{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:CSGNYT4AY2F4N34QX65YZTL2W6","short_pith_number":"pith:CSGNYT4A","canonical_record":{"source":{"id":"2411.09406","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-11-14T12:45:59Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"e636ec5ff9e1428e65b8441db2a73380a58c2fa1b2eda9460d6114891e480017","abstract_canon_sha256":"4c07b4fba2690f961ad41338422e89c6614e0014e8517cd823f373e611ec1a6e"},"schema_version":"1.0"},"canonical_sha256":"148cdc4f80c68bc6ef90bfbb8ccd7ab7a4d1d942c0b0b0c5edaa05620add0f58","source":{"kind":"arxiv","id":"2411.09406","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.09406","created_at":"2026-05-26T02:03:47Z"},{"alias_kind":"arxiv_version","alias_value":"2411.09406v4","created_at":"2026-05-26T02:03:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.09406","created_at":"2026-05-26T02:03:47Z"},{"alias_kind":"pith_short_12","alias_value":"CSGNYT4AY2F4","created_at":"2026-05-26T02:03:47Z"},{"alias_kind":"pith_short_16","alias_value":"CSGNYT4AY2F4N34Q","created_at":"2026-05-26T02:03:47Z"},{"alias_kind":"pith_short_8","alias_value":"CSGNYT4A","created_at":"2026-05-26T02:03:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:CSGNYT4AY2F4N34QX65YZTL2W6","target":"record","payload":{"canonical_record":{"source":{"id":"2411.09406","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-11-14T12:45:59Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"e636ec5ff9e1428e65b8441db2a73380a58c2fa1b2eda9460d6114891e480017","abstract_canon_sha256":"4c07b4fba2690f961ad41338422e89c6614e0014e8517cd823f373e611ec1a6e"},"schema_version":"1.0"},"canonical_sha256":"148cdc4f80c68bc6ef90bfbb8ccd7ab7a4d1d942c0b0b0c5edaa05620add0f58","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:03:47.154580Z","signature_b64":"EohPXafLoXO4SVCfzmno4PH9IaEt3Nj3g1eR0u35GLKFelahR4MR2+6CdyPSdA4p//6SOl0DN7Pj5v9gIP73Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"148cdc4f80c68bc6ef90bfbb8ccd7ab7a4d1d942c0b0b0c5edaa05620add0f58","last_reissued_at":"2026-05-26T02:03:47.153611Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:03:47.153611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.09406","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-26T02:03:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UiOOGU4y4PLSs/aOhnuvn+C99yKqb93M1fsI5DnFG0nf3cFnIj+mF7Z+IDd7jEQgrO8MIz0r7435E3cSaSEWDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T01:32:02.529334Z"},"content_sha256":"3ee138c1fce5060ad1cfb547060cc17e1c9ff34d4b57dadda32db0135fd0f634","schema_version":"1.0","event_id":"sha256:3ee138c1fce5060ad1cfb547060cc17e1c9ff34d4b57dadda32db0135fd0f634"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:CSGNYT4AY2F4N34QX65YZTL2W6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Left-Right Relative Entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Left-right relative entropy vanishes between certain orthogonal boundary states in 2D CFTs, defining new equivalence classes called relative entanglement sectors.","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"hep-th","authors_text":"Mostafa Ghasemi","submitted_at":"2024-11-14T12:45:59Z","abstract_excerpt":"The concept of distinguishability lies at the heart of quantum information theory. We introduce \\textit{left-right relative entropy} as a quantitative measure of distinguishability within the space of boundary states in two-dimensional conformal field theories (CFTs). By tracing over either the left- or right-moving modes, we derive a universal formula for arbitrary regularized boundary states defined on a circle. Remarkably, the resulting quantity reduces to a Kullback--Leibler divergence, where the associated probability distribution is determined entirely by the modular $\\mathcal{S}$-matrix"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the left-right relative entropy between certain reduced boundary states vanishes even though the corresponding global boundary states are orthogonal. This observation motivates the introduction of relative entanglement sectors, defined as equivalence classes of boundary states that are indistinguishable with respect to left-right relative entropy. These sectors transform as NIM-representations of global symmetries and exhibit level-dependent structures that mirror Z2 't Hooft anomalies.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that tracing over left- or right-moving modes of regularized boundary states on a circle produces a valid probability distribution determined entirely by the modular S-matrix and boundary data, allowing the quantity to be interpreted as a Kullback-Leibler divergence (abstract, paragraph on derivation of universal formula).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Introduces left-right relative entropy for 2d CFT boundary states that reduces to KL divergence via modular data, revealing relative entanglement sectors linked to 't Hooft anomalies in models like Ising and WZW.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Left-right relative entropy vanishes between certain orthogonal boundary states in 2D CFTs, defining new equivalence classes called relative entanglement sectors.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"508f975d664d2d068cc9ec1d8ee32c167f046e3bcfa0184ea4de1c548597da67"},"source":{"id":"2411.09406","kind":"arxiv","version":4},"verdict":{"id":"a8a6b3b5-fc2c-4ea2-b642-6879f435d4c5","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-23T17:50:17.111430Z","strongest_claim":"the left-right relative entropy between certain reduced boundary states vanishes even though the corresponding global boundary states are orthogonal. This observation motivates the introduction of relative entanglement sectors, defined as equivalence classes of boundary states that are indistinguishable with respect to left-right relative entropy. These sectors transform as NIM-representations of global symmetries and exhibit level-dependent structures that mirror Z2 't Hooft anomalies.","one_line_summary":"Introduces left-right relative entropy for 2d CFT boundary states that reduces to KL divergence via modular data, revealing relative entanglement sectors linked to 't Hooft anomalies in models like Ising and WZW.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that tracing over left- or right-moving modes of regularized boundary states on a circle produces a valid probability distribution determined entirely by the modular S-matrix and boundary data, allowing the quantity to be interpreted as a Kullback-Leibler divergence (abstract, paragraph on derivation of universal formula).","pith_extraction_headline":"Left-right relative entropy vanishes between certain orthogonal boundary states in 2D CFTs, defining new equivalence classes called relative entanglement sectors."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.09406/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":"a8a6b3b5-fc2c-4ea2-b642-6879f435d4c5"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-26T02:03:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zgkQF2uLdRRwaUI+H569RFq7LvBWFJvreKcteg6+v3gBfjGLko1ymvi4S77HDTYpflnEnOlt7mzhkfTSKunRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T01:32:02.530170Z"},"content_sha256":"6420ee15568f56c2d80c031b37688e94ff61b54288cc1bfb877e4b6d4eb1ae83","schema_version":"1.0","event_id":"sha256:6420ee15568f56c2d80c031b37688e94ff61b54288cc1bfb877e4b6d4eb1ae83"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CSGNYT4AY2F4N34QX65YZTL2W6/bundle.json","state_url":"https://pith.science/pith/CSGNYT4AY2F4N34QX65YZTL2W6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CSGNYT4AY2F4N34QX65YZTL2W6/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":"2026-06-06T01:32:02Z","links":{"resolver":"https://pith.science/pith/CSGNYT4AY2F4N34QX65YZTL2W6","bundle":"https://pith.science/pith/CSGNYT4AY2F4N34QX65YZTL2W6/bundle.json","state":"https://pith.science/pith/CSGNYT4AY2F4N34QX65YZTL2W6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CSGNYT4AY2F4N34QX65YZTL2W6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:CSGNYT4AY2F4N34QX65YZTL2W6","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":"4c07b4fba2690f961ad41338422e89c6614e0014e8517cd823f373e611ec1a6e","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-11-14T12:45:59Z","title_canon_sha256":"e636ec5ff9e1428e65b8441db2a73380a58c2fa1b2eda9460d6114891e480017"},"schema_version":"1.0","source":{"id":"2411.09406","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.09406","created_at":"2026-05-26T02:03:47Z"},{"alias_kind":"arxiv_version","alias_value":"2411.09406v4","created_at":"2026-05-26T02:03:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.09406","created_at":"2026-05-26T02:03:47Z"},{"alias_kind":"pith_short_12","alias_value":"CSGNYT4AY2F4","created_at":"2026-05-26T02:03:47Z"},{"alias_kind":"pith_short_16","alias_value":"CSGNYT4AY2F4N34Q","created_at":"2026-05-26T02:03:47Z"},{"alias_kind":"pith_short_8","alias_value":"CSGNYT4A","created_at":"2026-05-26T02:03:47Z"}],"graph_snapshots":[{"event_id":"sha256:6420ee15568f56c2d80c031b37688e94ff61b54288cc1bfb877e4b6d4eb1ae83","target":"graph","created_at":"2026-05-26T02:03:47Z","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 left-right relative entropy between certain reduced boundary states vanishes even though the corresponding global boundary states are orthogonal. This observation motivates the introduction of relative entanglement sectors, defined as equivalence classes of boundary states that are indistinguishable with respect to left-right relative entropy. These sectors transform as NIM-representations of global symmetries and exhibit level-dependent structures that mirror Z2 't Hooft anomalies."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The assumption that tracing over left- or right-moving modes of regularized boundary states on a circle produces a valid probability distribution determined entirely by the modular S-matrix and boundary data, allowing the quantity to be interpreted as a Kullback-Leibler divergence (abstract, paragraph on derivation of universal formula)."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Introduces left-right relative entropy for 2d CFT boundary states that reduces to KL divergence via modular data, revealing relative entanglement sectors linked to 't Hooft anomalies in models like Ising and WZW."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Left-right relative entropy vanishes between certain orthogonal boundary states in 2D CFTs, defining new equivalence classes called relative entanglement sectors."}],"snapshot_sha256":"508f975d664d2d068cc9ec1d8ee32c167f046e3bcfa0184ea4de1c548597da67"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.09406/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The concept of distinguishability lies at the heart of quantum information theory. We introduce \\textit{left-right relative entropy} as a quantitative measure of distinguishability within the space of boundary states in two-dimensional conformal field theories (CFTs). By tracing over either the left- or right-moving modes, we derive a universal formula for arbitrary regularized boundary states defined on a circle. Remarkably, the resulting quantity reduces to a Kullback--Leibler divergence, where the associated probability distribution is determined entirely by the modular $\\mathcal{S}$-matrix","authors_text":"Mostafa Ghasemi","cross_cats":["math-ph","math.MP","quant-ph"],"headline":"Left-right relative entropy vanishes between certain orthogonal boundary states in 2D CFTs, defining new equivalence classes called relative entanglement sectors.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-11-14T12:45:59Z","title":"Left-Right Relative Entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.09406","kind":"arxiv","version":4},"verdict":{"created_at":"2026-05-23T17:50:17.111430Z","id":"a8a6b3b5-fc2c-4ea2-b642-6879f435d4c5","model_set":{"reader":"grok-4.3"},"one_line_summary":"Introduces left-right relative entropy for 2d CFT boundary states that reduces to KL divergence via modular data, revealing relative entanglement sectors linked to 't Hooft anomalies in models like Ising and WZW.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Left-right relative entropy vanishes between certain orthogonal boundary states in 2D CFTs, defining new equivalence classes called relative entanglement sectors.","strongest_claim":"the left-right relative entropy between certain reduced boundary states vanishes even though the corresponding global boundary states are orthogonal. This observation motivates the introduction of relative entanglement sectors, defined as equivalence classes of boundary states that are indistinguishable with respect to left-right relative entropy. These sectors transform as NIM-representations of global symmetries and exhibit level-dependent structures that mirror Z2 't Hooft anomalies.","weakest_assumption":"The assumption that tracing over left- or right-moving modes of regularized boundary states on a circle produces a valid probability distribution determined entirely by the modular S-matrix and boundary data, allowing the quantity to be interpreted as a Kullback-Leibler divergence (abstract, paragraph on derivation of universal formula)."}},"verdict_id":"a8a6b3b5-fc2c-4ea2-b642-6879f435d4c5"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3ee138c1fce5060ad1cfb547060cc17e1c9ff34d4b57dadda32db0135fd0f634","target":"record","created_at":"2026-05-26T02:03:47Z","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":"4c07b4fba2690f961ad41338422e89c6614e0014e8517cd823f373e611ec1a6e","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-11-14T12:45:59Z","title_canon_sha256":"e636ec5ff9e1428e65b8441db2a73380a58c2fa1b2eda9460d6114891e480017"},"schema_version":"1.0","source":{"id":"2411.09406","kind":"arxiv","version":4}},"canonical_sha256":"148cdc4f80c68bc6ef90bfbb8ccd7ab7a4d1d942c0b0b0c5edaa05620add0f58","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"148cdc4f80c68bc6ef90bfbb8ccd7ab7a4d1d942c0b0b0c5edaa05620add0f58","first_computed_at":"2026-05-26T02:03:47.153611Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:03:47.153611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EohPXafLoXO4SVCfzmno4PH9IaEt3Nj3g1eR0u35GLKFelahR4MR2+6CdyPSdA4p//6SOl0DN7Pj5v9gIP73Bw==","signature_status":"signed_v1","signed_at":"2026-05-26T02:03:47.154580Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.09406","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ee138c1fce5060ad1cfb547060cc17e1c9ff34d4b57dadda32db0135fd0f634","sha256:6420ee15568f56c2d80c031b37688e94ff61b54288cc1bfb877e4b6d4eb1ae83"],"state_sha256":"29689f12e1fe2defb887bd20ba122dfb39af189e762ed893f5746a391f6c6b97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1eXvvbYg9H8ozNtz6BPxWnn2Z/zzum5ih1umQqPJzAI3trpNNUJALXc8LmeqN9Ab53+EzhGMy2ObqQA8yFmFCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T01:32:02.534347Z","bundle_sha256":"a2005637b06700ac88ce6f822bb7cbd37f2bd545e0a30ffd1fc5de5c6b877e67"}}