{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:7P64CKETMJFLHJWJO7SLFPML5G","short_pith_number":"pith:7P64CKET","schema_version":"1.0","canonical_sha256":"fbfdc12893624ab3a6c977e4b2bd8be98bfe57d1bb97cdfdd34504bfd20e2055","source":{"kind":"arxiv","id":"1512.01481","version":2},"attestation_state":"computed","paper":{"title":"Lace expansion for dummies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Erwin Bolthausen, Gady Kozma, Remco van der Hofstad","submitted_at":"2015-12-04T17:03:20Z","abstract_excerpt":"We show Green's function asymptotic upper bound for the two-point function of weakly self-avoiding walk in dimension bigger than 4, revisiting a classic problem. Our proof relies on Banach algebras to analyse the lace-expansion fixed point equation and is simpler than previous approaches in that it avoids Fourier transforms."},"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":"1512.01481","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-04T17:03:20Z","cross_cats_sorted":[],"title_canon_sha256":"302711b188fd5a38d102f370abd511e3a64212f26598866158df0aeebbaeac0d","abstract_canon_sha256":"f83de4d1fc2bd270f1367b8303415f6782c2cd5783b6f769ab12cc9b1ccd494b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:16.934440Z","signature_b64":"njSaAKnomA5CrWzZocC5g2NnPnSD7v4gJwm7WDUjquVWl/naAoLsO+oI5Ab2qI9TogKKnvSN1pfPN6cBVEeBBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbfdc12893624ab3a6c977e4b2bd8be98bfe57d1bb97cdfdd34504bfd20e2055","last_reissued_at":"2026-05-18T01:16:16.933811Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:16.933811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lace expansion for dummies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Erwin Bolthausen, Gady Kozma, Remco van der Hofstad","submitted_at":"2015-12-04T17:03:20Z","abstract_excerpt":"We show Green's function asymptotic upper bound for the two-point function of weakly self-avoiding walk in dimension bigger than 4, revisiting a classic problem. Our proof relies on Banach algebras to analyse the lace-expansion fixed point equation and is simpler than previous approaches in that it avoids Fourier transforms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01481","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":""},"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":"1512.01481","created_at":"2026-05-18T01:16:16.933913+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.01481v2","created_at":"2026-05-18T01:16:16.933913+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01481","created_at":"2026-05-18T01:16:16.933913+00:00"},{"alias_kind":"pith_short_12","alias_value":"7P64CKETMJFL","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"7P64CKETMJFLHJWJ","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"7P64CKET","created_at":"2026-05-18T12:29:10.953037+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/7P64CKETMJFLHJWJO7SLFPML5G","json":"https://pith.science/pith/7P64CKETMJFLHJWJO7SLFPML5G.json","graph_json":"https://pith.science/api/pith-number/7P64CKETMJFLHJWJO7SLFPML5G/graph.json","events_json":"https://pith.science/api/pith-number/7P64CKETMJFLHJWJO7SLFPML5G/events.json","paper":"https://pith.science/paper/7P64CKET"},"agent_actions":{"view_html":"https://pith.science/pith/7P64CKETMJFLHJWJO7SLFPML5G","download_json":"https://pith.science/pith/7P64CKETMJFLHJWJO7SLFPML5G.json","view_paper":"https://pith.science/paper/7P64CKET","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.01481&json=true","fetch_graph":"https://pith.science/api/pith-number/7P64CKETMJFLHJWJO7SLFPML5G/graph.json","fetch_events":"https://pith.science/api/pith-number/7P64CKETMJFLHJWJO7SLFPML5G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7P64CKETMJFLHJWJO7SLFPML5G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7P64CKETMJFLHJWJO7SLFPML5G/action/storage_attestation","attest_author":"https://pith.science/pith/7P64CKETMJFLHJWJO7SLFPML5G/action/author_attestation","sign_citation":"https://pith.science/pith/7P64CKETMJFLHJWJO7SLFPML5G/action/citation_signature","submit_replication":"https://pith.science/pith/7P64CKETMJFLHJWJO7SLFPML5G/action/replication_record"}},"created_at":"2026-05-18T01:16:16.933913+00:00","updated_at":"2026-05-18T01:16:16.933913+00:00"}