{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1995:F6U56TQO2NAYKXL3X3YDQRTYSZ","short_pith_number":"pith:F6U56TQO","schema_version":"1.0","canonical_sha256":"2fa9df4e0ed341855d7bbef0384678964fbfdad002886f5dd3580cf9b2af6771","source":{"kind":"arxiv","id":"hep-lat/9506012","version":1},"attestation_state":"computed","paper":{"title":"SPHERICALLY SYMMETRIC RANDOM WALKS II. DIMENSIONALLY DEPENDENT CRITICAL BEHAVIOR","license":"","headline":"","cross_cats":["cond-mat"],"primary_cat":"hep-lat","authors_text":"Carl M. Bender, Peter N. Meisinger (Washington U. in St. Louis), Stefan Boettcher (Brookhaven National Laboratory)","submitted_at":"1995-06-06T17:00:31Z","abstract_excerpt":"A recently developed model of random walks on a $D$-dimensional hyperspherical lattice, where $D$ is {\\sl not} restricted to integer values, is extended to include the possibility of creating and annihilating random walkers. Steady-state distributions of random walkers are obtained for all dimensions $D>0$ by solving a discrete eigenvalue problem. These distributions exhibit dimensionally dependent critical behavior as a function of the birth rate. This remarkably simple model exhibits a second-order phase transition with a nontrivial critical exponent for all dimensions $D>0$."},"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":"hep-lat/9506012","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-lat","submitted_at":"1995-06-06T17:00:31Z","cross_cats_sorted":["cond-mat"],"title_canon_sha256":"c7761f403fcca5839861aa109df25f4ead2add65fe768446c58ee6f5def4f1c1","abstract_canon_sha256":"47d91b76cdd9974b3fdeafe6f4f0a8118e1ffbc648536d3b8f05e2a2a5ff1c53"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:25.369512Z","signature_b64":"NOL/xn8o/4AQ0q9We9djRUY8sBez2hfGX1g18StrBJCeSKIsH1EQZiRqMNEx42k6qAGhEAD+/cqmeJ1r0Fr3AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fa9df4e0ed341855d7bbef0384678964fbfdad002886f5dd3580cf9b2af6771","last_reissued_at":"2026-05-18T04:35:25.368959Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:25.368959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"SPHERICALLY SYMMETRIC RANDOM WALKS II. DIMENSIONALLY DEPENDENT CRITICAL BEHAVIOR","license":"","headline":"","cross_cats":["cond-mat"],"primary_cat":"hep-lat","authors_text":"Carl M. Bender, Peter N. Meisinger (Washington U. in St. Louis), Stefan Boettcher (Brookhaven National Laboratory)","submitted_at":"1995-06-06T17:00:31Z","abstract_excerpt":"A recently developed model of random walks on a $D$-dimensional hyperspherical lattice, where $D$ is {\\sl not} restricted to integer values, is extended to include the possibility of creating and annihilating random walkers. Steady-state distributions of random walkers are obtained for all dimensions $D>0$ by solving a discrete eigenvalue problem. These distributions exhibit dimensionally dependent critical behavior as a function of the birth rate. This remarkably simple model exhibits a second-order phase transition with a nontrivial critical exponent for all dimensions $D>0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-lat/9506012","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":"hep-lat/9506012","created_at":"2026-05-18T04:35:25.369043+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-lat/9506012v1","created_at":"2026-05-18T04:35:25.369043+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-lat/9506012","created_at":"2026-05-18T04:35:25.369043+00:00"},{"alias_kind":"pith_short_12","alias_value":"F6U56TQO2NAY","created_at":"2026-05-18T12:25:47.700082+00:00"},{"alias_kind":"pith_short_16","alias_value":"F6U56TQO2NAYKXL3","created_at":"2026-05-18T12:25:47.700082+00:00"},{"alias_kind":"pith_short_8","alias_value":"F6U56TQO","created_at":"2026-05-18T12:25:47.700082+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/F6U56TQO2NAYKXL3X3YDQRTYSZ","json":"https://pith.science/pith/F6U56TQO2NAYKXL3X3YDQRTYSZ.json","graph_json":"https://pith.science/api/pith-number/F6U56TQO2NAYKXL3X3YDQRTYSZ/graph.json","events_json":"https://pith.science/api/pith-number/F6U56TQO2NAYKXL3X3YDQRTYSZ/events.json","paper":"https://pith.science/paper/F6U56TQO"},"agent_actions":{"view_html":"https://pith.science/pith/F6U56TQO2NAYKXL3X3YDQRTYSZ","download_json":"https://pith.science/pith/F6U56TQO2NAYKXL3X3YDQRTYSZ.json","view_paper":"https://pith.science/paper/F6U56TQO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-lat/9506012&json=true","fetch_graph":"https://pith.science/api/pith-number/F6U56TQO2NAYKXL3X3YDQRTYSZ/graph.json","fetch_events":"https://pith.science/api/pith-number/F6U56TQO2NAYKXL3X3YDQRTYSZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F6U56TQO2NAYKXL3X3YDQRTYSZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F6U56TQO2NAYKXL3X3YDQRTYSZ/action/storage_attestation","attest_author":"https://pith.science/pith/F6U56TQO2NAYKXL3X3YDQRTYSZ/action/author_attestation","sign_citation":"https://pith.science/pith/F6U56TQO2NAYKXL3X3YDQRTYSZ/action/citation_signature","submit_replication":"https://pith.science/pith/F6U56TQO2NAYKXL3X3YDQRTYSZ/action/replication_record"}},"created_at":"2026-05-18T04:35:25.369043+00:00","updated_at":"2026-05-18T04:35:25.369043+00:00"}