{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:K4SAVZ47T7MU2FGMVXXAXL4IMD","short_pith_number":"pith:K4SAVZ47","canonical_record":{"source":{"id":"1004.1083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-04-07T13:20:49Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"b1f5630f90c5a0d79bcf903aee96b94dea4c9e8d78e745955dda68a1afccdbaa","abstract_canon_sha256":"1f607e776cd73d2a0f09c22eedd9ec38430b01c74611202fa831fa6870385e31"},"schema_version":"1.0"},"canonical_sha256":"57240ae79f9fd94d14ccadee0baf8860cde1196440da61509eff8caf826a322f","source":{"kind":"arxiv","id":"1004.1083","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.1083","created_at":"2026-07-04T17:25:52Z"},{"alias_kind":"arxiv_version","alias_value":"1004.1083v1","created_at":"2026-07-04T17:25:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.1083","created_at":"2026-07-04T17:25:52Z"},{"alias_kind":"pith_short_12","alias_value":"K4SAVZ47T7MU","created_at":"2026-07-04T17:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"K4SAVZ47T7MU2FGM","created_at":"2026-07-04T17:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"K4SAVZ47","created_at":"2026-07-04T17:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:K4SAVZ47T7MU2FGMVXXAXL4IMD","target":"record","payload":{"canonical_record":{"source":{"id":"1004.1083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-04-07T13:20:49Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"b1f5630f90c5a0d79bcf903aee96b94dea4c9e8d78e745955dda68a1afccdbaa","abstract_canon_sha256":"1f607e776cd73d2a0f09c22eedd9ec38430b01c74611202fa831fa6870385e31"},"schema_version":"1.0"},"canonical_sha256":"57240ae79f9fd94d14ccadee0baf8860cde1196440da61509eff8caf826a322f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:25:52.022707Z","signature_b64":"Yy4YW2CCVgAAquGrfWL7aMChUwz5Yu/Sm2ytu+dVWZ+4nnGhmwtS/FKxcxmOhanki3C7sJ4CrNs5zfQiHtHZAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57240ae79f9fd94d14ccadee0baf8860cde1196440da61509eff8caf826a322f","last_reissued_at":"2026-07-04T17:25:52.022324Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:25:52.022324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.1083","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":"2026-07-04T17:25:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T5keXuND0GRCurDI/AmJMJkQPdppdEoX2MGmIqLYth+YygbNe+kHXun3dPkVlEAJJCucPlfaAc9LIPWLpiBUAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T08:38:07.405505Z"},"content_sha256":"58d055dfe38a13cff7cf31daad7b3fc019f60e97a01df9c8b74c1ccab6a5f616","schema_version":"1.0","event_id":"sha256:58d055dfe38a13cff7cf31daad7b3fc019f60e97a01df9c8b74c1ccab6a5f616"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:K4SAVZ47T7MU2FGMVXXAXL4IMD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The asymptotic growth of torsion homology for arithmetic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.NT","authors_text":"Akshay Venkatesh, Nicolas Bergeron","submitted_at":"2010-04-07T13:20:49Z","abstract_excerpt":"When does the amount of torsion in the homology of an arithmetic group grow exponentially with the covolume?  We give many examples where this is so, and conjecture precise conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1083","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1004.1083/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T17:25:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fe9MaXYAuS/W5djXzq3qzgBbCYcjqglo0u1Dphdv//2RxJ6Nn9uby30Elr03lekwv5UPGgiuk/EAa8FiaHpVDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T08:38:07.405981Z"},"content_sha256":"7fa93120d214139830c80ab6dbd9e2cb97caed3b1f582f77aebff4270dc60349","schema_version":"1.0","event_id":"sha256:7fa93120d214139830c80ab6dbd9e2cb97caed3b1f582f77aebff4270dc60349"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K4SAVZ47T7MU2FGMVXXAXL4IMD/bundle.json","state_url":"https://pith.science/pith/K4SAVZ47T7MU2FGMVXXAXL4IMD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K4SAVZ47T7MU2FGMVXXAXL4IMD/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":"2026-08-04T08:38:07Z","links":{"resolver":"https://pith.science/pith/K4SAVZ47T7MU2FGMVXXAXL4IMD","bundle":"https://pith.science/pith/K4SAVZ47T7MU2FGMVXXAXL4IMD/bundle.json","state":"https://pith.science/pith/K4SAVZ47T7MU2FGMVXXAXL4IMD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K4SAVZ47T7MU2FGMVXXAXL4IMD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:K4SAVZ47T7MU2FGMVXXAXL4IMD","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":"1f607e776cd73d2a0f09c22eedd9ec38430b01c74611202fa831fa6870385e31","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-04-07T13:20:49Z","title_canon_sha256":"b1f5630f90c5a0d79bcf903aee96b94dea4c9e8d78e745955dda68a1afccdbaa"},"schema_version":"1.0","source":{"id":"1004.1083","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.1083","created_at":"2026-07-04T17:25:52Z"},{"alias_kind":"arxiv_version","alias_value":"1004.1083v1","created_at":"2026-07-04T17:25:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.1083","created_at":"2026-07-04T17:25:52Z"},{"alias_kind":"pith_short_12","alias_value":"K4SAVZ47T7MU","created_at":"2026-07-04T17:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"K4SAVZ47T7MU2FGM","created_at":"2026-07-04T17:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"K4SAVZ47","created_at":"2026-07-04T17:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:7fa93120d214139830c80ab6dbd9e2cb97caed3b1f582f77aebff4270dc60349","target":"graph","created_at":"2026-07-04T17:25:52Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1004.1083/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"When does the amount of torsion in the homology of an arithmetic group grow exponentially with the covolume?  We give many examples where this is so, and conjecture precise conditions.","authors_text":"Akshay Venkatesh, Nicolas Bergeron","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-04-07T13:20:49Z","title":"The asymptotic growth of torsion homology for arithmetic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1083","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":"sha256:58d055dfe38a13cff7cf31daad7b3fc019f60e97a01df9c8b74c1ccab6a5f616","target":"record","created_at":"2026-07-04T17:25:52Z","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":"1f607e776cd73d2a0f09c22eedd9ec38430b01c74611202fa831fa6870385e31","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-04-07T13:20:49Z","title_canon_sha256":"b1f5630f90c5a0d79bcf903aee96b94dea4c9e8d78e745955dda68a1afccdbaa"},"schema_version":"1.0","source":{"id":"1004.1083","kind":"arxiv","version":1}},"canonical_sha256":"57240ae79f9fd94d14ccadee0baf8860cde1196440da61509eff8caf826a322f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57240ae79f9fd94d14ccadee0baf8860cde1196440da61509eff8caf826a322f","first_computed_at":"2026-07-04T17:25:52.022324Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:25:52.022324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yy4YW2CCVgAAquGrfWL7aMChUwz5Yu/Sm2ytu+dVWZ+4nnGhmwtS/FKxcxmOhanki3C7sJ4CrNs5zfQiHtHZAQ==","signature_status":"signed_v1","signed_at":"2026-07-04T17:25:52.022707Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.1083","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58d055dfe38a13cff7cf31daad7b3fc019f60e97a01df9c8b74c1ccab6a5f616","sha256:7fa93120d214139830c80ab6dbd9e2cb97caed3b1f582f77aebff4270dc60349"],"state_sha256":"9c835691dfff558a252c85c8cf2fd54f63dfacda10fbeaa8d39fdcbd74d0c9e6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8go9mtT17mswBhYXl7UeEDVQc4ARXjA7j81X8XDQtB4hVxXhagNv++gcUaB04dE2+oCHXkST9uFhPyaWP3BPDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T08:38:07.409612Z","bundle_sha256":"9cde1ed8c8f5ec87eb5a997708de3a32d8d99876112b01ebdb52a2868e21f9ab"}}