{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:K6I473FET2Y2FUCTVQLCL3NRSB","short_pith_number":"pith:K6I473FE","schema_version":"1.0","canonical_sha256":"5791cfeca49eb1a2d053ac1625edb1904b7bd79db53997a897e36d7c92997226","source":{"kind":"arxiv","id":"1105.2477","version":2},"attestation_state":"computed","paper":{"title":"Polynomial growth of volume of balls for zero-entropy geodesic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.DS","authors_text":"Cl\\'emence Labrousse","submitted_at":"2011-05-12T13:53:53Z","abstract_excerpt":"The aim of this paper is to state and prove polynomial analogues of the classical Manning inequality relating the topological entropy of a geodesic flow with the growth rate of the volume of balls in the universal covering. To this aim we use two numerical conjugacy invariants, the {\\em strong polynomial entropy $h_{pol}$} and the {\\em weak polynomial entropy $h_{pol}^*$}. Both are infinite when the topological entropy is positive and they satisfy $h_{pol}^*\\leq h_{pol}$. We first prove that the growth rate of the volume of balls is bounded above by means of the strong polynomial entropy and w"},"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":"1105.2477","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-12T13:53:53Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"26a6e23f7e1810167d14d233f46afebafc4b5fdbba1745a420144caef3cab622","abstract_canon_sha256":"83b04811b7194a295ff52dfb90ebd6ceae7b25dd138dfdfcf43b3499880bc0f0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:01:59.156668Z","signature_b64":"EIhVh8cU+iRaYY5YcfuA9Qqvdb/ampZZnBNVvqIlG/X/4ITaDzDfjpJ5iONWfAD0AJ8P+imeQMn/PRgomxfJDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5791cfeca49eb1a2d053ac1625edb1904b7bd79db53997a897e36d7c92997226","last_reissued_at":"2026-05-18T02:01:59.156087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:01:59.156087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polynomial growth of volume of balls for zero-entropy geodesic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.DS","authors_text":"Cl\\'emence Labrousse","submitted_at":"2011-05-12T13:53:53Z","abstract_excerpt":"The aim of this paper is to state and prove polynomial analogues of the classical Manning inequality relating the topological entropy of a geodesic flow with the growth rate of the volume of balls in the universal covering. To this aim we use two numerical conjugacy invariants, the {\\em strong polynomial entropy $h_{pol}$} and the {\\em weak polynomial entropy $h_{pol}^*$}. Both are infinite when the topological entropy is positive and they satisfy $h_{pol}^*\\leq h_{pol}$. We first prove that the growth rate of the volume of balls is bounded above by means of the strong polynomial entropy and w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2477","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":"1105.2477","created_at":"2026-05-18T02:01:59.156166+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.2477v2","created_at":"2026-05-18T02:01:59.156166+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2477","created_at":"2026-05-18T02:01:59.156166+00:00"},{"alias_kind":"pith_short_12","alias_value":"K6I473FET2Y2","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"K6I473FET2Y2FUCT","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"K6I473FE","created_at":"2026-05-18T12:26:32.869790+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/K6I473FET2Y2FUCTVQLCL3NRSB","json":"https://pith.science/pith/K6I473FET2Y2FUCTVQLCL3NRSB.json","graph_json":"https://pith.science/api/pith-number/K6I473FET2Y2FUCTVQLCL3NRSB/graph.json","events_json":"https://pith.science/api/pith-number/K6I473FET2Y2FUCTVQLCL3NRSB/events.json","paper":"https://pith.science/paper/K6I473FE"},"agent_actions":{"view_html":"https://pith.science/pith/K6I473FET2Y2FUCTVQLCL3NRSB","download_json":"https://pith.science/pith/K6I473FET2Y2FUCTVQLCL3NRSB.json","view_paper":"https://pith.science/paper/K6I473FE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.2477&json=true","fetch_graph":"https://pith.science/api/pith-number/K6I473FET2Y2FUCTVQLCL3NRSB/graph.json","fetch_events":"https://pith.science/api/pith-number/K6I473FET2Y2FUCTVQLCL3NRSB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K6I473FET2Y2FUCTVQLCL3NRSB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K6I473FET2Y2FUCTVQLCL3NRSB/action/storage_attestation","attest_author":"https://pith.science/pith/K6I473FET2Y2FUCTVQLCL3NRSB/action/author_attestation","sign_citation":"https://pith.science/pith/K6I473FET2Y2FUCTVQLCL3NRSB/action/citation_signature","submit_replication":"https://pith.science/pith/K6I473FET2Y2FUCTVQLCL3NRSB/action/replication_record"}},"created_at":"2026-05-18T02:01:59.156166+00:00","updated_at":"2026-05-18T02:01:59.156166+00:00"}