{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:2KQPKT3FYL2HRG32L34POHHGOL","short_pith_number":"pith:2KQPKT3F","schema_version":"1.0","canonical_sha256":"d2a0f54f65c2f4789b7a5ef8f71ce672cc99b9a1b8310c02218bd7f1511025af","source":{"kind":"arxiv","id":"1305.0104","version":1},"attestation_state":"computed","paper":{"title":"The shape of large balls in highly supercritical percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anne-Laure Basdevant (MODAL'X), Jean-Baptiste Gou\\'er\\'e (MAPMO), LPMA), Lucas Gerin (MODAL'X), Nathana\\\"el Enriquez (MODAL'X","submitted_at":"2013-05-01T06:33:21Z","abstract_excerpt":"We exploit a connection between distances in the infinite percolation cluster, when the parameter is close to one, and the discrete-time TASEP on $\\mathbb{Z}$. This shows that when the parameter goes to one, large balls in the cluster are asymptotically shaped near the axes like arcs of parabola."},"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":"1305.0104","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-01T06:33:21Z","cross_cats_sorted":[],"title_canon_sha256":"e7a3489df8e42b7ee78de3a9765e5af8715e3916ad31f375f33fa7ecca47b47d","abstract_canon_sha256":"747776a7f940183c15be8b98d857817a94bcd39a0670dcd4c61ef8ee8c136fda"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:41.985654Z","signature_b64":"bTk/B4AZHTQ7e5M+w8Bbj3jIMkpGVoJ1089IolA9e097Ci4YoWIEiWJYn0uPBRuVjzpBa22UhoW4uLioAuLNDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2a0f54f65c2f4789b7a5ef8f71ce672cc99b9a1b8310c02218bd7f1511025af","last_reissued_at":"2026-05-18T03:26:41.984905Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:41.984905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The shape of large balls in highly supercritical percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anne-Laure Basdevant (MODAL'X), Jean-Baptiste Gou\\'er\\'e (MAPMO), LPMA), Lucas Gerin (MODAL'X), Nathana\\\"el Enriquez (MODAL'X","submitted_at":"2013-05-01T06:33:21Z","abstract_excerpt":"We exploit a connection between distances in the infinite percolation cluster, when the parameter is close to one, and the discrete-time TASEP on $\\mathbb{Z}$. This shows that when the parameter goes to one, large balls in the cluster are asymptotically shaped near the axes like arcs of parabola."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0104","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":"1305.0104","created_at":"2026-05-18T03:26:41.985027+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.0104v1","created_at":"2026-05-18T03:26:41.985027+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0104","created_at":"2026-05-18T03:26:41.985027+00:00"},{"alias_kind":"pith_short_12","alias_value":"2KQPKT3FYL2H","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"2KQPKT3FYL2HRG32","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"2KQPKT3F","created_at":"2026-05-18T12:27:30.460161+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/2KQPKT3FYL2HRG32L34POHHGOL","json":"https://pith.science/pith/2KQPKT3FYL2HRG32L34POHHGOL.json","graph_json":"https://pith.science/api/pith-number/2KQPKT3FYL2HRG32L34POHHGOL/graph.json","events_json":"https://pith.science/api/pith-number/2KQPKT3FYL2HRG32L34POHHGOL/events.json","paper":"https://pith.science/paper/2KQPKT3F"},"agent_actions":{"view_html":"https://pith.science/pith/2KQPKT3FYL2HRG32L34POHHGOL","download_json":"https://pith.science/pith/2KQPKT3FYL2HRG32L34POHHGOL.json","view_paper":"https://pith.science/paper/2KQPKT3F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.0104&json=true","fetch_graph":"https://pith.science/api/pith-number/2KQPKT3FYL2HRG32L34POHHGOL/graph.json","fetch_events":"https://pith.science/api/pith-number/2KQPKT3FYL2HRG32L34POHHGOL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2KQPKT3FYL2HRG32L34POHHGOL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2KQPKT3FYL2HRG32L34POHHGOL/action/storage_attestation","attest_author":"https://pith.science/pith/2KQPKT3FYL2HRG32L34POHHGOL/action/author_attestation","sign_citation":"https://pith.science/pith/2KQPKT3FYL2HRG32L34POHHGOL/action/citation_signature","submit_replication":"https://pith.science/pith/2KQPKT3FYL2HRG32L34POHHGOL/action/replication_record"}},"created_at":"2026-05-18T03:26:41.985027+00:00","updated_at":"2026-05-18T03:26:41.985027+00:00"}