{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WRL5JSMLRASJ4B54JEQW2UALOP","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":"f757c50196f0834e2063671a04c44c4bf74da1e7dafcad3b5d6219c383d2bb0a","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-09T16:58:07Z","title_canon_sha256":"c111ccd33505d3e5c06320cf67f744144f92f343d3dffe12a5429bdd3c0507c6"},"schema_version":"1.0","source":{"id":"1103.1829","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1829","created_at":"2026-05-18T01:22:29Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1829v1","created_at":"2026-05-18T01:22:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1829","created_at":"2026-05-18T01:22:29Z"},{"alias_kind":"pith_short_12","alias_value":"WRL5JSMLRASJ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WRL5JSMLRASJ4B54","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WRL5JSML","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:e04371d267d7361dd4c320a26c30ed7a5e4b4e9849d3eed1bae8571a160328f8","target":"graph","created_at":"2026-05-18T01:22:29Z","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 the maximal entropy per unit generator of push-point mapping classes on the punctured disk. Our work is motivated by fluid mixing by rods in a planar domain. If a single rod moves among N-fixed obstacles, the resulting fluid diffeomorphism is in the push-point mapping class associated with the loop in \\pi_1(D^2 - {N points}) traversed by the single stirrer. The collection of motions in each of which the stirrer goes around a single obstacle generate the group of push-point mapping classes, and the entropy efficiency with respect to these generators gives a topological measure of the m","authors_text":"Jason Harrington, Philip Boyland","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-09T16:58:07Z","title":"The entropy efficiency of point-push mapping classes on the punctured disk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1829","kind":"arxiv","version":1},"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":"sha256:054e35666b6ecb9069acce35d94111802d9ba2666537b35823fc1b209cee1dc1","target":"record","created_at":"2026-05-18T01:22:29Z","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":"f757c50196f0834e2063671a04c44c4bf74da1e7dafcad3b5d6219c383d2bb0a","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-09T16:58:07Z","title_canon_sha256":"c111ccd33505d3e5c06320cf67f744144f92f343d3dffe12a5429bdd3c0507c6"},"schema_version":"1.0","source":{"id":"1103.1829","kind":"arxiv","version":1}},"canonical_sha256":"b457d4c98b88249e07bc49216d500b73d759809d86a25b7b2ae444539da8c7fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b457d4c98b88249e07bc49216d500b73d759809d86a25b7b2ae444539da8c7fb","first_computed_at":"2026-05-18T01:22:29.079949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:29.079949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8fye12bL+wCHqic+1Mo3MxkovyYeAAFD5q25U7Ix7rYFkeCT7lu8pq/7y82ohPc/59H+lxqI/yWLXoVZCmqIBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:29.080780Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.1829","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:054e35666b6ecb9069acce35d94111802d9ba2666537b35823fc1b209cee1dc1","sha256:e04371d267d7361dd4c320a26c30ed7a5e4b4e9849d3eed1bae8571a160328f8"],"state_sha256":"cbc433ef02c77d6800dbf98bf342529f301caf410a64b6b25f4a50edc5301741"}