{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:IJ7ZDT2XZ6HPGOFWNHMBEZ3VS3","short_pith_number":"pith:IJ7ZDT2X","schema_version":"1.0","canonical_sha256":"427f91cf57cf8ef338b669d812677596fb57d1f0fe5de1f9ae67e642650de3c2","source":{"kind":"arxiv","id":"0912.1425","version":2},"attestation_state":"computed","paper":{"title":"The action of the affine diffeomorphisms on the relative homology group of certain exceptionally symmetric origamis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Matheus, Jean-Christophe Yoccoz","submitted_at":"2009-12-08T07:43:49Z","abstract_excerpt":"We compute explicitly the action of the group of affine diffeomorphisms on the relative homology of two remarkable origamis discovered respectively by Forni (in genus 3) and Forni-Matheus (in genus 4). We show that, in both cases, the action on the non trivial part of the homology is through finite groups. In particular, the action on some 4-dimensional invariant subspace of the homology leaves invariant a root system of $D_4$ type. This provides as a by-product a new proof of (slightly stronger versions of) the results of Forni and Matheus: the non trivial Lyapunov exponents of the Kontsevich"},"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":"0912.1425","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-12-08T07:43:49Z","cross_cats_sorted":[],"title_canon_sha256":"2b74350ecc625a96cfc1b48b5ccdc43bc691a094c8ce9760b5e5e1ac904387d0","abstract_canon_sha256":"8e78248b09f66f2044a225de57d975ccb59dd6f13452b269e61c077407d4762c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:50.340992Z","signature_b64":"uaCEP8iCaJOEWaRDAQiOdjuZuCbAcIx3MCd00guL0fVQ/EIEEVa33GHfx7kudIjwc4osDUuNrgv62AIJJ27tDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"427f91cf57cf8ef338b669d812677596fb57d1f0fe5de1f9ae67e642650de3c2","last_reissued_at":"2026-05-18T04:39:50.340514Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:50.340514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The action of the affine diffeomorphisms on the relative homology group of certain exceptionally symmetric origamis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Matheus, Jean-Christophe Yoccoz","submitted_at":"2009-12-08T07:43:49Z","abstract_excerpt":"We compute explicitly the action of the group of affine diffeomorphisms on the relative homology of two remarkable origamis discovered respectively by Forni (in genus 3) and Forni-Matheus (in genus 4). We show that, in both cases, the action on the non trivial part of the homology is through finite groups. In particular, the action on some 4-dimensional invariant subspace of the homology leaves invariant a root system of $D_4$ type. This provides as a by-product a new proof of (slightly stronger versions of) the results of Forni and Matheus: the non trivial Lyapunov exponents of the Kontsevich"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.1425","kind":"arxiv","version":2},"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":"0912.1425","created_at":"2026-05-18T04:39:50.340587+00:00"},{"alias_kind":"arxiv_version","alias_value":"0912.1425v2","created_at":"2026-05-18T04:39:50.340587+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.1425","created_at":"2026-05-18T04:39:50.340587+00:00"},{"alias_kind":"pith_short_12","alias_value":"IJ7ZDT2XZ6HP","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"IJ7ZDT2XZ6HPGOFW","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"IJ7ZDT2X","created_at":"2026-05-18T12:26:00.592388+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/IJ7ZDT2XZ6HPGOFWNHMBEZ3VS3","json":"https://pith.science/pith/IJ7ZDT2XZ6HPGOFWNHMBEZ3VS3.json","graph_json":"https://pith.science/api/pith-number/IJ7ZDT2XZ6HPGOFWNHMBEZ3VS3/graph.json","events_json":"https://pith.science/api/pith-number/IJ7ZDT2XZ6HPGOFWNHMBEZ3VS3/events.json","paper":"https://pith.science/paper/IJ7ZDT2X"},"agent_actions":{"view_html":"https://pith.science/pith/IJ7ZDT2XZ6HPGOFWNHMBEZ3VS3","download_json":"https://pith.science/pith/IJ7ZDT2XZ6HPGOFWNHMBEZ3VS3.json","view_paper":"https://pith.science/paper/IJ7ZDT2X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0912.1425&json=true","fetch_graph":"https://pith.science/api/pith-number/IJ7ZDT2XZ6HPGOFWNHMBEZ3VS3/graph.json","fetch_events":"https://pith.science/api/pith-number/IJ7ZDT2XZ6HPGOFWNHMBEZ3VS3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IJ7ZDT2XZ6HPGOFWNHMBEZ3VS3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IJ7ZDT2XZ6HPGOFWNHMBEZ3VS3/action/storage_attestation","attest_author":"https://pith.science/pith/IJ7ZDT2XZ6HPGOFWNHMBEZ3VS3/action/author_attestation","sign_citation":"https://pith.science/pith/IJ7ZDT2XZ6HPGOFWNHMBEZ3VS3/action/citation_signature","submit_replication":"https://pith.science/pith/IJ7ZDT2XZ6HPGOFWNHMBEZ3VS3/action/replication_record"}},"created_at":"2026-05-18T04:39:50.340587+00:00","updated_at":"2026-05-18T04:39:50.340587+00:00"}