{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6NP3IQ7B5FS7G4SPLZH7YR3MP3","short_pith_number":"pith:6NP3IQ7B","canonical_record":{"source":{"id":"1310.4265","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-16T04:27:06Z","cross_cats_sorted":[],"title_canon_sha256":"2c3e0294b35678c89d4bade426b8b58880a31ba4cadd6330e4f7b6be60b49bf8","abstract_canon_sha256":"66d5a47d7cc7e72258997a99573977efe6e1ba75061fb138412023ad32e5c0be"},"schema_version":"1.0"},"canonical_sha256":"f35fb443e1e965f3724f5e4ffc476c7efe154ad1fe6d2edfc864d7f586a4b8fb","source":{"kind":"arxiv","id":"1310.4265","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4265","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4265v2","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4265","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"pith_short_12","alias_value":"6NP3IQ7B5FS7","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6NP3IQ7B5FS7G4SP","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6NP3IQ7B","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6NP3IQ7B5FS7G4SPLZH7YR3MP3","target":"record","payload":{"canonical_record":{"source":{"id":"1310.4265","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-16T04:27:06Z","cross_cats_sorted":[],"title_canon_sha256":"2c3e0294b35678c89d4bade426b8b58880a31ba4cadd6330e4f7b6be60b49bf8","abstract_canon_sha256":"66d5a47d7cc7e72258997a99573977efe6e1ba75061fb138412023ad32e5c0be"},"schema_version":"1.0"},"canonical_sha256":"f35fb443e1e965f3724f5e4ffc476c7efe154ad1fe6d2edfc864d7f586a4b8fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:46.800970Z","signature_b64":"7wXVxKGRlNGxsH+dvgj0T5kxTcYlRWgRXd8MD7Dso0f9kpFubCket5yZTUtQT7/UYKgy0hr7Oelwgd6nT6ogAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f35fb443e1e965f3724f5e4ffc476c7efe154ad1fe6d2edfc864d7f586a4b8fb","last_reissued_at":"2026-05-18T01:31:46.800579Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:46.800579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.4265","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:31:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hNnD1Oh1iMHoILUtQ/9kiVu8lT/0DtMUoQQ+YS1TexJnxo99GGBvi2C1rL9CbaXwxhhY9JTIPy2mEn3b785RBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:04:30.740833Z"},"content_sha256":"bf62c3714925a45431b637f862d2d78b8ae19de73d59fab194b46fde1603139c","schema_version":"1.0","event_id":"sha256:bf62c3714925a45431b637f862d2d78b8ae19de73d59fab194b46fde1603139c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6NP3IQ7B5FS7G4SPLZH7YR3MP3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A numerical lower bound for the spectral radius of random walks on surface groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Sebastien Gouezel (IRMAR)","submitted_at":"2013-10-16T04:27:06Z","abstract_excerpt":"Estimating numerically the spectral radius of a random walk on a nonamenable graph is complicated, since the cardinality of balls grows exponentially fast with the radius. We propose an algorithm to get a bound from below for this spectral radius in Cayley graphs with finitely many cone types (including for instance hyperbolic groups). In the genus $2$ surface group, it improves by an order of magnitude the previous best bound, due to Bartholdi."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4265","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:31:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yr3Dngidii4rPNmjnDoDNVti7nyt7k5uKjbulYEW/FU6mVvSUwoBYnJjlbhyrTs0mF/NfyfL/qkgSJzWPzSLCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:04:30.741174Z"},"content_sha256":"d07e6708ce289e4c3654c2c5b1e2564a30f66cd7ad7598afa4e1a68a4f6597cd","schema_version":"1.0","event_id":"sha256:d07e6708ce289e4c3654c2c5b1e2564a30f66cd7ad7598afa4e1a68a4f6597cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6NP3IQ7B5FS7G4SPLZH7YR3MP3/bundle.json","state_url":"https://pith.science/pith/6NP3IQ7B5FS7G4SPLZH7YR3MP3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6NP3IQ7B5FS7G4SPLZH7YR3MP3/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":"2026-06-23T15:04:30Z","links":{"resolver":"https://pith.science/pith/6NP3IQ7B5FS7G4SPLZH7YR3MP3","bundle":"https://pith.science/pith/6NP3IQ7B5FS7G4SPLZH7YR3MP3/bundle.json","state":"https://pith.science/pith/6NP3IQ7B5FS7G4SPLZH7YR3MP3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6NP3IQ7B5FS7G4SPLZH7YR3MP3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6NP3IQ7B5FS7G4SPLZH7YR3MP3","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":"66d5a47d7cc7e72258997a99573977efe6e1ba75061fb138412023ad32e5c0be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-16T04:27:06Z","title_canon_sha256":"2c3e0294b35678c89d4bade426b8b58880a31ba4cadd6330e4f7b6be60b49bf8"},"schema_version":"1.0","source":{"id":"1310.4265","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4265","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4265v2","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4265","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"pith_short_12","alias_value":"6NP3IQ7B5FS7","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6NP3IQ7B5FS7G4SP","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6NP3IQ7B","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:d07e6708ce289e4c3654c2c5b1e2564a30f66cd7ad7598afa4e1a68a4f6597cd","target":"graph","created_at":"2026-05-18T01:31:46Z","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":"Estimating numerically the spectral radius of a random walk on a nonamenable graph is complicated, since the cardinality of balls grows exponentially fast with the radius. We propose an algorithm to get a bound from below for this spectral radius in Cayley graphs with finitely many cone types (including for instance hyperbolic groups). In the genus $2$ surface group, it improves by an order of magnitude the previous best bound, due to Bartholdi.","authors_text":"Sebastien Gouezel (IRMAR)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-16T04:27:06Z","title":"A numerical lower bound for the spectral radius of random walks on surface groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4265","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:bf62c3714925a45431b637f862d2d78b8ae19de73d59fab194b46fde1603139c","target":"record","created_at":"2026-05-18T01:31:46Z","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":"66d5a47d7cc7e72258997a99573977efe6e1ba75061fb138412023ad32e5c0be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-16T04:27:06Z","title_canon_sha256":"2c3e0294b35678c89d4bade426b8b58880a31ba4cadd6330e4f7b6be60b49bf8"},"schema_version":"1.0","source":{"id":"1310.4265","kind":"arxiv","version":2}},"canonical_sha256":"f35fb443e1e965f3724f5e4ffc476c7efe154ad1fe6d2edfc864d7f586a4b8fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f35fb443e1e965f3724f5e4ffc476c7efe154ad1fe6d2edfc864d7f586a4b8fb","first_computed_at":"2026-05-18T01:31:46.800579Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:46.800579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7wXVxKGRlNGxsH+dvgj0T5kxTcYlRWgRXd8MD7Dso0f9kpFubCket5yZTUtQT7/UYKgy0hr7Oelwgd6nT6ogAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:46.800970Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.4265","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf62c3714925a45431b637f862d2d78b8ae19de73d59fab194b46fde1603139c","sha256:d07e6708ce289e4c3654c2c5b1e2564a30f66cd7ad7598afa4e1a68a4f6597cd"],"state_sha256":"0490443cd665fdf1dfb58494afa2a1ba87daf343acfc2669e3c5169bad360bf8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nEapIaVKWE3RU+E123mkgGMU2NoVryhSf+slvjaV/swePlX88+LJEI+tb/PGo0u6HFnrDmCI8t9+BdsRssDkDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:04:30.743138Z","bundle_sha256":"da01f73c4f18464addaa0f4b5e68523c3525feef27e9dc351ba03ebc1e05dcda"}}