{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:YLGAVC2RADGW5SM74AVCZMI6F5","short_pith_number":"pith:YLGAVC2R","canonical_record":{"source":{"id":"0902.2315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-02-13T13:57:40Z","cross_cats_sorted":[],"title_canon_sha256":"7aaac74030460ddfda404f737608cd9b489eab48445b982613160deacf2bdc39","abstract_canon_sha256":"692207050b7ccde05c95f0d9c4b9fccfb4032f281011fd14c9c8fd467135cff7"},"schema_version":"1.0"},"canonical_sha256":"c2cc0a8b5100cd6ec99fe02a2cb11e2f726938aea927ebb1a07020b54ab8fe85","source":{"kind":"arxiv","id":"0902.2315","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.2315","created_at":"2026-05-17T23:39:42Z"},{"alias_kind":"arxiv_version","alias_value":"0902.2315v1","created_at":"2026-05-17T23:39:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.2315","created_at":"2026-05-17T23:39:42Z"},{"alias_kind":"pith_short_12","alias_value":"YLGAVC2RADGW","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YLGAVC2RADGW5SM7","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YLGAVC2R","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:YLGAVC2RADGW5SM74AVCZMI6F5","target":"record","payload":{"canonical_record":{"source":{"id":"0902.2315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-02-13T13:57:40Z","cross_cats_sorted":[],"title_canon_sha256":"7aaac74030460ddfda404f737608cd9b489eab48445b982613160deacf2bdc39","abstract_canon_sha256":"692207050b7ccde05c95f0d9c4b9fccfb4032f281011fd14c9c8fd467135cff7"},"schema_version":"1.0"},"canonical_sha256":"c2cc0a8b5100cd6ec99fe02a2cb11e2f726938aea927ebb1a07020b54ab8fe85","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:42.647333Z","signature_b64":"TTPfYAOHrOjLQh2UrUXT4cziouHhOxoDYS6F70cnU89Gapo/wO/YfSPBYyFRSCkhBFjrMLM3RZy8JvXcHJUnDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2cc0a8b5100cd6ec99fe02a2cb11e2f726938aea927ebb1a07020b54ab8fe85","last_reissued_at":"2026-05-17T23:39:42.646631Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:42.646631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0902.2315","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:39:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AvyC9e6+lcrrJCP9oKNcUDVfIzCevsRlZyATSoGN7fHadO1PnGRSSYggXjWXtq7F7i6I1eG5mqEj7kH0so0cDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:10:03.857166Z"},"content_sha256":"3ffffc98005b2eef91f658a7bed40c4b9b876f8413a0dc1c4ce9cd20edbb1e93","schema_version":"1.0","event_id":"sha256:3ffffc98005b2eef91f658a7bed40c4b9b876f8413a0dc1c4ce9cd20edbb1e93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:YLGAVC2RADGW5SM74AVCZMI6F5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the growth of nonuniform lattices in pinched negatively curved manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Andrea Sambusetti, Fran\\c{c}oise Dal'Bo (IRMAR), Jean-Claude Picaud (LMPT), Marc Peign\\'e (LMPT)","submitted_at":"2009-02-13T13:57:40Z","abstract_excerpt":"We study the relation between the exponential growth rate of volume in a pinched negatively curved manifold and the critical exponent of its lattices. These objects have a long and interesting story and are closely related to the geometry and the dynamical properties of the geodesic flow of the manifold ."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.2315","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:39:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MiW7E0aWipO8nO1IMUDRnj3Zpjywi0/qZcuhYMtFzFjbqxQqw4Rwd8iPg16hQs2LZyLkxVlfa1GP0p15CnLcDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:10:03.857640Z"},"content_sha256":"aa8f202aaa70cf7348047dae10000aaccde8943f3e02881fd646f1069de4f616","schema_version":"1.0","event_id":"sha256:aa8f202aaa70cf7348047dae10000aaccde8943f3e02881fd646f1069de4f616"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YLGAVC2RADGW5SM74AVCZMI6F5/bundle.json","state_url":"https://pith.science/pith/YLGAVC2RADGW5SM74AVCZMI6F5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YLGAVC2RADGW5SM74AVCZMI6F5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T16:10:03Z","links":{"resolver":"https://pith.science/pith/YLGAVC2RADGW5SM74AVCZMI6F5","bundle":"https://pith.science/pith/YLGAVC2RADGW5SM74AVCZMI6F5/bundle.json","state":"https://pith.science/pith/YLGAVC2RADGW5SM74AVCZMI6F5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YLGAVC2RADGW5SM74AVCZMI6F5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:YLGAVC2RADGW5SM74AVCZMI6F5","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":"692207050b7ccde05c95f0d9c4b9fccfb4032f281011fd14c9c8fd467135cff7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-02-13T13:57:40Z","title_canon_sha256":"7aaac74030460ddfda404f737608cd9b489eab48445b982613160deacf2bdc39"},"schema_version":"1.0","source":{"id":"0902.2315","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.2315","created_at":"2026-05-17T23:39:42Z"},{"alias_kind":"arxiv_version","alias_value":"0902.2315v1","created_at":"2026-05-17T23:39:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.2315","created_at":"2026-05-17T23:39:42Z"},{"alias_kind":"pith_short_12","alias_value":"YLGAVC2RADGW","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YLGAVC2RADGW5SM7","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YLGAVC2R","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:aa8f202aaa70cf7348047dae10000aaccde8943f3e02881fd646f1069de4f616","target":"graph","created_at":"2026-05-17T23:39:42Z","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":"We study the relation between the exponential growth rate of volume in a pinched negatively curved manifold and the critical exponent of its lattices. These objects have a long and interesting story and are closely related to the geometry and the dynamical properties of the geodesic flow of the manifold .","authors_text":"Andrea Sambusetti, Fran\\c{c}oise Dal'Bo (IRMAR), Jean-Claude Picaud (LMPT), Marc Peign\\'e (LMPT)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-02-13T13:57:40Z","title":"On the growth of nonuniform lattices in pinched negatively curved manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.2315","kind":"arxiv","version":1},"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":"sha256:3ffffc98005b2eef91f658a7bed40c4b9b876f8413a0dc1c4ce9cd20edbb1e93","target":"record","created_at":"2026-05-17T23:39:42Z","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":"692207050b7ccde05c95f0d9c4b9fccfb4032f281011fd14c9c8fd467135cff7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-02-13T13:57:40Z","title_canon_sha256":"7aaac74030460ddfda404f737608cd9b489eab48445b982613160deacf2bdc39"},"schema_version":"1.0","source":{"id":"0902.2315","kind":"arxiv","version":1}},"canonical_sha256":"c2cc0a8b5100cd6ec99fe02a2cb11e2f726938aea927ebb1a07020b54ab8fe85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2cc0a8b5100cd6ec99fe02a2cb11e2f726938aea927ebb1a07020b54ab8fe85","first_computed_at":"2026-05-17T23:39:42.646631Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:42.646631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TTPfYAOHrOjLQh2UrUXT4cziouHhOxoDYS6F70cnU89Gapo/wO/YfSPBYyFRSCkhBFjrMLM3RZy8JvXcHJUnDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:42.647333Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.2315","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ffffc98005b2eef91f658a7bed40c4b9b876f8413a0dc1c4ce9cd20edbb1e93","sha256:aa8f202aaa70cf7348047dae10000aaccde8943f3e02881fd646f1069de4f616"],"state_sha256":"be3d958c704b8f707ab7f3c9157fbf5b7583144700ce7888536bcfff393626d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"03tsrJ+tQmxuXuR2RA31r2KAM/4/niPZT9HJwNuhIXSuq4WQZ2t+gBEJKbVKpSi52E0j1uwoDpK1R5CP/zuODA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T16:10:03.860399Z","bundle_sha256":"55cb62056e3bb52569c592ba1f1b25bc0a6d3ce3aafafb9e0bdbde83c7e16140"}}