{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AQZKRJL25MVEKU7WDFC4QZKQG6","short_pith_number":"pith:AQZKRJL2","canonical_record":{"source":{"id":"1603.02684","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2016-03-08T21:00:04Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"348d77cffa06df1b967773f9fb8ce01c745ed150a2da3d0e237deb1c664a7538","abstract_canon_sha256":"14b73ae759f30a4d7f388b661abe5f2788ae588d8e80e5dd4c37874d85da39f9"},"schema_version":"1.0"},"canonical_sha256":"0432a8a57aeb2a4553f61945c86550378dca67ba3ce8ada6ae5549ac8d24e98b","source":{"kind":"arxiv","id":"1603.02684","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.02684","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1603.02684v3","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.02684","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"AQZKRJL25MVE","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AQZKRJL25MVEKU7W","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AQZKRJL2","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AQZKRJL25MVEKU7WDFC4QZKQG6","target":"record","payload":{"canonical_record":{"source":{"id":"1603.02684","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2016-03-08T21:00:04Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"348d77cffa06df1b967773f9fb8ce01c745ed150a2da3d0e237deb1c664a7538","abstract_canon_sha256":"14b73ae759f30a4d7f388b661abe5f2788ae588d8e80e5dd4c37874d85da39f9"},"schema_version":"1.0"},"canonical_sha256":"0432a8a57aeb2a4553f61945c86550378dca67ba3ce8ada6ae5549ac8d24e98b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:13.703237Z","signature_b64":"FQbw33sSoV2Jb/k765igAj24Jt39EGHLNU7m7oeP/rHG72WtFbLPJ32ZCBhPFB8NYZ3vPl1zROPNFv6MbjVtAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0432a8a57aeb2a4553f61945c86550378dca67ba3ce8ada6ae5549ac8d24e98b","last_reissued_at":"2026-05-18T00:50:13.702804Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:13.702804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.02684","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":"2026-05-18T00:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VVj0qNlXzmaeHiWw84AtkbghiqhVRIN0FoF8JBZoEHiDp8lWcV+LvS9nYHg5qQTpwrS6MPDvbuDo67gM64QQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:46:10.187919Z"},"content_sha256":"f9d01dc4270ac5a44aa89a547976fcddf9f381779747f6bcc41558e65db67435","schema_version":"1.0","event_id":"sha256:f9d01dc4270ac5a44aa89a547976fcddf9f381779747f6bcc41558e65db67435"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AQZKRJL25MVEKU7WDFC4QZKQG6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cornering gapless quantum states via their torus entanglement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"cond-mat.str-el","authors_text":"Lauren E. Hayward Sierens, Roger G. Melko, William Witczak-Krempa","submitted_at":"2016-03-08T21:00:04Z","abstract_excerpt":"The entanglement entropy (EE) has emerged as an important window into the structure of complex quantum states of matter. We analyze the universal part of the EE for gapless systems put on tori in 2d/3d, denoted by $\\chi$. Focusing on scale invariant systems, we derive general non-perturbative properties for the shape dependence of $\\chi$, and reveal surprising relations to the EE associated with corners in the entangling surface. We obtain closed-form expressions for $\\chi$ in 2d/3d within a model that arises in the study of conformal field theories (CFTs), and use them to obtain ansatzes with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02684","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":"2026-05-18T00:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OeoMnpIxoZrzcjj9R01lIcw09L7JDWqmR1bTBsW7EJzD0n2MXIy7uOtJh8DZaaMy+UDgxXOYnylnPr54d0+YBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:46:10.188265Z"},"content_sha256":"a24fa0655d885d9e19c893ddf1a7d9a0aead13f837cd95df244e7bcc02ebc9d9","schema_version":"1.0","event_id":"sha256:a24fa0655d885d9e19c893ddf1a7d9a0aead13f837cd95df244e7bcc02ebc9d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AQZKRJL25MVEKU7WDFC4QZKQG6/bundle.json","state_url":"https://pith.science/pith/AQZKRJL25MVEKU7WDFC4QZKQG6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AQZKRJL25MVEKU7WDFC4QZKQG6/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":"2026-06-24T22:46:10Z","links":{"resolver":"https://pith.science/pith/AQZKRJL25MVEKU7WDFC4QZKQG6","bundle":"https://pith.science/pith/AQZKRJL25MVEKU7WDFC4QZKQG6/bundle.json","state":"https://pith.science/pith/AQZKRJL25MVEKU7WDFC4QZKQG6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AQZKRJL25MVEKU7WDFC4QZKQG6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AQZKRJL25MVEKU7WDFC4QZKQG6","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":"14b73ae759f30a4d7f388b661abe5f2788ae588d8e80e5dd4c37874d85da39f9","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2016-03-08T21:00:04Z","title_canon_sha256":"348d77cffa06df1b967773f9fb8ce01c745ed150a2da3d0e237deb1c664a7538"},"schema_version":"1.0","source":{"id":"1603.02684","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.02684","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1603.02684v3","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.02684","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"AQZKRJL25MVE","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AQZKRJL25MVEKU7W","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AQZKRJL2","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:a24fa0655d885d9e19c893ddf1a7d9a0aead13f837cd95df244e7bcc02ebc9d9","target":"graph","created_at":"2026-05-18T00:50:13Z","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":"The entanglement entropy (EE) has emerged as an important window into the structure of complex quantum states of matter. We analyze the universal part of the EE for gapless systems put on tori in 2d/3d, denoted by $\\chi$. Focusing on scale invariant systems, we derive general non-perturbative properties for the shape dependence of $\\chi$, and reveal surprising relations to the EE associated with corners in the entangling surface. We obtain closed-form expressions for $\\chi$ in 2d/3d within a model that arises in the study of conformal field theories (CFTs), and use them to obtain ansatzes with","authors_text":"Lauren E. Hayward Sierens, Roger G. Melko, William Witczak-Krempa","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2016-03-08T21:00:04Z","title":"Cornering gapless quantum states via their torus entanglement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02684","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:f9d01dc4270ac5a44aa89a547976fcddf9f381779747f6bcc41558e65db67435","target":"record","created_at":"2026-05-18T00:50:13Z","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":"14b73ae759f30a4d7f388b661abe5f2788ae588d8e80e5dd4c37874d85da39f9","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2016-03-08T21:00:04Z","title_canon_sha256":"348d77cffa06df1b967773f9fb8ce01c745ed150a2da3d0e237deb1c664a7538"},"schema_version":"1.0","source":{"id":"1603.02684","kind":"arxiv","version":3}},"canonical_sha256":"0432a8a57aeb2a4553f61945c86550378dca67ba3ce8ada6ae5549ac8d24e98b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0432a8a57aeb2a4553f61945c86550378dca67ba3ce8ada6ae5549ac8d24e98b","first_computed_at":"2026-05-18T00:50:13.702804Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:13.702804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FQbw33sSoV2Jb/k765igAj24Jt39EGHLNU7m7oeP/rHG72WtFbLPJ32ZCBhPFB8NYZ3vPl1zROPNFv6MbjVtAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:13.703237Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.02684","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9d01dc4270ac5a44aa89a547976fcddf9f381779747f6bcc41558e65db67435","sha256:a24fa0655d885d9e19c893ddf1a7d9a0aead13f837cd95df244e7bcc02ebc9d9"],"state_sha256":"325d7b9080434b06da63c0af4e1794fd7e84f31e33ca77fdfdc644a1c98d9b47"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Egk6zK5yyaaTb/LGgwvSoHkK5kIkrpMlyZbZ/r8N0gUx9Gynjyz++pj3ybkiW5uVuim+uAYpFVzY61LHp3KCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:46:10.190210Z","bundle_sha256":"0bc09fb2c95f2e53b6397a3c44350b386b79d08e72adcad1ff9a426f808451e4"}}