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(2) The unique homogeneous quasimorphism on F dual to this face (up to scale and elements of H^1) is the rotation quasimorphism associated to the action of F on the ideal boundary of the hyperbolic plane, coming from a hyperbolic structure on S.\n  These facts follow from the fact 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":"0807.0395","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-07-02T16:42:39Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"b13485d4f80dbcbd1403791960054ae57596d413ff1cfc7a943f9a65bb427be1","abstract_canon_sha256":"099f269597a095929d4750375471af26d55fc86c2a518782608a3363256ddeb1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:19.103712Z","signature_b64":"gdlawxyuh5jChwwQt03xaJTp3hNKQUQadORFOwAb6probZ0yJKQUtIE+QIY+kCiAEe7dgTDvk+sZJr5++PnQAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17c4f267bb5333e1825f56e0b0328f5739a90db177086d5ea9a5c4ad1d1221c6","last_reissued_at":"2026-05-18T02:38:19.103182Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:19.103182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Faces of the scl norm ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Danny Calegari","submitted_at":"2008-07-02T16:42:39Z","abstract_excerpt":"Let F be the fundamental group of S, where S is a compact, connected, oriented surface with negative Euler characteristic and nonempty boundary.\n  (1) The projective class of the chain \\partial S in B_1(F) intersects the interior of a codimension one face of the unit ball in the stable commutator length pseudo-norm. 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