{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:RFVJCKNEUQ2Z73XDYFZXF3TKIH","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":"8ccea03eed3419238dc7ca605e78edd1a65d7aae0f15ccf92dbfb25326725715","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.DS","submitted_at":"2006-08-02T20:16:50Z","title_canon_sha256":"0787ec0e64b6a70eb42385b9ba5a577c1d210af18cb99ca2b8b2121ad763de8b"},"schema_version":"1.0","source":{"id":"math/0608066","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0608066","created_at":"2026-05-18T02:41:31Z"},{"alias_kind":"arxiv_version","alias_value":"math/0608066v1","created_at":"2026-05-18T02:41:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0608066","created_at":"2026-05-18T02:41:31Z"},{"alias_kind":"pith_short_12","alias_value":"RFVJCKNEUQ2Z","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"RFVJCKNEUQ2Z73XD","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"RFVJCKNE","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:05ff54b78d33c0cf49eddb37b17680a658a82ea1a923660b7438df65a7270074","target":"graph","created_at":"2026-05-18T02:41:31Z","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 give a presentation for the baseleaf preserving mapping class group $Mod(\\S)$ of the punctured solenoid $\\S$. The generators for our presentation were introduced previously, and several relations among them were derived. In addition, we show that $Mod(\\S)$ has no non-trivial central elements. Our main tool is a new complex of triangulations of the disk upon which $Mod(\\S)$ acts.","authors_text":"D. Saric, R. C. Penner, S. Bonnot","cross_cats":["math.GT"],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"2006-08-02T20:16:50Z","title":"A presentation for the baseleaf preserving mapping class group of the punctured solenoid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608066","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:c7391e95c4ed12bc9ca0c6dc605312baa8fc90281a3db7374502a5f2bfd505c6","target":"record","created_at":"2026-05-18T02:41:31Z","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":"8ccea03eed3419238dc7ca605e78edd1a65d7aae0f15ccf92dbfb25326725715","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.DS","submitted_at":"2006-08-02T20:16:50Z","title_canon_sha256":"0787ec0e64b6a70eb42385b9ba5a577c1d210af18cb99ca2b8b2121ad763de8b"},"schema_version":"1.0","source":{"id":"math/0608066","kind":"arxiv","version":1}},"canonical_sha256":"896a9129a4a4359feee3c17372ee6a41d5e37a9b5f5ca92f30e7044f92b730f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"896a9129a4a4359feee3c17372ee6a41d5e37a9b5f5ca92f30e7044f92b730f0","first_computed_at":"2026-05-18T02:41:31.818659Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:31.818659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i9WVan8drrhHfc5bz4TO0fbWBWI/Bk1Hlqr7l1eU8AzdSPTQzGOZlhxfvZ7ufiWRWtsDGWXwzPasQmIZlFVXCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:31.818997Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0608066","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7391e95c4ed12bc9ca0c6dc605312baa8fc90281a3db7374502a5f2bfd505c6","sha256:05ff54b78d33c0cf49eddb37b17680a658a82ea1a923660b7438df65a7270074"],"state_sha256":"9f31baf503b1b3212186b33cd5a8cdc4e6689c2072db7647b0cbecbd44db4305"}