over quantized moduli spaces of vacua."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.20959/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-20T01:30:57.721809Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"533dcbf6d4b00b24cdb39aace88bc863b7a58090d37048bdfd8a47e377809e80"},"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":"7d19ef24-25d8-4893-972e-282680173823"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-21T01:05:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/eTBNvFm+5y7Ui4j8Dm5OIMgRSTpOHDoxwT5pg7B/3gbfQrZzgdGGTMNJZvkuuox16+LhPURQH+HYugd+EGZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:31:47.588103Z"},"content_sha256":"a27d9dcf85ab6f68689f8aaf147b3585674bf927ab114480197b0655fef42521","schema_version":"1.0","event_id":"sha256:a27d9dcf85ab6f68689f8aaf147b3585674bf927ab114480197b0655fef42521"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MC7UOKIU2KL2XYD5UD73AZI22D/bundle.json","state_url":"https://pith.science/pith/MC7UOKIU2KL2XYD5UD73AZI22D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MC7UOKIU2KL2XYD5UD73AZI22D/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":"2026-05-26T07:31:47Z","links":{"resolver":"https://pith.science/pith/MC7UOKIU2KL2XYD5UD73AZI22D","bundle":"https://pith.science/pith/MC7UOKIU2KL2XYD5UD73AZI22D/bundle.json","state":"https://pith.science/pith/MC7UOKIU2KL2XYD5UD73AZI22D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MC7UOKIU2KL2XYD5UD73AZI22D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MC7UOKIU2KL2XYD5UD73AZI22D","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":"260ff2c36e7a3898bd9475cd64df946230c0512ecf0beb360342c98f00923606","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-04-22T18:00:04Z","title_canon_sha256":"2a880e57349b911954ad0b25dd181c61eb1b85e509039f1f635f69134f35cef1"},"schema_version":"1.0","source":{"id":"2604.20959","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.20959","created_at":"2026-05-21T01:05:19Z"},{"alias_kind":"arxiv_version","alias_value":"2604.20959v2","created_at":"2026-05-21T01:05:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.20959","created_at":"2026-05-21T01:05:19Z"},{"alias_kind":"pith_short_12","alias_value":"MC7UOKIU2KL2","created_at":"2026-05-21T01:05:19Z"},{"alias_kind":"pith_short_16","alias_value":"MC7UOKIU2KL2XYD5","created_at":"2026-05-21T01:05:19Z"},{"alias_kind":"pith_short_8","alias_value":"MC7UOKIU","created_at":"2026-05-21T01:05:19Z"}],"graph_snapshots":[{"event_id":"sha256:a27d9dcf85ab6f68689f8aaf147b3585674bf927ab114480197b0655fef42521","target":"graph","created_at":"2026-05-21T01:05:19Z","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":"The sphere partition function of 3d N=4 Chern-Simons-matter theories equals a sum of twisted traces on tensor products of Verma modules over the quantization of the moduli spaces of vacua."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the quantization of the moduli spaces of vacua is well-defined for the theories under consideration and that the twisted traces on the corresponding Verma modules reproduce the physical partition function."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Sphere partition functions of 3d N=4 Chern-Simons-matter theories are conjectured to equal sums of twisted traces on Verma modules over quantized moduli stacks of vacua."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Sphere partition functions of 3d N=4 Chern-Simons-matter theories equal sums of twisted traces on tensor products of Verma modules over quantized moduli spaces of vacua."}],"snapshot_sha256":"a60cb13b19d58f464b414d749738165092f983691140bf49dd48bebda0797db0"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-20T01:30:57.721809Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2604.20959/integrity.json","findings":[],"snapshot_sha256":"533dcbf6d4b00b24cdb39aace88bc863b7a58090d37048bdfd8a47e377809e80","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We conjecture, and show in a plethora of examples, that the sphere partition function of 3d $\\mathcal{N}=4$ Chern-Simons-matter theories equals a sum of twisted traces on tensor products of Verma modules over the quantization of the moduli spaces of vacua. This extends a conjecture of Gaiotto-Okazaki to Chern-Simons-matter theories. We also show that the partition function of every Abelian gauge theory with higher charges has such twisted trace decomposition, and uncover new Abelian dualities between theories with and without Chern-Simons couplings.","authors_text":"Leonardo Santilli","cross_cats":["math.AG","math.RT"],"headline":"Sphere partition functions of 3d N=4 Chern-Simons-matter theories equal sums of twisted traces on tensor products of Verma modules over quantized moduli spaces of vacua.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-04-22T18:00:04Z","title":"Twisted traces and quantization of moduli stacks of 3d $\\mathcal{N}=4$ Chern-Simons-matter theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.20959","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-09T23:24:38.963613Z","id":"7d19ef24-25d8-4893-972e-282680173823","model_set":{"reader":"grok-4.3"},"one_line_summary":"Sphere partition functions of 3d N=4 Chern-Simons-matter theories are conjectured to equal sums of twisted traces on Verma modules over quantized moduli stacks of vacua.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Sphere partition functions of 3d N=4 Chern-Simons-matter theories equal sums of twisted traces on tensor products of Verma modules over quantized moduli spaces of vacua.","strongest_claim":"The sphere partition function of 3d N=4 Chern-Simons-matter theories equals a sum of twisted traces on tensor products of Verma modules over the quantization of the moduli spaces of vacua.","weakest_assumption":"That the quantization of the moduli spaces of vacua is well-defined for the theories under consideration and that the twisted traces on the corresponding Verma modules reproduce the physical partition function."}},"verdict_id":"7d19ef24-25d8-4893-972e-282680173823"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:944f71cec217424b4b0800fa7b4df48844168e9d94c4e19b475154eb49bacdf0","target":"record","created_at":"2026-05-21T01:05:19Z","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":"260ff2c36e7a3898bd9475cd64df946230c0512ecf0beb360342c98f00923606","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-04-22T18:00:04Z","title_canon_sha256":"2a880e57349b911954ad0b25dd181c61eb1b85e509039f1f635f69134f35cef1"},"schema_version":"1.0","source":{"id":"2604.20959","kind":"arxiv","version":2}},"canonical_sha256":"60bf472914d297abe07da0ffb0651ad0d57b6690a77836f8a39aef726943175b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60bf472914d297abe07da0ffb0651ad0d57b6690a77836f8a39aef726943175b","first_computed_at":"2026-05-21T01:05:19.348472Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:05:19.348472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WYUW5a+TyuqOB4cev9kqk0J1/CBKkSx040HlYU1tdmAE4kDUbOBwNCBikxJtD15ioYQXt/zP9SBDpXNFcRkJCg==","signature_status":"signed_v1","signed_at":"2026-05-21T01:05:19.348936Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.20959","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:944f71cec217424b4b0800fa7b4df48844168e9d94c4e19b475154eb49bacdf0","sha256:a27d9dcf85ab6f68689f8aaf147b3585674bf927ab114480197b0655fef42521"],"state_sha256":"90984c0dd147983584f2944afc7d614616e59d9358c7557af1e2608e257ab2c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YywmM8y+VOqCyx1zG4lR/0Tg/dzhU/BP5mkYnXCEiaKW968ifhIvrp8MQbcQxKqcGx9ZPRkO7M6yFeDD5kH+BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T07:31:47.590901Z","bundle_sha256":"3c599b8735a012885bd6c28423e16ab85ae6128fea17f1f4ff3c468dcd81f762"}}