{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6U5SU3NQHQLCE4OJOYDDN5DVYZ","short_pith_number":"pith:6U5SU3NQ","schema_version":"1.0","canonical_sha256":"f53b2a6db03c162271c9760636f475c67d4d427a4844664a84edb1f65faaea14","source":{"kind":"arxiv","id":"1503.04739","version":3},"attestation_state":"computed","paper":{"title":"Complex Quantum Network Geometries: Evolution and Phase Transitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","gr-qc"],"primary_cat":"cond-mat.dis-nn","authors_text":"Christoph Rahmede, Ginestra Bianconi, Zhihao Wu","submitted_at":"2015-03-16T17:23:42Z","abstract_excerpt":"Networks are topological and geometric structures used to describe systems as different as the Internet, the brain or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e. simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a non-equilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network st"},"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":"1503.04739","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-03-16T17:23:42Z","cross_cats_sorted":["cond-mat.stat-mech","gr-qc"],"title_canon_sha256":"fb857e6aea9869d7936fab64fb3157be8dfe90b4906a1c9b8112a5aa8db10471","abstract_canon_sha256":"687c1004e59a2fb250a8595cb262096476da9fa30b855ec434f3b7bec97e3b69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:24.169232Z","signature_b64":"/zltCbrL3L+VdlTeJ8DnlATnitb5PN1NVO/QDZyW7Gc8hvvAxIgpUtjK9ZICCv0+cY/sKMfQWollJLP16BE6CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f53b2a6db03c162271c9760636f475c67d4d427a4844664a84edb1f65faaea14","last_reissued_at":"2026-05-18T01:34:24.168628Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:24.168628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complex Quantum Network Geometries: Evolution and Phase Transitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","gr-qc"],"primary_cat":"cond-mat.dis-nn","authors_text":"Christoph Rahmede, Ginestra Bianconi, Zhihao Wu","submitted_at":"2015-03-16T17:23:42Z","abstract_excerpt":"Networks are topological and geometric structures used to describe systems as different as the Internet, the brain or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e. simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a non-equilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04739","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1503.04739","created_at":"2026-05-18T01:34:24.168711+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.04739v3","created_at":"2026-05-18T01:34:24.168711+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04739","created_at":"2026-05-18T01:34:24.168711+00:00"},{"alias_kind":"pith_short_12","alias_value":"6U5SU3NQHQLC","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6U5SU3NQHQLCE4OJ","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6U5SU3NQ","created_at":"2026-05-18T12:29:07.941421+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/6U5SU3NQHQLCE4OJOYDDN5DVYZ","json":"https://pith.science/pith/6U5SU3NQHQLCE4OJOYDDN5DVYZ.json","graph_json":"https://pith.science/api/pith-number/6U5SU3NQHQLCE4OJOYDDN5DVYZ/graph.json","events_json":"https://pith.science/api/pith-number/6U5SU3NQHQLCE4OJOYDDN5DVYZ/events.json","paper":"https://pith.science/paper/6U5SU3NQ"},"agent_actions":{"view_html":"https://pith.science/pith/6U5SU3NQHQLCE4OJOYDDN5DVYZ","download_json":"https://pith.science/pith/6U5SU3NQHQLCE4OJOYDDN5DVYZ.json","view_paper":"https://pith.science/paper/6U5SU3NQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.04739&json=true","fetch_graph":"https://pith.science/api/pith-number/6U5SU3NQHQLCE4OJOYDDN5DVYZ/graph.json","fetch_events":"https://pith.science/api/pith-number/6U5SU3NQHQLCE4OJOYDDN5DVYZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6U5SU3NQHQLCE4OJOYDDN5DVYZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6U5SU3NQHQLCE4OJOYDDN5DVYZ/action/storage_attestation","attest_author":"https://pith.science/pith/6U5SU3NQHQLCE4OJOYDDN5DVYZ/action/author_attestation","sign_citation":"https://pith.science/pith/6U5SU3NQHQLCE4OJOYDDN5DVYZ/action/citation_signature","submit_replication":"https://pith.science/pith/6U5SU3NQHQLCE4OJOYDDN5DVYZ/action/replication_record"}},"created_at":"2026-05-18T01:34:24.168711+00:00","updated_at":"2026-05-18T01:34:24.168711+00:00"}