{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:VZWBUKFRWAIQOBIZDB3ZNHKAWD","short_pith_number":"pith:VZWBUKFR","schema_version":"1.0","canonical_sha256":"ae6c1a28b1b0110705191877969d40b0cb117445c49737580a6cc29711eba710","source":{"kind":"arxiv","id":"1610.00200","version":1},"attestation_state":"computed","paper":{"title":"One-dimensional long-range percolation: a numerical study","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"A. Trombettoni, G. Gori, M. Michelangeli, N. Defenu","submitted_at":"2016-10-01T22:58:25Z","abstract_excerpt":"In this paper we study bond percolation on a one-dimensional chain with power-law bond probability $C/ r^{1+\\sigma}$, where $r$ is the distance length between distinct sites. We introduce and test an order $N$ Monte Carlo algorithm and we determine as a function of $\\sigma$ the critical value $C_{c}$ at which percolation occurs. The critical exponents in the range $0<\\sigma<1$ are reported and compared with mean-field and $\\varepsilon$-expansion results. Our analysis is in agreement, up to a numerical precision $\\approx 10^{-3}$, with the mean field result for the anomalous dimension $\\eta=2-\\"},"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":"1610.00200","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-10-01T22:58:25Z","cross_cats_sorted":[],"title_canon_sha256":"707e739e68403f896e07774754f9fa96d7217bbec5fb4f2d2e467ce85cfd00ee","abstract_canon_sha256":"6b163d41da8206d59699c4c86109cff7850e2674e98744893daf15c597393c01"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:33.267502Z","signature_b64":"9v5mwQDTGPb/8Ul0/u+pXNrV+aoOyYnH338OT2Z4q1euRVNY0EK9Il8oWdvgBLiw7/aBgLOj6bA8zLkJcVmgAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae6c1a28b1b0110705191877969d40b0cb117445c49737580a6cc29711eba710","last_reissued_at":"2026-05-18T00:40:33.266204Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:33.266204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"One-dimensional long-range percolation: a numerical study","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"A. Trombettoni, G. Gori, M. Michelangeli, N. Defenu","submitted_at":"2016-10-01T22:58:25Z","abstract_excerpt":"In this paper we study bond percolation on a one-dimensional chain with power-law bond probability $C/ r^{1+\\sigma}$, where $r$ is the distance length between distinct sites. We introduce and test an order $N$ Monte Carlo algorithm and we determine as a function of $\\sigma$ the critical value $C_{c}$ at which percolation occurs. The critical exponents in the range $0<\\sigma<1$ are reported and compared with mean-field and $\\varepsilon$-expansion results. Our analysis is in agreement, up to a numerical precision $\\approx 10^{-3}$, with the mean field result for the anomalous dimension $\\eta=2-\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00200","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":"1610.00200","created_at":"2026-05-18T00:40:33.266336+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.00200v1","created_at":"2026-05-18T00:40:33.266336+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00200","created_at":"2026-05-18T00:40:33.266336+00:00"},{"alias_kind":"pith_short_12","alias_value":"VZWBUKFRWAIQ","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"VZWBUKFRWAIQOBIZ","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"VZWBUKFR","created_at":"2026-05-18T12:30:48.956258+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/VZWBUKFRWAIQOBIZDB3ZNHKAWD","json":"https://pith.science/pith/VZWBUKFRWAIQOBIZDB3ZNHKAWD.json","graph_json":"https://pith.science/api/pith-number/VZWBUKFRWAIQOBIZDB3ZNHKAWD/graph.json","events_json":"https://pith.science/api/pith-number/VZWBUKFRWAIQOBIZDB3ZNHKAWD/events.json","paper":"https://pith.science/paper/VZWBUKFR"},"agent_actions":{"view_html":"https://pith.science/pith/VZWBUKFRWAIQOBIZDB3ZNHKAWD","download_json":"https://pith.science/pith/VZWBUKFRWAIQOBIZDB3ZNHKAWD.json","view_paper":"https://pith.science/paper/VZWBUKFR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.00200&json=true","fetch_graph":"https://pith.science/api/pith-number/VZWBUKFRWAIQOBIZDB3ZNHKAWD/graph.json","fetch_events":"https://pith.science/api/pith-number/VZWBUKFRWAIQOBIZDB3ZNHKAWD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VZWBUKFRWAIQOBIZDB3ZNHKAWD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VZWBUKFRWAIQOBIZDB3ZNHKAWD/action/storage_attestation","attest_author":"https://pith.science/pith/VZWBUKFRWAIQOBIZDB3ZNHKAWD/action/author_attestation","sign_citation":"https://pith.science/pith/VZWBUKFRWAIQOBIZDB3ZNHKAWD/action/citation_signature","submit_replication":"https://pith.science/pith/VZWBUKFRWAIQOBIZDB3ZNHKAWD/action/replication_record"}},"created_at":"2026-05-18T00:40:33.266336+00:00","updated_at":"2026-05-18T00:40:33.266336+00:00"}