{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:CJA4QUEUHCC4UKTEEGBDNJIKQP","short_pith_number":"pith:CJA4QUEU","canonical_record":{"source":{"id":"1811.12426","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2018-11-29T19:00:14Z","cross_cats_sorted":["cond-mat.dis-nn","quant-ph"],"title_canon_sha256":"44588b6cee632d46cc3a6b859d5c1518329a69a7da6a6ffc89b7a1c271ebb2f6","abstract_canon_sha256":"8b7a60d78daf600302101a7f87d98d1512bd4cbe848ea5fdb530869facc1826c"},"schema_version":"1.0"},"canonical_sha256":"1241c850943885ca2a64218236a50a83e3f4f5fc53d67797d04b0306e3912ba9","source":{"kind":"arxiv","id":"1811.12426","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12426","created_at":"2026-05-17T23:50:58Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12426v1","created_at":"2026-05-17T23:50:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12426","created_at":"2026-05-17T23:50:58Z"},{"alias_kind":"pith_short_12","alias_value":"CJA4QUEUHCC4","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CJA4QUEUHCC4UKTE","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CJA4QUEU","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:CJA4QUEUHCC4UKTEEGBDNJIKQP","target":"record","payload":{"canonical_record":{"source":{"id":"1811.12426","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2018-11-29T19:00:14Z","cross_cats_sorted":["cond-mat.dis-nn","quant-ph"],"title_canon_sha256":"44588b6cee632d46cc3a6b859d5c1518329a69a7da6a6ffc89b7a1c271ebb2f6","abstract_canon_sha256":"8b7a60d78daf600302101a7f87d98d1512bd4cbe848ea5fdb530869facc1826c"},"schema_version":"1.0"},"canonical_sha256":"1241c850943885ca2a64218236a50a83e3f4f5fc53d67797d04b0306e3912ba9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:58.785148Z","signature_b64":"6ObdMEWPjoZ0xyIq8fbejEQKinjDMzuiYiprKV1oJEThSdPiZnCaz3B0AaOFeINCoAreOS7RtuyC8SsiuG/5BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1241c850943885ca2a64218236a50a83e3f4f5fc53d67797d04b0306e3912ba9","last_reissued_at":"2026-05-17T23:50:58.784379Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:58.784379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.12426","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:50:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D6Zqf0dp1Ks/aQqS98Wc/hGy5LGFqmjhxTpr9AFqyaAEYuP+NDAfHt0twZlJRhlHBf0YRktqlpyntjH6/W2dCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T11:37:41.142862Z"},"content_sha256":"13a54eaf48dfe6aab7076b0d74752f494d1731f6703443c6d280be0540f8b642","schema_version":"1.0","event_id":"sha256:13a54eaf48dfe6aab7076b0d74752f494d1731f6703443c6d280be0540f8b642"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:CJA4QUEUHCC4UKTEEGBDNJIKQP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Floquet time crystals in clock models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","quant-ph"],"primary_cat":"cond-mat.quant-gas","authors_text":"Alessandro Silva, Angelo Russomanno, Federica Maria Surace, Fernando Iemini, Marcello Dalmonte, Rosario Fazio","submitted_at":"2018-11-29T19:00:14Z","abstract_excerpt":"We construct a class of period-$n$-tupling discrete time crystals based on $\\mathbb{Z}_n$ clock variables, for all the integers $n$. We consider two classes of systems where this phenomenology occurs, disordered models with short-range interactions and fully connected models. In the case of short-range models we provide a complete classification of time-crystal phases for generic $n$. For the specific cases of $n=3$ and $n=4$ we study in details the dynamics by means of exact diagonalisation. In both cases, through an extensive analysis of the Floquet spectrum, we are able to fully map the pha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12426","kind":"arxiv","version":1},"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":"2026-05-17T23:50:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"99COZaZLiL3LKb3H/JybvFvTIMn6afnw1X1EVecjML5Z8bpakpOBFnVNf1tzLkhqE8hBqLqrTJcdqD2Qbx+TAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T11:37:41.143653Z"},"content_sha256":"88addf5871799cb5eebac2a2c70c3681c4b46037b15b3af1b91460d58f3e503e","schema_version":"1.0","event_id":"sha256:88addf5871799cb5eebac2a2c70c3681c4b46037b15b3af1b91460d58f3e503e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CJA4QUEUHCC4UKTEEGBDNJIKQP/bundle.json","state_url":"https://pith.science/pith/CJA4QUEUHCC4UKTEEGBDNJIKQP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CJA4QUEUHCC4UKTEEGBDNJIKQP/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":"2026-06-02T11:37:41Z","links":{"resolver":"https://pith.science/pith/CJA4QUEUHCC4UKTEEGBDNJIKQP","bundle":"https://pith.science/pith/CJA4QUEUHCC4UKTEEGBDNJIKQP/bundle.json","state":"https://pith.science/pith/CJA4QUEUHCC4UKTEEGBDNJIKQP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CJA4QUEUHCC4UKTEEGBDNJIKQP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CJA4QUEUHCC4UKTEEGBDNJIKQP","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":"8b7a60d78daf600302101a7f87d98d1512bd4cbe848ea5fdb530869facc1826c","cross_cats_sorted":["cond-mat.dis-nn","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2018-11-29T19:00:14Z","title_canon_sha256":"44588b6cee632d46cc3a6b859d5c1518329a69a7da6a6ffc89b7a1c271ebb2f6"},"schema_version":"1.0","source":{"id":"1811.12426","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12426","created_at":"2026-05-17T23:50:58Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12426v1","created_at":"2026-05-17T23:50:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12426","created_at":"2026-05-17T23:50:58Z"},{"alias_kind":"pith_short_12","alias_value":"CJA4QUEUHCC4","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CJA4QUEUHCC4UKTE","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CJA4QUEU","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:88addf5871799cb5eebac2a2c70c3681c4b46037b15b3af1b91460d58f3e503e","target":"graph","created_at":"2026-05-17T23:50:58Z","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 construct a class of period-$n$-tupling discrete time crystals based on $\\mathbb{Z}_n$ clock variables, for all the integers $n$. We consider two classes of systems where this phenomenology occurs, disordered models with short-range interactions and fully connected models. In the case of short-range models we provide a complete classification of time-crystal phases for generic $n$. For the specific cases of $n=3$ and $n=4$ we study in details the dynamics by means of exact diagonalisation. In both cases, through an extensive analysis of the Floquet spectrum, we are able to fully map the pha","authors_text":"Alessandro Silva, Angelo Russomanno, Federica Maria Surace, Fernando Iemini, Marcello Dalmonte, Rosario Fazio","cross_cats":["cond-mat.dis-nn","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2018-11-29T19:00:14Z","title":"Floquet time crystals in clock models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12426","kind":"arxiv","version":1},"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":"sha256:13a54eaf48dfe6aab7076b0d74752f494d1731f6703443c6d280be0540f8b642","target":"record","created_at":"2026-05-17T23:50:58Z","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":"8b7a60d78daf600302101a7f87d98d1512bd4cbe848ea5fdb530869facc1826c","cross_cats_sorted":["cond-mat.dis-nn","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2018-11-29T19:00:14Z","title_canon_sha256":"44588b6cee632d46cc3a6b859d5c1518329a69a7da6a6ffc89b7a1c271ebb2f6"},"schema_version":"1.0","source":{"id":"1811.12426","kind":"arxiv","version":1}},"canonical_sha256":"1241c850943885ca2a64218236a50a83e3f4f5fc53d67797d04b0306e3912ba9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1241c850943885ca2a64218236a50a83e3f4f5fc53d67797d04b0306e3912ba9","first_computed_at":"2026-05-17T23:50:58.784379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:58.784379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6ObdMEWPjoZ0xyIq8fbejEQKinjDMzuiYiprKV1oJEThSdPiZnCaz3B0AaOFeINCoAreOS7RtuyC8SsiuG/5BA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:58.785148Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.12426","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13a54eaf48dfe6aab7076b0d74752f494d1731f6703443c6d280be0540f8b642","sha256:88addf5871799cb5eebac2a2c70c3681c4b46037b15b3af1b91460d58f3e503e"],"state_sha256":"c48e6e7686c0870044210e5486aba08a4a98ae4e4d9c35d6eddef21a930d5d21"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xk7fsgrJ+/1OMVyHhlS7op2Jlf92VHTDV4a1fgSvyBSCDe+SQojUd9KJIj8Uum27Gqkryu/siSVFzjRDphU9Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T11:37:41.147161Z","bundle_sha256":"ba061cb5ac111d51e00bb733a9e952b47fc220512f2f523a12f963603e84d6f7"}}