{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:HI4XDWEKJQ22FFZTX22DXSUPSI","short_pith_number":"pith:HI4XDWEK","canonical_record":{"source":{"id":"1911.01470","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2019-11-04T19:59:32Z","cross_cats_sorted":["hep-th","math.QA","quant-ph"],"title_canon_sha256":"edbc2b54053b7ded66dac1ef70332e13d258eaf5f5e0e8753d851342a96bddbf","abstract_canon_sha256":"113e80a85201691407a1cd4316e47e796aeca3bf55ec6bb3f0ff12f37e19d1cd"},"schema_version":"1.0"},"canonical_sha256":"3a3971d88a4c35a29733beb43bca8f9209290d6b51dd30d194e818d6b9042274","source":{"kind":"arxiv","id":"1911.01470","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.01470","created_at":"2026-07-05T01:09:01Z"},{"alias_kind":"arxiv_version","alias_value":"1911.01470v3","created_at":"2026-07-05T01:09:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.01470","created_at":"2026-07-05T01:09:01Z"},{"alias_kind":"pith_short_12","alias_value":"HI4XDWEKJQ22","created_at":"2026-07-05T01:09:01Z"},{"alias_kind":"pith_short_16","alias_value":"HI4XDWEKJQ22FFZT","created_at":"2026-07-05T01:09:01Z"},{"alias_kind":"pith_short_8","alias_value":"HI4XDWEK","created_at":"2026-07-05T01:09:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:HI4XDWEKJQ22FFZTX22DXSUPSI","target":"record","payload":{"canonical_record":{"source":{"id":"1911.01470","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2019-11-04T19:59:32Z","cross_cats_sorted":["hep-th","math.QA","quant-ph"],"title_canon_sha256":"edbc2b54053b7ded66dac1ef70332e13d258eaf5f5e0e8753d851342a96bddbf","abstract_canon_sha256":"113e80a85201691407a1cd4316e47e796aeca3bf55ec6bb3f0ff12f37e19d1cd"},"schema_version":"1.0"},"canonical_sha256":"3a3971d88a4c35a29733beb43bca8f9209290d6b51dd30d194e818d6b9042274","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:09:01.657132Z","signature_b64":"GkFrx3tGXtl4+58nihijLKpb9TgLI607Hp2BnFoLwG1RTux1eMH2DxvJe51MXGN8hPH9zK3Sf2Y6CU3cdm3hBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a3971d88a4c35a29733beb43bca8f9209290d6b51dd30d194e818d6b9042274","last_reissued_at":"2026-07-05T01:09:01.656632Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:09:01.656632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1911.01470","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":"2026-07-05T01:09:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Cl+WjBzc2+7R0YPkBYgXh4j7eN9DSllDkBk50/UKWlFdfa3aKnwhh/4rhhQVP4li/X81rH2yhqyRrObz+grBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T11:11:00.385058Z"},"content_sha256":"3193c8c372c3901adb2e988892a97e8f8db340e6a55d481fa5969c4e7045539d","schema_version":"1.0","event_id":"sha256:3193c8c372c3901adb2e988892a97e8f8db340e6a55d481fa5969c4e7045539d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:HI4XDWEKJQ22FFZTX22DXSUPSI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Verlinde formula from entanglement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.QA","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Bowen Shi","submitted_at":"2019-11-04T19:59:32Z","abstract_excerpt":"We derive the Verlinde formula from a recently advocated set of axioms about entanglement entropy [B. Shi, K. Kato, I. H. Kim, arXiv:1906.09376 (2019)]. For any state that obeys these axioms, we can define a quantity that can be identified as the topological $S$-matrix of an abstract anyon theory. We show that the $S$-matrix is unitary and that it recovers the fusion multiplicities of the underlying anyon theory through the Verlinde formula. Importantly, we rigorously prove the modularity of the theory, which further implies that the mutual braiding statistics of anyons are nontrivial. The key"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.01470","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1911.01470/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":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:09:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/DQ4YL0A7qL1cp2n7JFoGXmDbMfZyPh9nOueqQF4AmR/88M/FTPHfs2QnlsNVTMAZwSi+hkl2yIpePqJHqETDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T11:11:00.386074Z"},"content_sha256":"88949787c8d2977620da10bec723ef1096e3f5979d1c46382681bdf1ee11ca41","schema_version":"1.0","event_id":"sha256:88949787c8d2977620da10bec723ef1096e3f5979d1c46382681bdf1ee11ca41"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HI4XDWEKJQ22FFZTX22DXSUPSI/bundle.json","state_url":"https://pith.science/pith/HI4XDWEKJQ22FFZTX22DXSUPSI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HI4XDWEKJQ22FFZTX22DXSUPSI/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":"2026-08-18T11:11:00Z","links":{"resolver":"https://pith.science/pith/HI4XDWEKJQ22FFZTX22DXSUPSI","bundle":"https://pith.science/pith/HI4XDWEKJQ22FFZTX22DXSUPSI/bundle.json","state":"https://pith.science/pith/HI4XDWEKJQ22FFZTX22DXSUPSI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HI4XDWEKJQ22FFZTX22DXSUPSI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:HI4XDWEKJQ22FFZTX22DXSUPSI","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":"113e80a85201691407a1cd4316e47e796aeca3bf55ec6bb3f0ff12f37e19d1cd","cross_cats_sorted":["hep-th","math.QA","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2019-11-04T19:59:32Z","title_canon_sha256":"edbc2b54053b7ded66dac1ef70332e13d258eaf5f5e0e8753d851342a96bddbf"},"schema_version":"1.0","source":{"id":"1911.01470","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.01470","created_at":"2026-07-05T01:09:01Z"},{"alias_kind":"arxiv_version","alias_value":"1911.01470v3","created_at":"2026-07-05T01:09:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.01470","created_at":"2026-07-05T01:09:01Z"},{"alias_kind":"pith_short_12","alias_value":"HI4XDWEKJQ22","created_at":"2026-07-05T01:09:01Z"},{"alias_kind":"pith_short_16","alias_value":"HI4XDWEKJQ22FFZT","created_at":"2026-07-05T01:09:01Z"},{"alias_kind":"pith_short_8","alias_value":"HI4XDWEK","created_at":"2026-07-05T01:09:01Z"}],"graph_snapshots":[{"event_id":"sha256:88949787c8d2977620da10bec723ef1096e3f5979d1c46382681bdf1ee11ca41","target":"graph","created_at":"2026-07-05T01:09:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1911.01470/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive the Verlinde formula from a recently advocated set of axioms about entanglement entropy [B. Shi, K. Kato, I. H. Kim, arXiv:1906.09376 (2019)]. For any state that obeys these axioms, we can define a quantity that can be identified as the topological $S$-matrix of an abstract anyon theory. We show that the $S$-matrix is unitary and that it recovers the fusion multiplicities of the underlying anyon theory through the Verlinde formula. Importantly, we rigorously prove the modularity of the theory, which further implies that the mutual braiding statistics of anyons are nontrivial. The key","authors_text":"Bowen Shi","cross_cats":["hep-th","math.QA","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2019-11-04T19:59:32Z","title":"Verlinde formula from entanglement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.01470","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":"sha256:3193c8c372c3901adb2e988892a97e8f8db340e6a55d481fa5969c4e7045539d","target":"record","created_at":"2026-07-05T01:09:01Z","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":"113e80a85201691407a1cd4316e47e796aeca3bf55ec6bb3f0ff12f37e19d1cd","cross_cats_sorted":["hep-th","math.QA","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2019-11-04T19:59:32Z","title_canon_sha256":"edbc2b54053b7ded66dac1ef70332e13d258eaf5f5e0e8753d851342a96bddbf"},"schema_version":"1.0","source":{"id":"1911.01470","kind":"arxiv","version":3}},"canonical_sha256":"3a3971d88a4c35a29733beb43bca8f9209290d6b51dd30d194e818d6b9042274","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a3971d88a4c35a29733beb43bca8f9209290d6b51dd30d194e818d6b9042274","first_computed_at":"2026-07-05T01:09:01.656632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:09:01.656632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GkFrx3tGXtl4+58nihijLKpb9TgLI607Hp2BnFoLwG1RTux1eMH2DxvJe51MXGN8hPH9zK3Sf2Y6CU3cdm3hBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:09:01.657132Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.01470","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3193c8c372c3901adb2e988892a97e8f8db340e6a55d481fa5969c4e7045539d","sha256:88949787c8d2977620da10bec723ef1096e3f5979d1c46382681bdf1ee11ca41"],"state_sha256":"c6c1b1904e260f954b23b9348434e449750b087852afbda418232a6a41253b97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qXHfsy8QbfxAezSrUT4xnkr6o3esDdAITt0m/f8726PCMcLGBOFu6ROaCUqgNa211vXl6yQOj9+T1PYrQv05AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T11:11:00.393698Z","bundle_sha256":"ae6b153c10af21f049166be9ff667708ebb2f4e86decfb57ba5bf392aa38430c"}}