{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:B2A4MJPMGEUFR3Z2I6NHYJKUVJ","short_pith_number":"pith:B2A4MJPM","schema_version":"1.0","canonical_sha256":"0e81c625ec312858ef3a479a7c2554aa797de91a6fd9107eb457ea85fec2b7b5","source":{"kind":"arxiv","id":"2011.02060","version":2},"attestation_state":"computed","paper":{"title":"Constrained-degree percolation in random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Diogo C. dos Santos, R\\'emy Sanchis, Roger W.C. Silva","submitted_at":"2020-11-03T23:22:54Z","abstract_excerpt":"We consider the Constrained-degree percolation model in random environment on the square lattice. In this model, each vertex $v$ has an independent random constraint ${\\kappa}_v$ which takes the value $j\\in \\{0,1,2,3\\}$ with probability $\\rho_j$. Each edge $e$ attempts to open at a random uniform time $U_e$ in $[0,1]$, independently of all other edges. It succeeds if at time $U_e$ both its end-vertices have degrees strictly smaller than their respectively attached constraints. We show that this model undergoes a non-trivial phase transition when $\\rho_3$ is sufficiently large. The proof consis"},"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":"2011.02060","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-11-03T23:22:54Z","cross_cats_sorted":[],"title_canon_sha256":"120bda958d88b20b730680fe9ad02ad33082953fd7104db34655fe4aaba15056","abstract_canon_sha256":"121c9a6dceaa4b5385efd1f3bcea8554270d47bfa8e2450348e820f515dc0489"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:27:26.997249Z","signature_b64":"Pmj+mdj1M8gbRUDKG12EffgbbDh7fSUl1RYCfjkPya3JVj1gubc56x2xZUMiG/Sm3ejvEgi8yRl7HOHd1AhCAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e81c625ec312858ef3a479a7c2554aa797de91a6fd9107eb457ea85fec2b7b5","last_reissued_at":"2026-07-05T03:27:26.996817Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:27:26.996817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constrained-degree percolation in random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Diogo C. dos Santos, R\\'emy Sanchis, Roger W.C. Silva","submitted_at":"2020-11-03T23:22:54Z","abstract_excerpt":"We consider the Constrained-degree percolation model in random environment on the square lattice. In this model, each vertex $v$ has an independent random constraint ${\\kappa}_v$ which takes the value $j\\in \\{0,1,2,3\\}$ with probability $\\rho_j$. Each edge $e$ attempts to open at a random uniform time $U_e$ in $[0,1]$, independently of all other edges. It succeeds if at time $U_e$ both its end-vertices have degrees strictly smaller than their respectively attached constraints. We show that this model undergoes a non-trivial phase transition when $\\rho_3$ is sufficiently large. The proof consis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.02060","kind":"arxiv","version":2},"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/2011.02060/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":"2011.02060","created_at":"2026-07-05T03:27:26.996874+00:00"},{"alias_kind":"arxiv_version","alias_value":"2011.02060v2","created_at":"2026-07-05T03:27:26.996874+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.02060","created_at":"2026-07-05T03:27:26.996874+00:00"},{"alias_kind":"pith_short_12","alias_value":"B2A4MJPMGEUF","created_at":"2026-07-05T03:27:26.996874+00:00"},{"alias_kind":"pith_short_16","alias_value":"B2A4MJPMGEUFR3Z2","created_at":"2026-07-05T03:27:26.996874+00:00"},{"alias_kind":"pith_short_8","alias_value":"B2A4MJPM","created_at":"2026-07-05T03:27:26.996874+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.14526","citing_title":"Knowledge Distillation in RNN-Attention Models for Early Prediction of Student Performance","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/B2A4MJPMGEUFR3Z2I6NHYJKUVJ","json":"https://pith.science/pith/B2A4MJPMGEUFR3Z2I6NHYJKUVJ.json","graph_json":"https://pith.science/api/pith-number/B2A4MJPMGEUFR3Z2I6NHYJKUVJ/graph.json","events_json":"https://pith.science/api/pith-number/B2A4MJPMGEUFR3Z2I6NHYJKUVJ/events.json","paper":"https://pith.science/paper/B2A4MJPM"},"agent_actions":{"view_html":"https://pith.science/pith/B2A4MJPMGEUFR3Z2I6NHYJKUVJ","download_json":"https://pith.science/pith/B2A4MJPMGEUFR3Z2I6NHYJKUVJ.json","view_paper":"https://pith.science/paper/B2A4MJPM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2011.02060&json=true","fetch_graph":"https://pith.science/api/pith-number/B2A4MJPMGEUFR3Z2I6NHYJKUVJ/graph.json","fetch_events":"https://pith.science/api/pith-number/B2A4MJPMGEUFR3Z2I6NHYJKUVJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B2A4MJPMGEUFR3Z2I6NHYJKUVJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B2A4MJPMGEUFR3Z2I6NHYJKUVJ/action/storage_attestation","attest_author":"https://pith.science/pith/B2A4MJPMGEUFR3Z2I6NHYJKUVJ/action/author_attestation","sign_citation":"https://pith.science/pith/B2A4MJPMGEUFR3Z2I6NHYJKUVJ/action/citation_signature","submit_replication":"https://pith.science/pith/B2A4MJPMGEUFR3Z2I6NHYJKUVJ/action/replication_record"}},"created_at":"2026-07-05T03:27:26.996874+00:00","updated_at":"2026-07-05T03:27:26.996874+00:00"}