{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:FSWFRGNY3U22TQVQXZX6RNBNMJ","short_pith_number":"pith:FSWFRGNY","schema_version":"1.0","canonical_sha256":"2cac5899b8dd35a9c2b0be6fe8b42d6252730662b99d80c9ef849b3e8d0979bb","source":{"kind":"arxiv","id":"2601.04102","version":1},"attestation_state":"computed","paper":{"title":"Random knotting in very long off-lattice self-avoiding polygons","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT","math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Clayton Shonkwiler, Erica Uehara, Henrik Schumacher, Jason Cantarella, Tetsuo Deguchi","submitted_at":"2026-01-07T17:07:12Z","abstract_excerpt":"We present experimental results on knotting in off-lattice self-avoiding polygons in the bead-chain model. Using Clisby's tree data structure and the scale-free pivot algorithm, for each $k$ between $10$ and $27$ we generated $2^{43-k}$ polygons of size $n=2^k$. Using a new knot diagram simplification and invariant-free knot classification code, we were able to determine the precise knot type of each polygon. The results show that the number of prime summands of knot type $K$ in a random $n$-gon is very well described by a Poisson distribution. We estimate the characteristic length of knotting"},"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":"2601.04102","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-01-07T17:07:12Z","cross_cats_sorted":["math.GT","math.PR"],"title_canon_sha256":"7ead6731e3f78cfe77c9e0ce90b90b8fe218b10cf6b1c07a62813bcb2af91402","abstract_canon_sha256":"9ebea75a0b7f7570556721c005c54521d0099e430fb2b5267a1ccc3d63706acf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:02:08.232835Z","signature_b64":"/QJee1NHoGfPIlXlHToHzI+Dfi8hqa5TGbmfpDnMYvGMx8ewebDDzGnKKjGkrnPM9AdFRnPcdZ8vresyM2pNDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2cac5899b8dd35a9c2b0be6fe8b42d6252730662b99d80c9ef849b3e8d0979bb","last_reissued_at":"2026-05-20T00:02:08.232025Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:02:08.232025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Random knotting in very long off-lattice self-avoiding polygons","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT","math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Clayton Shonkwiler, Erica Uehara, Henrik Schumacher, Jason Cantarella, Tetsuo Deguchi","submitted_at":"2026-01-07T17:07:12Z","abstract_excerpt":"We present experimental results on knotting in off-lattice self-avoiding polygons in the bead-chain model. Using Clisby's tree data structure and the scale-free pivot algorithm, for each $k$ between $10$ and $27$ we generated $2^{43-k}$ polygons of size $n=2^k$. Using a new knot diagram simplification and invariant-free knot classification code, we were able to determine the precise knot type of each polygon. The results show that the number of prime summands of knot type $K$ in a random $n$-gon is very well described by a Poisson distribution. We estimate the characteristic length of knotting"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.04102","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/2601.04102/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":"2601.04102","created_at":"2026-05-20T00:02:08.232159+00:00"},{"alias_kind":"arxiv_version","alias_value":"2601.04102v1","created_at":"2026-05-20T00:02:08.232159+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.04102","created_at":"2026-05-20T00:02:08.232159+00:00"},{"alias_kind":"pith_short_12","alias_value":"FSWFRGNY3U22","created_at":"2026-05-20T00:02:08.232159+00:00"},{"alias_kind":"pith_short_16","alias_value":"FSWFRGNY3U22TQVQ","created_at":"2026-05-20T00:02:08.232159+00:00"},{"alias_kind":"pith_short_8","alias_value":"FSWFRGNY","created_at":"2026-05-20T00:02:08.232159+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/FSWFRGNY3U22TQVQXZX6RNBNMJ","json":"https://pith.science/pith/FSWFRGNY3U22TQVQXZX6RNBNMJ.json","graph_json":"https://pith.science/api/pith-number/FSWFRGNY3U22TQVQXZX6RNBNMJ/graph.json","events_json":"https://pith.science/api/pith-number/FSWFRGNY3U22TQVQXZX6RNBNMJ/events.json","paper":"https://pith.science/paper/FSWFRGNY"},"agent_actions":{"view_html":"https://pith.science/pith/FSWFRGNY3U22TQVQXZX6RNBNMJ","download_json":"https://pith.science/pith/FSWFRGNY3U22TQVQXZX6RNBNMJ.json","view_paper":"https://pith.science/paper/FSWFRGNY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2601.04102&json=true","fetch_graph":"https://pith.science/api/pith-number/FSWFRGNY3U22TQVQXZX6RNBNMJ/graph.json","fetch_events":"https://pith.science/api/pith-number/FSWFRGNY3U22TQVQXZX6RNBNMJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FSWFRGNY3U22TQVQXZX6RNBNMJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FSWFRGNY3U22TQVQXZX6RNBNMJ/action/storage_attestation","attest_author":"https://pith.science/pith/FSWFRGNY3U22TQVQXZX6RNBNMJ/action/author_attestation","sign_citation":"https://pith.science/pith/FSWFRGNY3U22TQVQXZX6RNBNMJ/action/citation_signature","submit_replication":"https://pith.science/pith/FSWFRGNY3U22TQVQXZX6RNBNMJ/action/replication_record"}},"created_at":"2026-05-20T00:02:08.232159+00:00","updated_at":"2026-05-20T00:02:08.232159+00:00"}