{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HKH4BJIPU2J5IEM56H2XHQUSP4","short_pith_number":"pith:HKH4BJIP","canonical_record":{"source":{"id":"1604.05809","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-20T03:54:29Z","cross_cats_sorted":["math.FA","math.MP"],"title_canon_sha256":"dce5e2a0da8e522830d99a550fbedd135db160f34dbb58d2b37b8a0dfeac1fd2","abstract_canon_sha256":"4cd9aa489a20ed121fea672440bead05632209d71fe9dc65e3d887af393c27b7"},"schema_version":"1.0"},"canonical_sha256":"3a8fc0a50fa693d4119df1f573c2927f1bc36ff6b9f4ce6ea7e9b0edd405b1c4","source":{"kind":"arxiv","id":"1604.05809","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.05809","created_at":"2026-05-18T00:47:14Z"},{"alias_kind":"arxiv_version","alias_value":"1604.05809v2","created_at":"2026-05-18T00:47:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.05809","created_at":"2026-05-18T00:47:14Z"},{"alias_kind":"pith_short_12","alias_value":"HKH4BJIPU2J5","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HKH4BJIPU2J5IEM5","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HKH4BJIP","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HKH4BJIPU2J5IEM56H2XHQUSP4","target":"record","payload":{"canonical_record":{"source":{"id":"1604.05809","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-20T03:54:29Z","cross_cats_sorted":["math.FA","math.MP"],"title_canon_sha256":"dce5e2a0da8e522830d99a550fbedd135db160f34dbb58d2b37b8a0dfeac1fd2","abstract_canon_sha256":"4cd9aa489a20ed121fea672440bead05632209d71fe9dc65e3d887af393c27b7"},"schema_version":"1.0"},"canonical_sha256":"3a8fc0a50fa693d4119df1f573c2927f1bc36ff6b9f4ce6ea7e9b0edd405b1c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:14.973113Z","signature_b64":"iCe5EgMZYqwdOPbgDDe+OuftRPbTLsrwjOkjWUA2xLHqyC+zev5mM7erKdF0eSgeeFC1V+v67Ey2YCB0UVs5CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a8fc0a50fa693d4119df1f573c2927f1bc36ff6b9f4ce6ea7e9b0edd405b1c4","last_reissued_at":"2026-05-18T00:47:14.972462Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:14.972462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.05809","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":"2026-05-18T00:47:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BWHn4llwIunhpV1xe4exCzdcDpmxn8IqXQaJUiqASs9IN6HBvVcrurHT5kb6OQAUz111Byil4VCnvwJv4HtXAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T08:38:39.334246Z"},"content_sha256":"6307938f7caae5f38b2824a235d61b827ead4b28dfb10bf7f8aa2854ef74410b","schema_version":"1.0","event_id":"sha256:6307938f7caae5f38b2824a235d61b827ead4b28dfb10bf7f8aa2854ef74410b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HKH4BJIPU2J5IEM56H2XHQUSP4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improving the Lieb-Robinson bound for long-range interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"S. Nakamura, T. Koma, T. Matsuta","submitted_at":"2016-04-20T03:54:29Z","abstract_excerpt":"We improve the Lieb-Robinson bound for a wide class of quantum many-body systems with long-range interactions decaying by power law. As an application, we show that the group velocity of information propagation grows by power law in time for such systems, whereas systems with short-range interactions exhibit a finite group velocity as shown by Lieb and Robinson."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05809","kind":"arxiv","version":2},"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":"2026-05-18T00:47:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ciDRKtiAiMjF5w2qYM9Qz7bvPEVSY3L6NzGQiMexamKrP+RpaqeETYE4z9CasIBV5antGF1d1UtDhI8hVXOhAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T08:38:39.334694Z"},"content_sha256":"17b5b3f9eb033d12aa8cb038e16e18161a71335fdf043961a4a0a14154adc32a","schema_version":"1.0","event_id":"sha256:17b5b3f9eb033d12aa8cb038e16e18161a71335fdf043961a4a0a14154adc32a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HKH4BJIPU2J5IEM56H2XHQUSP4/bundle.json","state_url":"https://pith.science/pith/HKH4BJIPU2J5IEM56H2XHQUSP4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HKH4BJIPU2J5IEM56H2XHQUSP4/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":"2026-08-15T08:38:39Z","links":{"resolver":"https://pith.science/pith/HKH4BJIPU2J5IEM56H2XHQUSP4","bundle":"https://pith.science/pith/HKH4BJIPU2J5IEM56H2XHQUSP4/bundle.json","state":"https://pith.science/pith/HKH4BJIPU2J5IEM56H2XHQUSP4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HKH4BJIPU2J5IEM56H2XHQUSP4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HKH4BJIPU2J5IEM56H2XHQUSP4","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":"4cd9aa489a20ed121fea672440bead05632209d71fe9dc65e3d887af393c27b7","cross_cats_sorted":["math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-20T03:54:29Z","title_canon_sha256":"dce5e2a0da8e522830d99a550fbedd135db160f34dbb58d2b37b8a0dfeac1fd2"},"schema_version":"1.0","source":{"id":"1604.05809","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.05809","created_at":"2026-05-18T00:47:14Z"},{"alias_kind":"arxiv_version","alias_value":"1604.05809v2","created_at":"2026-05-18T00:47:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.05809","created_at":"2026-05-18T00:47:14Z"},{"alias_kind":"pith_short_12","alias_value":"HKH4BJIPU2J5","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HKH4BJIPU2J5IEM5","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HKH4BJIP","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:17b5b3f9eb033d12aa8cb038e16e18161a71335fdf043961a4a0a14154adc32a","target":"graph","created_at":"2026-05-18T00:47:14Z","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":"We improve the Lieb-Robinson bound for a wide class of quantum many-body systems with long-range interactions decaying by power law. As an application, we show that the group velocity of information propagation grows by power law in time for such systems, whereas systems with short-range interactions exhibit a finite group velocity as shown by Lieb and Robinson.","authors_text":"S. Nakamura, T. Koma, T. Matsuta","cross_cats":["math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-20T03:54:29Z","title":"Improving the Lieb-Robinson bound for long-range interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05809","kind":"arxiv","version":2},"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":"sha256:6307938f7caae5f38b2824a235d61b827ead4b28dfb10bf7f8aa2854ef74410b","target":"record","created_at":"2026-05-18T00:47:14Z","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":"4cd9aa489a20ed121fea672440bead05632209d71fe9dc65e3d887af393c27b7","cross_cats_sorted":["math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-20T03:54:29Z","title_canon_sha256":"dce5e2a0da8e522830d99a550fbedd135db160f34dbb58d2b37b8a0dfeac1fd2"},"schema_version":"1.0","source":{"id":"1604.05809","kind":"arxiv","version":2}},"canonical_sha256":"3a8fc0a50fa693d4119df1f573c2927f1bc36ff6b9f4ce6ea7e9b0edd405b1c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a8fc0a50fa693d4119df1f573c2927f1bc36ff6b9f4ce6ea7e9b0edd405b1c4","first_computed_at":"2026-05-18T00:47:14.972462Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:14.972462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iCe5EgMZYqwdOPbgDDe+OuftRPbTLsrwjOkjWUA2xLHqyC+zev5mM7erKdF0eSgeeFC1V+v67Ey2YCB0UVs5CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:14.973113Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.05809","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6307938f7caae5f38b2824a235d61b827ead4b28dfb10bf7f8aa2854ef74410b","sha256:17b5b3f9eb033d12aa8cb038e16e18161a71335fdf043961a4a0a14154adc32a"],"state_sha256":"5f3a028a842ba031c5e0a19cb72b7fdd337c01e75bca548c1ac6ff9b22b4c1f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lwmzW4WiErXvJtRhx5e0Ln6pdURd5S8XT2QAl9GOa/70ThIiw9bL0L0FVcoz3l5Ha1k90Ct/nVWGp7n30L8fAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T08:38:39.338351Z","bundle_sha256":"7c4b6191321bbec9be9b980780a8f3f49c8daeab45b1e38766482752f3a185be"}}