{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MUJXNZ63I3FLSEFSWKA67HVPCL","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":"9b78c677666cfb1f0d2a153398e02c071a05ba16ac836912493cdead97ac09d1","cross_cats_sorted":["q-bio.BM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2012-11-08T15:18:40Z","title_canon_sha256":"6298a8973cb65a858dcc4129600449ba4100044080c32b1dda9919306516a49f"},"schema_version":"1.0","source":{"id":"1211.1879","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1879","created_at":"2026-05-18T03:41:04Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1879v2","created_at":"2026-05-18T03:41:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1879","created_at":"2026-05-18T03:41:04Z"},{"alias_kind":"pith_short_12","alias_value":"MUJXNZ63I3FL","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MUJXNZ63I3FLSEFS","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MUJXNZ63","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:fbfa9d15aef0ce98151260dbce3a6a9fc761872fd80dc2be18a29003b78b4b78","target":"graph","created_at":"2026-05-18T03:41:04Z","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":"A coarse-grained computational model is used to investigate how the bending rigidity of a polymer under tension affects the formation of a trefoil knot. Thermodynamic integration techniques are applied to demonstrate that the free-energy cost of forming a knot has a minimum at non-zero bending rigidity. The position of the minimum exhibits a power-law dependence on the applied tension. For knotted polymers with non-uniform bending rigidity, the knots preferentially localize in the region with a bending rigidity that minimizes the free-energy.","authors_text":"Ard A. Louis, Christos N. Likos, Richard Matthews","cross_cats":["q-bio.BM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2012-11-08T15:18:40Z","title":"Effect of bending rigidity on the knotting of a polymer under tension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1879","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":"sha256:6fa241106bf4b4c7b34bd92c1102063b3f1ac874436d772f8745aea853ea477b","target":"record","created_at":"2026-05-18T03:41:04Z","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":"9b78c677666cfb1f0d2a153398e02c071a05ba16ac836912493cdead97ac09d1","cross_cats_sorted":["q-bio.BM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2012-11-08T15:18:40Z","title_canon_sha256":"6298a8973cb65a858dcc4129600449ba4100044080c32b1dda9919306516a49f"},"schema_version":"1.0","source":{"id":"1211.1879","kind":"arxiv","version":2}},"canonical_sha256":"651376e7db46cab910b2b281ef9eaf12f73fe64633ea4fdbbaeaa0677ec2bafd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"651376e7db46cab910b2b281ef9eaf12f73fe64633ea4fdbbaeaa0677ec2bafd","first_computed_at":"2026-05-18T03:41:04.025217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:04.025217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y8L1b6K+/67g4XWtjpXQPLb4X4yWwTn3vPmpPefWR5q2pbUNT+G4BKMtMWd9EpHm3C8HFU7REYpqGYjYqx5+AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:04.025711Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.1879","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fa241106bf4b4c7b34bd92c1102063b3f1ac874436d772f8745aea853ea477b","sha256:fbfa9d15aef0ce98151260dbce3a6a9fc761872fd80dc2be18a29003b78b4b78"],"state_sha256":"674319c7a32a28c4c34875db66f16c056f7fde6d11f0e4b57d09d865b308a51b"}