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Unlike a root of a $t_C$, a fractional power $h$ can exchange the sides of $C$. We derive necessary and sufficient conditions for the existence of both side-exchanging and side-preserving fractional powers. We show in the side-preserving case that if $\\gcd(\\ell,n) = 1$, then $h$ will be isotopic to t"},"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":"1207.3581","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-07-16T05:35:21Z","cross_cats_sorted":[],"title_canon_sha256":"0ac76c2dd4a3b59b9a68eb9100f68468607c86f46f0727e6324859671b69bff4","abstract_canon_sha256":"24f6e4b1defad8a0163f0f590965d201bf822731d08b53322b99041ba0a30c2f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:00.705294Z","signature_b64":"haaN9rL3JOwcOrHxak0xlk3VlXmBtj9Y8vaNSl7r4MOjHJdrIZIPNObN86rk8KtypgD2p5KnM/6AAVW91wMrCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"995eb062123edc288bed1b1fd02b364aa619c91c3604064154d58623b2473321","last_reissued_at":"2026-05-18T03:51:00.704587Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:00.704587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fractional powers of Dehn twists about nonseparating curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kashyap Rajeevsarathy","submitted_at":"2012-07-16T05:35:21Z","abstract_excerpt":"Let $S_g$ be a closed orientable surface of genus $g \\geq 2$ and $C$ a simple closed nonseparating curve in $F$. Let $t_C$ denote a left handed Dehn twist about $C$. A \\textit{fractional power} of $t_C$ of \\textit{exponent} $\\fraction{\\ell}{n}$ is an $h \\in \\Mod(S_g)$ such that $h^n = t_C^{\\ell}$. Unlike a root of a $t_C$, a fractional power $h$ can exchange the sides of $C$. We derive necessary and sufficient conditions for the existence of both side-exchanging and side-preserving fractional powers. We show in the side-preserving case that if $\\gcd(\\ell,n) = 1$, then $h$ will be isotopic to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3581","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":""},"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":"1207.3581","created_at":"2026-05-18T03:51:00.704706+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.3581v1","created_at":"2026-05-18T03:51:00.704706+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3581","created_at":"2026-05-18T03:51:00.704706+00:00"},{"alias_kind":"pith_short_12","alias_value":"TFPLAYQSH3OC","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"TFPLAYQSH3OCRC7N","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"TFPLAYQS","created_at":"2026-05-18T12:27:23.164592+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/TFPLAYQSH3OCRC7NDMP5AKZWJK","json":"https://pith.science/pith/TFPLAYQSH3OCRC7NDMP5AKZWJK.json","graph_json":"https://pith.science/api/pith-number/TFPLAYQSH3OCRC7NDMP5AKZWJK/graph.json","events_json":"https://pith.science/api/pith-number/TFPLAYQSH3OCRC7NDMP5AKZWJK/events.json","paper":"https://pith.science/paper/TFPLAYQS"},"agent_actions":{"view_html":"https://pith.science/pith/TFPLAYQSH3OCRC7NDMP5AKZWJK","download_json":"https://pith.science/pith/TFPLAYQSH3OCRC7NDMP5AKZWJK.json","view_paper":"https://pith.science/paper/TFPLAYQS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.3581&json=true","fetch_graph":"https://pith.science/api/pith-number/TFPLAYQSH3OCRC7NDMP5AKZWJK/graph.json","fetch_events":"https://pith.science/api/pith-number/TFPLAYQSH3OCRC7NDMP5AKZWJK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TFPLAYQSH3OCRC7NDMP5AKZWJK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TFPLAYQSH3OCRC7NDMP5AKZWJK/action/storage_attestation","attest_author":"https://pith.science/pith/TFPLAYQSH3OCRC7NDMP5AKZWJK/action/author_attestation","sign_citation":"https://pith.science/pith/TFPLAYQSH3OCRC7NDMP5AKZWJK/action/citation_signature","submit_replication":"https://pith.science/pith/TFPLAYQSH3OCRC7NDMP5AKZWJK/action/replication_record"}},"created_at":"2026-05-18T03:51:00.704706+00:00","updated_at":"2026-05-18T03:51:00.704706+00:00"}