{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UEWRN6J4MWVZ552O2L36XEAIKY","short_pith_number":"pith:UEWRN6J4","canonical_record":{"source":{"id":"1209.3217","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-14T15:07:31Z","cross_cats_sorted":[],"title_canon_sha256":"b4a765b895ae3ab8c576e121d63860ca79efcaf2ceb40e382c5f6058457b03fc","abstract_canon_sha256":"214b8618538c402711c8c0978da32a6b13978ce1fe0c649704f0e22e76195203"},"schema_version":"1.0"},"canonical_sha256":"a12d16f93c65ab9ef74ed2f7eb9008563dba1c61bfba7f84e337ff47214ac4b2","source":{"kind":"arxiv","id":"1209.3217","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3217","created_at":"2026-05-18T03:45:32Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3217v1","created_at":"2026-05-18T03:45:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3217","created_at":"2026-05-18T03:45:32Z"},{"alias_kind":"pith_short_12","alias_value":"UEWRN6J4MWVZ","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UEWRN6J4MWVZ552O","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UEWRN6J4","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UEWRN6J4MWVZ552O2L36XEAIKY","target":"record","payload":{"canonical_record":{"source":{"id":"1209.3217","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-14T15:07:31Z","cross_cats_sorted":[],"title_canon_sha256":"b4a765b895ae3ab8c576e121d63860ca79efcaf2ceb40e382c5f6058457b03fc","abstract_canon_sha256":"214b8618538c402711c8c0978da32a6b13978ce1fe0c649704f0e22e76195203"},"schema_version":"1.0"},"canonical_sha256":"a12d16f93c65ab9ef74ed2f7eb9008563dba1c61bfba7f84e337ff47214ac4b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:32.480612Z","signature_b64":"05hsXJjeXYoNbT1BHd4Q5hgLDHSA2DswRmhkfk2JNaDOc6JlMYBg5wmmQrxn6jfafZOeasw89zDLHWdQPqYeAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a12d16f93c65ab9ef74ed2f7eb9008563dba1c61bfba7f84e337ff47214ac4b2","last_reissued_at":"2026-05-18T03:45:32.480122Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:32.480122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.3217","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":"2026-05-18T03:45:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4EmJDvnh8dt1Ls+rbMi8VQEy2xJWTx1n6W77WFXF9VEN09BHXqdvqG4czg0BGms3yvLoZw2WiE38vtgK9tv0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:01:22.687339Z"},"content_sha256":"32e538e1f294de41f87af1a377ed1411dd07b612173ec8a37377e869439dbcad","schema_version":"1.0","event_id":"sha256:32e538e1f294de41f87af1a377ed1411dd07b612173ec8a37377e869439dbcad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UEWRN6J4MWVZ552O2L36XEAIKY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local limit theorem for symmetric random walks in Gromov-hyperbolic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sebastien Gouezel (IRMAR)","submitted_at":"2012-09-14T15:07:31Z","abstract_excerpt":"Completing a strategy of Gou\\\"ezel and Lalley, we prove a local limit theorem for the random walk generated by any symmetric finitely supported probability measure on a non-elementary Gromov-hyperbolic group: denoting by $R$ the inverse of the spectral radius of the random walk, the probability to return to the identity at time $n$ behaves like $C R^{-n}n^{-3/2}$. An important step in the proof is to extend Ancona's results on the Martin boundary up to the spectral radius: we show that the Martin boundary for $R$-harmonic functions coincides with the geometric boundary of the group. In an appe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3217","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":"2026-05-18T03:45:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"daJN+qfFV6dagKzI3QtbGmDQpSEzjSsQcfgSTUmu1osTgt8yniheoXzobBUJgllXlWYY5r5Eo5BfYECrEgTwDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:01:22.687701Z"},"content_sha256":"093edb187403d8bd8f62baa7ac7dd314088e50fc322e67bb31dd9d9ebc795fd4","schema_version":"1.0","event_id":"sha256:093edb187403d8bd8f62baa7ac7dd314088e50fc322e67bb31dd9d9ebc795fd4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UEWRN6J4MWVZ552O2L36XEAIKY/bundle.json","state_url":"https://pith.science/pith/UEWRN6J4MWVZ552O2L36XEAIKY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UEWRN6J4MWVZ552O2L36XEAIKY/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":"2026-06-23T15:01:22Z","links":{"resolver":"https://pith.science/pith/UEWRN6J4MWVZ552O2L36XEAIKY","bundle":"https://pith.science/pith/UEWRN6J4MWVZ552O2L36XEAIKY/bundle.json","state":"https://pith.science/pith/UEWRN6J4MWVZ552O2L36XEAIKY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UEWRN6J4MWVZ552O2L36XEAIKY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UEWRN6J4MWVZ552O2L36XEAIKY","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":"214b8618538c402711c8c0978da32a6b13978ce1fe0c649704f0e22e76195203","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-14T15:07:31Z","title_canon_sha256":"b4a765b895ae3ab8c576e121d63860ca79efcaf2ceb40e382c5f6058457b03fc"},"schema_version":"1.0","source":{"id":"1209.3217","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3217","created_at":"2026-05-18T03:45:32Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3217v1","created_at":"2026-05-18T03:45:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3217","created_at":"2026-05-18T03:45:32Z"},{"alias_kind":"pith_short_12","alias_value":"UEWRN6J4MWVZ","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UEWRN6J4MWVZ552O","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UEWRN6J4","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:093edb187403d8bd8f62baa7ac7dd314088e50fc322e67bb31dd9d9ebc795fd4","target":"graph","created_at":"2026-05-18T03:45:32Z","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":"Completing a strategy of Gou\\\"ezel and Lalley, we prove a local limit theorem for the random walk generated by any symmetric finitely supported probability measure on a non-elementary Gromov-hyperbolic group: denoting by $R$ the inverse of the spectral radius of the random walk, the probability to return to the identity at time $n$ behaves like $C R^{-n}n^{-3/2}$. An important step in the proof is to extend Ancona's results on the Martin boundary up to the spectral radius: we show that the Martin boundary for $R$-harmonic functions coincides with the geometric boundary of the group. In an appe","authors_text":"Sebastien Gouezel (IRMAR)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-14T15:07:31Z","title":"Local limit theorem for symmetric random walks in Gromov-hyperbolic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3217","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":"sha256:32e538e1f294de41f87af1a377ed1411dd07b612173ec8a37377e869439dbcad","target":"record","created_at":"2026-05-18T03:45:32Z","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":"214b8618538c402711c8c0978da32a6b13978ce1fe0c649704f0e22e76195203","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-14T15:07:31Z","title_canon_sha256":"b4a765b895ae3ab8c576e121d63860ca79efcaf2ceb40e382c5f6058457b03fc"},"schema_version":"1.0","source":{"id":"1209.3217","kind":"arxiv","version":1}},"canonical_sha256":"a12d16f93c65ab9ef74ed2f7eb9008563dba1c61bfba7f84e337ff47214ac4b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a12d16f93c65ab9ef74ed2f7eb9008563dba1c61bfba7f84e337ff47214ac4b2","first_computed_at":"2026-05-18T03:45:32.480122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:32.480122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"05hsXJjeXYoNbT1BHd4Q5hgLDHSA2DswRmhkfk2JNaDOc6JlMYBg5wmmQrxn6jfafZOeasw89zDLHWdQPqYeAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:32.480612Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.3217","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32e538e1f294de41f87af1a377ed1411dd07b612173ec8a37377e869439dbcad","sha256:093edb187403d8bd8f62baa7ac7dd314088e50fc322e67bb31dd9d9ebc795fd4"],"state_sha256":"ef7ccc662db9aa95f3d5e62b43abf5a1c048abf704f663580d4767f78c0ae956"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TwBE9/6lGzjlNAhfRD4kzXF9uJyjtF2Q9ApVCal3VpmrxsV+ifXqI2GVHnxWO/A3z6H3cSFh1nh3mkW8nyKiBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:01:22.689734Z","bundle_sha256":"c7830ec3cec8b45e34c934da53f03be68bed3b9b032bd26835c496a82a457138"}}