{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:62Q54WUHRGEB5NBVQZWYLZCGMZ","short_pith_number":"pith:62Q54WUH","canonical_record":{"source":{"id":"1112.4158","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2011-12-18T14:02:11Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"e12fbf7ed1045a1f9acc9b3678712540102a96dc99aacee6a1b77e26d216ebba","abstract_canon_sha256":"e1f713a2685a392b7e2fe5368ef940e975dcc2182b7bdb880906f390f797951d"},"schema_version":"1.0"},"canonical_sha256":"f6a1de5a8789881eb435866d85e446664aad28d3a77c4fefe8ca3885ef5719c2","source":{"kind":"arxiv","id":"1112.4158","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4158","created_at":"2026-05-18T03:22:53Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4158v1","created_at":"2026-05-18T03:22:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4158","created_at":"2026-05-18T03:22:53Z"},{"alias_kind":"pith_short_12","alias_value":"62Q54WUHRGEB","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"62Q54WUHRGEB5NBV","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"62Q54WUH","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:62Q54WUHRGEB5NBVQZWYLZCGMZ","target":"record","payload":{"canonical_record":{"source":{"id":"1112.4158","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2011-12-18T14:02:11Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"e12fbf7ed1045a1f9acc9b3678712540102a96dc99aacee6a1b77e26d216ebba","abstract_canon_sha256":"e1f713a2685a392b7e2fe5368ef940e975dcc2182b7bdb880906f390f797951d"},"schema_version":"1.0"},"canonical_sha256":"f6a1de5a8789881eb435866d85e446664aad28d3a77c4fefe8ca3885ef5719c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:22:53.904659Z","signature_b64":"JcS3h5SXdIQPHXULYqoHCTVliYG4xiWAya4UGNBYT6xdWNn7W8Lu9ZToHv4lKsdgCQ2sGUaghVigagiNLmkGDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6a1de5a8789881eb435866d85e446664aad28d3a77c4fefe8ca3885ef5719c2","last_reissued_at":"2026-05-18T03:22:53.904152Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:22:53.904152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.4158","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":"2026-05-18T03:22:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"feeDqohozUgOW9GL8pvqK5RCHpykuTSO/Zd3bEzVDrjSgU6LZIPhFOLgPl61HqZSh7kazlalvCVkbegkrenWCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:07:29.936500Z"},"content_sha256":"73d802816fca941a7be197ddc3246165caaa56ffb6825a8c5f6fa45d87900c6b","schema_version":"1.0","event_id":"sha256:73d802816fca941a7be197ddc3246165caaa56ffb6825a8c5f6fa45d87900c6b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:62Q54WUHRGEB5NBVQZWYLZCGMZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Controlling synchronization in large laser networks using number theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"physics.optics","authors_text":"Asher A. Friesem, Eitan Ronen, Ido Kanter, Micha Nixon, Moti Fridman, Nir Davidson","submitted_at":"2011-12-18T14:02:11Z","abstract_excerpt":"Synchronization in networks with delayed coupling are ubiquitous in nature and play a key role in almost all fields of science including physics, biology, ecology, climatology and sociology. In general, the published works on network synchronization are based on data analysis and simulations, with little experimental verification. Here we develop and experimentally demonstrate various multi-cluster phase synchronization scenarios within coupled laser networks. Synchronization is controlled by the network connectivity in accordance to number theory, whereby the number of synchronized clusters e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4158","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":"2026-05-18T03:22:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nWImu0SFo1TqxXcYu0zptDDZK/6bAyfOwL3qoytPyHBOyKc562GViKiTa9hxwZsADNcjcU4xtzHjOCJlWtIzBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:07:29.936851Z"},"content_sha256":"5ef9c5f9dc8f9eefdc0438b196a161e029cb2892c1e4cdb7c3d62a4925bf9935","schema_version":"1.0","event_id":"sha256:5ef9c5f9dc8f9eefdc0438b196a161e029cb2892c1e4cdb7c3d62a4925bf9935"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/62Q54WUHRGEB5NBVQZWYLZCGMZ/bundle.json","state_url":"https://pith.science/pith/62Q54WUHRGEB5NBVQZWYLZCGMZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/62Q54WUHRGEB5NBVQZWYLZCGMZ/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":"2026-06-04T04:07:29Z","links":{"resolver":"https://pith.science/pith/62Q54WUHRGEB5NBVQZWYLZCGMZ","bundle":"https://pith.science/pith/62Q54WUHRGEB5NBVQZWYLZCGMZ/bundle.json","state":"https://pith.science/pith/62Q54WUHRGEB5NBVQZWYLZCGMZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/62Q54WUHRGEB5NBVQZWYLZCGMZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:62Q54WUHRGEB5NBVQZWYLZCGMZ","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":"e1f713a2685a392b7e2fe5368ef940e975dcc2182b7bdb880906f390f797951d","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2011-12-18T14:02:11Z","title_canon_sha256":"e12fbf7ed1045a1f9acc9b3678712540102a96dc99aacee6a1b77e26d216ebba"},"schema_version":"1.0","source":{"id":"1112.4158","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4158","created_at":"2026-05-18T03:22:53Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4158v1","created_at":"2026-05-18T03:22:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4158","created_at":"2026-05-18T03:22:53Z"},{"alias_kind":"pith_short_12","alias_value":"62Q54WUHRGEB","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"62Q54WUHRGEB5NBV","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"62Q54WUH","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:5ef9c5f9dc8f9eefdc0438b196a161e029cb2892c1e4cdb7c3d62a4925bf9935","target":"graph","created_at":"2026-05-18T03:22:53Z","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":"Synchronization in networks with delayed coupling are ubiquitous in nature and play a key role in almost all fields of science including physics, biology, ecology, climatology and sociology. In general, the published works on network synchronization are based on data analysis and simulations, with little experimental verification. Here we develop and experimentally demonstrate various multi-cluster phase synchronization scenarios within coupled laser networks. Synchronization is controlled by the network connectivity in accordance to number theory, whereby the number of synchronized clusters e","authors_text":"Asher A. Friesem, Eitan Ronen, Ido Kanter, Micha Nixon, Moti Fridman, Nir Davidson","cross_cats":["nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2011-12-18T14:02:11Z","title":"Controlling synchronization in large laser networks using number theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4158","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":"sha256:73d802816fca941a7be197ddc3246165caaa56ffb6825a8c5f6fa45d87900c6b","target":"record","created_at":"2026-05-18T03:22:53Z","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":"e1f713a2685a392b7e2fe5368ef940e975dcc2182b7bdb880906f390f797951d","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2011-12-18T14:02:11Z","title_canon_sha256":"e12fbf7ed1045a1f9acc9b3678712540102a96dc99aacee6a1b77e26d216ebba"},"schema_version":"1.0","source":{"id":"1112.4158","kind":"arxiv","version":1}},"canonical_sha256":"f6a1de5a8789881eb435866d85e446664aad28d3a77c4fefe8ca3885ef5719c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6a1de5a8789881eb435866d85e446664aad28d3a77c4fefe8ca3885ef5719c2","first_computed_at":"2026-05-18T03:22:53.904152Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:22:53.904152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JcS3h5SXdIQPHXULYqoHCTVliYG4xiWAya4UGNBYT6xdWNn7W8Lu9ZToHv4lKsdgCQ2sGUaghVigagiNLmkGDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:22:53.904659Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4158","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73d802816fca941a7be197ddc3246165caaa56ffb6825a8c5f6fa45d87900c6b","sha256:5ef9c5f9dc8f9eefdc0438b196a161e029cb2892c1e4cdb7c3d62a4925bf9935"],"state_sha256":"2992a6152917ac5172b727e40b2bafb68473ed07827a192a52545cd3902ec68c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"crcEm40rPwh1+n5Tw27WkRTBX4WXAUVFDypfIK9tDBBvrweXLylW1XBAFw28Fx/KAdMK1h8JWjtsPhBrw/yxCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T04:07:29.938784Z","bundle_sha256":"fb30a5c7467e7e3440fe3ea497ffad06622e3c2fe574fb6de63c08a71ba98aa2"}}