{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:LXQ422Z7NKCQSMZKTE2GSYMV7G","short_pith_number":"pith:LXQ422Z7","schema_version":"1.0","canonical_sha256":"5de1cd6b3f6a8509332a9934696195f9bcefe194fb2f4aa2d9506893cdf7da60","source":{"kind":"arxiv","id":"1406.7259","version":1},"attestation_state":"computed","paper":{"title":"Mandala Networks: ultra-robust, ultra-small-world and highly sparse graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"A. A. Moreira, C. I. N. Sampaio Filho, H. J. Herrmann, J. S. Andrade Jr, R. F. S. Andrade","submitted_at":"2014-06-27T18:13:11Z","abstract_excerpt":"The increasing demands in security and reliability of infrastructures call for the optimal design of their embedded complex networks topologies. The following question then arises: what is the optimal layout to fulfill best all the demands? Here we present a general solution for this problem with scale-free networks, like the Internet and airline networks. Precisely, we disclose a way to systematically construct networks which are 100$\\%$ robust against random failures as well as to malicious attacks. Furthermore, as the sizes of these networks increase, their shortest paths become asymptotica"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1406.7259","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-06-27T18:13:11Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"b391aa37cb3490e81eb9bf16cfe20a8884f283d10132eb65935712bf8f6c6ef4","abstract_canon_sha256":"81c65e929136fe322b2e8a15274ed4a1d5da58d2442bb0e7be9789bc7e1dd201"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:53.757813Z","signature_b64":"09IEgszpe5Lf9+95ZX3+F2wgQ9+0obkGLMmU7YAnymXMU/sSzgQe/AfK5EYApN7easNQfXFwN3VilfevKCG2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5de1cd6b3f6a8509332a9934696195f9bcefe194fb2f4aa2d9506893cdf7da60","last_reissued_at":"2026-05-18T02:48:53.757237Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:53.757237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mandala Networks: ultra-robust, ultra-small-world and highly sparse graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"A. A. Moreira, C. I. N. Sampaio Filho, H. J. Herrmann, J. S. Andrade Jr, R. F. S. Andrade","submitted_at":"2014-06-27T18:13:11Z","abstract_excerpt":"The increasing demands in security and reliability of infrastructures call for the optimal design of their embedded complex networks topologies. The following question then arises: what is the optimal layout to fulfill best all the demands? Here we present a general solution for this problem with scale-free networks, like the Internet and airline networks. Precisely, we disclose a way to systematically construct networks which are 100$\\%$ robust against random failures as well as to malicious attacks. Furthermore, as the sizes of these networks increase, their shortest paths become asymptotica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7259","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1406.7259","created_at":"2026-05-18T02:48:53.757334+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.7259v1","created_at":"2026-05-18T02:48:53.757334+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7259","created_at":"2026-05-18T02:48:53.757334+00:00"},{"alias_kind":"pith_short_12","alias_value":"LXQ422Z7NKCQ","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_16","alias_value":"LXQ422Z7NKCQSMZK","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_8","alias_value":"LXQ422Z7","created_at":"2026-05-18T12:28:38.356838+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LXQ422Z7NKCQSMZKTE2GSYMV7G","json":"https://pith.science/pith/LXQ422Z7NKCQSMZKTE2GSYMV7G.json","graph_json":"https://pith.science/api/pith-number/LXQ422Z7NKCQSMZKTE2GSYMV7G/graph.json","events_json":"https://pith.science/api/pith-number/LXQ422Z7NKCQSMZKTE2GSYMV7G/events.json","paper":"https://pith.science/paper/LXQ422Z7"},"agent_actions":{"view_html":"https://pith.science/pith/LXQ422Z7NKCQSMZKTE2GSYMV7G","download_json":"https://pith.science/pith/LXQ422Z7NKCQSMZKTE2GSYMV7G.json","view_paper":"https://pith.science/paper/LXQ422Z7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.7259&json=true","fetch_graph":"https://pith.science/api/pith-number/LXQ422Z7NKCQSMZKTE2GSYMV7G/graph.json","fetch_events":"https://pith.science/api/pith-number/LXQ422Z7NKCQSMZKTE2GSYMV7G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LXQ422Z7NKCQSMZKTE2GSYMV7G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LXQ422Z7NKCQSMZKTE2GSYMV7G/action/storage_attestation","attest_author":"https://pith.science/pith/LXQ422Z7NKCQSMZKTE2GSYMV7G/action/author_attestation","sign_citation":"https://pith.science/pith/LXQ422Z7NKCQSMZKTE2GSYMV7G/action/citation_signature","submit_replication":"https://pith.science/pith/LXQ422Z7NKCQSMZKTE2GSYMV7G/action/replication_record"}},"created_at":"2026-05-18T02:48:53.757334+00:00","updated_at":"2026-05-18T02:48:53.757334+00:00"}