{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:Y6XNGTJBBXLZXQ5X6SFGETLK5M","short_pith_number":"pith:Y6XNGTJB","schema_version":"1.0","canonical_sha256":"c7aed34d210dd79bc3b7f48a624d6aeb2a06f71711f63101b52dc531933a8a6c","source":{"kind":"arxiv","id":"1407.1648","version":1},"attestation_state":"computed","paper":{"title":"Volume entropy for minimal presentations of surface groups in all ranks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"David Juher, Francesc Ma\\~nosas, J\\'er\\^ome Los, Llu\\'is Alsed\\`a","submitted_at":"2014-07-07T10:05:14Z","abstract_excerpt":"We study the volume entropy of a class of presentations (including the classical ones) for all surface groups, called \\emph{minimal geometric presentations}. We rediscover a formula first obtained by Cannon and Wagreich with the computation in a non published manuscript by Cannon. The result is surprising: an explicit polynomial of degree $n$, the rank of the group, encodes the volume entropy of all classical presentations of surface groups. The approach we use is completely different. It is based on a dynamical system construction following an idea due to Bowen and Series and extended to all "},"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":"1407.1648","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-07T10:05:14Z","cross_cats_sorted":[],"title_canon_sha256":"039b2a3d3865212c75101f73433af5130f3fd169526d90fbcf3c1e469f84f55c","abstract_canon_sha256":"4169fbb068e9f8a9f41ef8412465b66e3d85dd05c8ec8209641817174a1c09e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:10.799733Z","signature_b64":"XIes2XwAghb3AojbPlkpDGbBy9BFd5xONoUxzi2w6HZ0tC9sWch7mScT0VQ+Rb+Fjo/MSu7WziohFmXPzZ50BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7aed34d210dd79bc3b7f48a624d6aeb2a06f71711f63101b52dc531933a8a6c","last_reissued_at":"2026-05-18T02:48:10.799299Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:10.799299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Volume entropy for minimal presentations of surface groups in all ranks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"David Juher, Francesc Ma\\~nosas, J\\'er\\^ome Los, Llu\\'is Alsed\\`a","submitted_at":"2014-07-07T10:05:14Z","abstract_excerpt":"We study the volume entropy of a class of presentations (including the classical ones) for all surface groups, called \\emph{minimal geometric presentations}. We rediscover a formula first obtained by Cannon and Wagreich with the computation in a non published manuscript by Cannon. The result is surprising: an explicit polynomial of degree $n$, the rank of the group, encodes the volume entropy of all classical presentations of surface groups. The approach we use is completely different. It is based on a dynamical system construction following an idea due to Bowen and Series and extended to all "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1648","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":"1407.1648","created_at":"2026-05-18T02:48:10.799374+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.1648v1","created_at":"2026-05-18T02:48:10.799374+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1648","created_at":"2026-05-18T02:48:10.799374+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y6XNGTJBBXLZ","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y6XNGTJBBXLZXQ5X","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y6XNGTJB","created_at":"2026-05-18T12:28:57.508820+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/Y6XNGTJBBXLZXQ5X6SFGETLK5M","json":"https://pith.science/pith/Y6XNGTJBBXLZXQ5X6SFGETLK5M.json","graph_json":"https://pith.science/api/pith-number/Y6XNGTJBBXLZXQ5X6SFGETLK5M/graph.json","events_json":"https://pith.science/api/pith-number/Y6XNGTJBBXLZXQ5X6SFGETLK5M/events.json","paper":"https://pith.science/paper/Y6XNGTJB"},"agent_actions":{"view_html":"https://pith.science/pith/Y6XNGTJBBXLZXQ5X6SFGETLK5M","download_json":"https://pith.science/pith/Y6XNGTJBBXLZXQ5X6SFGETLK5M.json","view_paper":"https://pith.science/paper/Y6XNGTJB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.1648&json=true","fetch_graph":"https://pith.science/api/pith-number/Y6XNGTJBBXLZXQ5X6SFGETLK5M/graph.json","fetch_events":"https://pith.science/api/pith-number/Y6XNGTJBBXLZXQ5X6SFGETLK5M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y6XNGTJBBXLZXQ5X6SFGETLK5M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y6XNGTJBBXLZXQ5X6SFGETLK5M/action/storage_attestation","attest_author":"https://pith.science/pith/Y6XNGTJBBXLZXQ5X6SFGETLK5M/action/author_attestation","sign_citation":"https://pith.science/pith/Y6XNGTJBBXLZXQ5X6SFGETLK5M/action/citation_signature","submit_replication":"https://pith.science/pith/Y6XNGTJBBXLZXQ5X6SFGETLK5M/action/replication_record"}},"created_at":"2026-05-18T02:48:10.799374+00:00","updated_at":"2026-05-18T02:48:10.799374+00:00"}