{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OZ6UL7SRK23WGEBT2HIG5WKPSK","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":"e2c51b0cf11fb6fcb16f276cee357072e5b12568730ce48ad5b1becfe2bc27b2","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-31T10:02:51Z","title_canon_sha256":"d11329cfda300b39bf8ba9cba41153c52fe554ec68276b34b4d65f69dab90dbc"},"schema_version":"1.0","source":{"id":"1301.7568","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.7568","created_at":"2026-05-18T03:26:08Z"},{"alias_kind":"arxiv_version","alias_value":"1301.7568v2","created_at":"2026-05-18T03:26:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7568","created_at":"2026-05-18T03:26:08Z"},{"alias_kind":"pith_short_12","alias_value":"OZ6UL7SRK23W","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OZ6UL7SRK23WGEBT","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OZ6UL7SR","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:1ed70d6e49bb96c09ae347ce994bbf51dc11cfed2123b999f24a5af37f58ab03","target":"graph","created_at":"2026-05-18T03:26:08Z","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":"Seeds of sunflowers are often modelled by the map $n\\longmapsto \\varphi_\\theta(n)=\\sqrt{n}e^{2i\\pi n\\theta}$ leading to a roughly uniform repartition with two consecutive seeds separated by the divergence angle $2\\pi\\theta$ for $\\theta$ the golden ratio. We associate to an arbitrary real divergence angle $2\\pi \\theta$ a geodesic path $\\gamma_\\theta: \\mathbb R_{>0}\\longrightarrow \\mathrm{PSL}_2(\\mathbb Z)\\backslash \\mathbb H$ of the modular curve and use it for local descriptions of the image $\\varphi_\\theta(\\mathbb N)$ of the phyllotactic map $\\varphi_\\theta$.","authors_text":"Roland Bacher (IF)","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-31T10:02:51Z","title":"On geodesics of phyllotaxis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7568","kind":"arxiv","version":2},"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":"sha256:07522f65edbc6b0b96ea8a293d53f6685ccfa49fef9d0e4e4b32140dd02964c9","target":"record","created_at":"2026-05-18T03:26:08Z","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":"e2c51b0cf11fb6fcb16f276cee357072e5b12568730ce48ad5b1becfe2bc27b2","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-31T10:02:51Z","title_canon_sha256":"d11329cfda300b39bf8ba9cba41153c52fe554ec68276b34b4d65f69dab90dbc"},"schema_version":"1.0","source":{"id":"1301.7568","kind":"arxiv","version":2}},"canonical_sha256":"767d45fe5156b7631033d1d06ed94f928f026f1caba5f97f8aa1bc7004286d0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"767d45fe5156b7631033d1d06ed94f928f026f1caba5f97f8aa1bc7004286d0e","first_computed_at":"2026-05-18T03:26:08.599600Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:08.599600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DMO5EZaAs7tCazsBmpEdQu4aVsu4rjNAP9BvtDTkW9VqlbExXZfq/wcSegZ9ySAozwx/8SyWSedkEQHFLU1aDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:08.600156Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.7568","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07522f65edbc6b0b96ea8a293d53f6685ccfa49fef9d0e4e4b32140dd02964c9","sha256:1ed70d6e49bb96c09ae347ce994bbf51dc11cfed2123b999f24a5af37f58ab03"],"state_sha256":"2b49159380d145b4c3e9b41c17d7a2996bb3f11c9edf506c877ba9975291c7ca"}