{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:JISJIUZOAATKXL6NFLBMKAWE2D","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e3e09d9505be1f09ced91b15e10fbc34020602b1e6449ddf2ccd2dd6aca11c7f","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-06-14T23:25:50Z","title_canon_sha256":"80bf8e1a1093ee8683ca4d169416081c85b2969aca9f38435baa813f9c6285b6"},"schema_version":"1.0","source":{"id":"cond-mat/0506341","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0506341","created_at":"2026-05-18T01:06:52Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0506341v2","created_at":"2026-05-18T01:06:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0506341","created_at":"2026-05-18T01:06:52Z"},{"alias_kind":"pith_short_12","alias_value":"JISJIUZOAATK","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"JISJIUZOAATKXL6N","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"JISJIUZO","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:71901e40dcf29a86f47d021849441e718348a8ad9d4601b7a57108c988953094","target":"graph","created_at":"2026-05-18T01:06:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study a restricted class of self-avoiding walks (SAW) which start at the origin (0, 0), end at $(L, L)$, and are entirely contained in the square $[0, L] \\times [0, L]$ on the square lattice ${\\mathbb Z}^2$. The number of distinct walks is known to grow as $\\lambda^{L^2+o(L^2)}$. We estimate $\\lambda = 1.744550 \\pm 0.000005$ as well as obtaining strict upper and lower bounds, $1.628 < \\lambda < 1.782.$ We give exact results for the number of SAW of length $2L + 2K$ for $K = 0, 1, 2$ and asymptotic results for $K = o(L^{1/3})$.\n  We also consider the model in which a weight or {\\em fugacity}","authors_text":"A. J. Guttmann, I. Jensen, M. Bousquet-M\\'elou","cross_cats":["math.CO"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-06-14T23:25:50Z","title":"Self-avoiding walks crossing a square"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0506341","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fe8b42e39f95c2eefa815dbc11e73a2dfd83ce970be9d6f6c787e7562396d73f","target":"record","created_at":"2026-05-18T01:06:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e3e09d9505be1f09ced91b15e10fbc34020602b1e6449ddf2ccd2dd6aca11c7f","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-06-14T23:25:50Z","title_canon_sha256":"80bf8e1a1093ee8683ca4d169416081c85b2969aca9f38435baa813f9c6285b6"},"schema_version":"1.0","source":{"id":"cond-mat/0506341","kind":"arxiv","version":2}},"canonical_sha256":"4a2494532e0026abafcd2ac2c502c4d0e910022e45cfa2caf705117691a2c833","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a2494532e0026abafcd2ac2c502c4d0e910022e45cfa2caf705117691a2c833","first_computed_at":"2026-05-18T01:06:52.585962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:52.585962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J3KqZ6IQx4O1P1Mg9N25WOk9KYpDCX19xg1SOBssHuSrZje20f7vjOx3tuGoAqb5X3AaSFh9GS5+cyt82ANnCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:52.586400Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0506341","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe8b42e39f95c2eefa815dbc11e73a2dfd83ce970be9d6f6c787e7562396d73f","sha256:71901e40dcf29a86f47d021849441e718348a8ad9d4601b7a57108c988953094"],"state_sha256":"0f6e71f310e2c53352f7f796499064110ec556f525bf74a4f827ab26e83ed82f"}