{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:R6M37KSFY7WWQQTWDUXBU7AR4L","short_pith_number":"pith:R6M37KSF","schema_version":"1.0","canonical_sha256":"8f99bfaa45c7ed6842761d2e1a7c11e2fca38344ed0d37c312cef3c875f1e219","source":{"kind":"arxiv","id":"2607.24975","version":1},"attestation_state":"computed","paper":{"title":"Strongly-connected percolation on directed lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"M. E. J. Newman, P. Grassberger, R. M. Ziff","submitted_at":"2026-07-27T18:28:38Z","abstract_excerpt":"We study percolation on lattices with directed bonds, focusing on the behavior of strongly-connected percolation clusters -- clusters in which every site is reachable from every other along a directed path. We consider the two-dimensional square lattice and various globally isotropic arrangements of the directions of the bonds. Performing simulations using a range of algorithmic approaches, we calculate high-precision values for critical exponents, fractal dimensions, crossing probabilities, and percolation thresholds for bond percolation with each bond arrangement. We find that the critical b"},"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":"2607.24975","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-07-27T18:28:38Z","cross_cats_sorted":[],"title_canon_sha256":"c0b24d5e5833b8f3a1ae0e165104b461953584eb26b270d4749b895e9c15b6dc","abstract_canon_sha256":"158523fac136330ce1121595fba834031b2542ecfee65b7c5d0b54fc913f563e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-29T00:24:55.927694Z","signature_b64":"KsP0TlYNmQ5AhcEdXazGwTTDNNKZVTAu996paH5gAnUIk4PWTHCKMLAonzyO6NfLr99dUAGMtMsbm/bCn1yyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f99bfaa45c7ed6842761d2e1a7c11e2fca38344ed0d37c312cef3c875f1e219","last_reissued_at":"2026-07-29T00:24:55.926831Z","signature_status":"signed_v1","first_computed_at":"2026-07-29T00:24:55.926831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strongly-connected percolation on directed lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"M. E. J. Newman, P. Grassberger, R. M. Ziff","submitted_at":"2026-07-27T18:28:38Z","abstract_excerpt":"We study percolation on lattices with directed bonds, focusing on the behavior of strongly-connected percolation clusters -- clusters in which every site is reachable from every other along a directed path. We consider the two-dimensional square lattice and various globally isotropic arrangements of the directions of the bonds. Performing simulations using a range of algorithmic approaches, we calculate high-precision values for critical exponents, fractal dimensions, crossing probabilities, and percolation thresholds for bond percolation with each bond arrangement. We find that the critical b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24975","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.24975/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2607.24975","created_at":"2026-07-29T00:24:55.927259+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.24975v1","created_at":"2026-07-29T00:24:55.927259+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.24975","created_at":"2026-07-29T00:24:55.927259+00:00"},{"alias_kind":"pith_short_12","alias_value":"R6M37KSFY7WW","created_at":"2026-07-29T00:24:55.927259+00:00"},{"alias_kind":"pith_short_16","alias_value":"R6M37KSFY7WWQQTW","created_at":"2026-07-29T00:24:55.927259+00:00"},{"alias_kind":"pith_short_8","alias_value":"R6M37KSF","created_at":"2026-07-29T00:24:55.927259+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/R6M37KSFY7WWQQTWDUXBU7AR4L","json":"https://pith.science/pith/R6M37KSFY7WWQQTWDUXBU7AR4L.json","graph_json":"https://pith.science/api/pith-number/R6M37KSFY7WWQQTWDUXBU7AR4L/graph.json","events_json":"https://pith.science/api/pith-number/R6M37KSFY7WWQQTWDUXBU7AR4L/events.json","paper":"https://pith.science/paper/R6M37KSF"},"agent_actions":{"view_html":"https://pith.science/pith/R6M37KSFY7WWQQTWDUXBU7AR4L","download_json":"https://pith.science/pith/R6M37KSFY7WWQQTWDUXBU7AR4L.json","view_paper":"https://pith.science/paper/R6M37KSF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.24975&json=true","fetch_graph":"https://pith.science/api/pith-number/R6M37KSFY7WWQQTWDUXBU7AR4L/graph.json","fetch_events":"https://pith.science/api/pith-number/R6M37KSFY7WWQQTWDUXBU7AR4L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R6M37KSFY7WWQQTWDUXBU7AR4L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R6M37KSFY7WWQQTWDUXBU7AR4L/action/storage_attestation","attest_author":"https://pith.science/pith/R6M37KSFY7WWQQTWDUXBU7AR4L/action/author_attestation","sign_citation":"https://pith.science/pith/R6M37KSFY7WWQQTWDUXBU7AR4L/action/citation_signature","submit_replication":"https://pith.science/pith/R6M37KSFY7WWQQTWDUXBU7AR4L/action/replication_record"}},"created_at":"2026-07-29T00:24:55.927259+00:00","updated_at":"2026-07-29T00:24:55.927259+00:00"}