{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:RJG2ZDSHH2Z3PLSKZ2P7GYEZEO","short_pith_number":"pith:RJG2ZDSH","schema_version":"1.0","canonical_sha256":"8a4dac8e473eb3b7ae4ace9ff36099239dab51baa302326d57ab8d5626627a24","source":{"kind":"arxiv","id":"1707.08264","version":1},"attestation_state":"computed","paper":{"title":"Counting for some convergent groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Marc Peign\\'e, Pierre Vidotto, Samuel Tapie","submitted_at":"2017-07-26T01:14:41Z","abstract_excerpt":"We present examples of geometrically finite manifolds with pinched negative curvature, whose geodesic flow has infinite non-ergodic Bowen-Margulis measure and whose Poincar\\'e series converges at the critical exponent $\\delta_\\Gamma$. We obtain an explicit asymptotic for their orbital growth function. Namely, for any $\\alpha \\in ]1, 2[ $ and any slowly varying function $L : \\mathbb R\\to (0, +\\infty)$, we construct $N$-dimensional Hadamard manifolds $(X, g)$ of negative and pinched curvature, whose group of oriented isometries admits convergent geometrically finite subgroups $\\Gamma$ such that,"},"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":"1707.08264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-07-26T01:14:41Z","cross_cats_sorted":[],"title_canon_sha256":"694014ca5f3518ca55123b937fc8cc672a047fb5bc89e6d5bad180c99125ebe3","abstract_canon_sha256":"1f9d5902ecca13daf2560f4e139c4a9f781a8ebcc85d00bdb07a722f64d38969"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:24.757146Z","signature_b64":"NkTfU08QL9KbLyWqh9l/hvtKvzlgC4rmGwlp0M0c3zDWt8zBCMsxo1UPQJVGsxtQDDg5Eih+UVu+1Ejg5w03DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a4dac8e473eb3b7ae4ace9ff36099239dab51baa302326d57ab8d5626627a24","last_reissued_at":"2026-05-18T00:39:24.756296Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:24.756296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting for some convergent groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Marc Peign\\'e, Pierre Vidotto, Samuel Tapie","submitted_at":"2017-07-26T01:14:41Z","abstract_excerpt":"We present examples of geometrically finite manifolds with pinched negative curvature, whose geodesic flow has infinite non-ergodic Bowen-Margulis measure and whose Poincar\\'e series converges at the critical exponent $\\delta_\\Gamma$. We obtain an explicit asymptotic for their orbital growth function. Namely, for any $\\alpha \\in ]1, 2[ $ and any slowly varying function $L : \\mathbb R\\to (0, +\\infty)$, we construct $N$-dimensional Hadamard manifolds $(X, g)$ of negative and pinched curvature, whose group of oriented isometries admits convergent geometrically finite subgroups $\\Gamma$ such that,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08264","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":"1707.08264","created_at":"2026-05-18T00:39:24.756423+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.08264v1","created_at":"2026-05-18T00:39:24.756423+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.08264","created_at":"2026-05-18T00:39:24.756423+00:00"},{"alias_kind":"pith_short_12","alias_value":"RJG2ZDSHH2Z3","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_16","alias_value":"RJG2ZDSHH2Z3PLSK","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_8","alias_value":"RJG2ZDSH","created_at":"2026-05-18T12:31:39.905425+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/RJG2ZDSHH2Z3PLSKZ2P7GYEZEO","json":"https://pith.science/pith/RJG2ZDSHH2Z3PLSKZ2P7GYEZEO.json","graph_json":"https://pith.science/api/pith-number/RJG2ZDSHH2Z3PLSKZ2P7GYEZEO/graph.json","events_json":"https://pith.science/api/pith-number/RJG2ZDSHH2Z3PLSKZ2P7GYEZEO/events.json","paper":"https://pith.science/paper/RJG2ZDSH"},"agent_actions":{"view_html":"https://pith.science/pith/RJG2ZDSHH2Z3PLSKZ2P7GYEZEO","download_json":"https://pith.science/pith/RJG2ZDSHH2Z3PLSKZ2P7GYEZEO.json","view_paper":"https://pith.science/paper/RJG2ZDSH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.08264&json=true","fetch_graph":"https://pith.science/api/pith-number/RJG2ZDSHH2Z3PLSKZ2P7GYEZEO/graph.json","fetch_events":"https://pith.science/api/pith-number/RJG2ZDSHH2Z3PLSKZ2P7GYEZEO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RJG2ZDSHH2Z3PLSKZ2P7GYEZEO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RJG2ZDSHH2Z3PLSKZ2P7GYEZEO/action/storage_attestation","attest_author":"https://pith.science/pith/RJG2ZDSHH2Z3PLSKZ2P7GYEZEO/action/author_attestation","sign_citation":"https://pith.science/pith/RJG2ZDSHH2Z3PLSKZ2P7GYEZEO/action/citation_signature","submit_replication":"https://pith.science/pith/RJG2ZDSHH2Z3PLSKZ2P7GYEZEO/action/replication_record"}},"created_at":"2026-05-18T00:39:24.756423+00:00","updated_at":"2026-05-18T00:39:24.756423+00:00"}