{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:LEPN677IBLJWL75EJVY6HTFOWN","short_pith_number":"pith:LEPN677I","canonical_record":{"source":{"id":"1005.2347","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-05-13T15:33:42Z","cross_cats_sorted":["math.CO","math.OA"],"title_canon_sha256":"27427b688ab9e5fdd598f449e16550e95cb6b1afea74ab87f2caa31f38ad390c","abstract_canon_sha256":"2479fb4bcb4f6ec7f40149ac1e86acca9edfa5da5b774ee5cda05f3960069f8a"},"schema_version":"1.0"},"canonical_sha256":"591edf7fe80ad365ffa44d71e3ccaeb3672cb34683344ebf5b68162af2334d5f","source":{"kind":"arxiv","id":"1005.2347","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2347","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2347v2","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2347","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"LEPN677IBLJW","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LEPN677IBLJWL75E","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LEPN677I","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:LEPN677IBLJWL75EJVY6HTFOWN","target":"record","payload":{"canonical_record":{"source":{"id":"1005.2347","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-05-13T15:33:42Z","cross_cats_sorted":["math.CO","math.OA"],"title_canon_sha256":"27427b688ab9e5fdd598f449e16550e95cb6b1afea74ab87f2caa31f38ad390c","abstract_canon_sha256":"2479fb4bcb4f6ec7f40149ac1e86acca9edfa5da5b774ee5cda05f3960069f8a"},"schema_version":"1.0"},"canonical_sha256":"591edf7fe80ad365ffa44d71e3ccaeb3672cb34683344ebf5b68162af2334d5f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:21.794159Z","signature_b64":"aZgJwxcXHfuCyAN3r+15YjG5GMIoyC+jSW4n4Zpn8Fhpb5li3g6YklgxUSeED31mS+bVT+c8tYAIwwiLfwN8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"591edf7fe80ad365ffa44d71e3ccaeb3672cb34683344ebf5b68162af2334d5f","last_reissued_at":"2026-05-18T02:45:21.793674Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:21.793674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.2347","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":"2026-05-18T02:45:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OMWwvwpjI24wpHDUL7c8v3qkvd1XbEk0qlDcLdhJWAj9Ja+x1bVv6xkETsNR0pqk28ozNKmo4Yyov6kK7yDCCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:54:43.363827Z"},"content_sha256":"aa8fd40f5e2fb923d24a6011c0f6ecd66fe896de986c48e54153067bf889dcfb","schema_version":"1.0","event_id":"sha256:aa8fd40f5e2fb923d24a6011c0f6ecd66fe896de986c48e54153067bf889dcfb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:LEPN677IBLJWL75EJVY6HTFOWN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Free Lamplighter Groups and a Question of Atiyah","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.OA"],"primary_cat":"math.GR","authors_text":"Franz Lehner, Stephan Wagner","submitted_at":"2010-05-13T15:33:42Z","abstract_excerpt":"We compute the von Neumann dimensions of the kernels of adjacency operators on free lamplighter groups and show that they are irrational, thus providing an elementary constructive answer to a question of Atiyah."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2347","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":"2026-05-18T02:45:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RZOWckPlK0ahy42gedLdpsE+qsWWQxRyCDT+xM+270ABVSHm/aZ5YjVIIvHlDrwhx5EHtPvzXh9g6tSzK9MMAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:54:43.364184Z"},"content_sha256":"0cf3ddd5bb69bf96acdac3c51d2ca3a6bbdaf82277982cf67d34099483af3c79","schema_version":"1.0","event_id":"sha256:0cf3ddd5bb69bf96acdac3c51d2ca3a6bbdaf82277982cf67d34099483af3c79"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LEPN677IBLJWL75EJVY6HTFOWN/bundle.json","state_url":"https://pith.science/pith/LEPN677IBLJWL75EJVY6HTFOWN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LEPN677IBLJWL75EJVY6HTFOWN/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":"2026-05-28T01:54:43Z","links":{"resolver":"https://pith.science/pith/LEPN677IBLJWL75EJVY6HTFOWN","bundle":"https://pith.science/pith/LEPN677IBLJWL75EJVY6HTFOWN/bundle.json","state":"https://pith.science/pith/LEPN677IBLJWL75EJVY6HTFOWN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LEPN677IBLJWL75EJVY6HTFOWN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:LEPN677IBLJWL75EJVY6HTFOWN","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":"2479fb4bcb4f6ec7f40149ac1e86acca9edfa5da5b774ee5cda05f3960069f8a","cross_cats_sorted":["math.CO","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-05-13T15:33:42Z","title_canon_sha256":"27427b688ab9e5fdd598f449e16550e95cb6b1afea74ab87f2caa31f38ad390c"},"schema_version":"1.0","source":{"id":"1005.2347","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2347","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2347v2","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2347","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"LEPN677IBLJW","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LEPN677IBLJWL75E","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LEPN677I","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:0cf3ddd5bb69bf96acdac3c51d2ca3a6bbdaf82277982cf67d34099483af3c79","target":"graph","created_at":"2026-05-18T02:45:21Z","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 compute the von Neumann dimensions of the kernels of adjacency operators on free lamplighter groups and show that they are irrational, thus providing an elementary constructive answer to a question of Atiyah.","authors_text":"Franz Lehner, Stephan Wagner","cross_cats":["math.CO","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-05-13T15:33:42Z","title":"Free Lamplighter Groups and a Question of Atiyah"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2347","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:aa8fd40f5e2fb923d24a6011c0f6ecd66fe896de986c48e54153067bf889dcfb","target":"record","created_at":"2026-05-18T02:45:21Z","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":"2479fb4bcb4f6ec7f40149ac1e86acca9edfa5da5b774ee5cda05f3960069f8a","cross_cats_sorted":["math.CO","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-05-13T15:33:42Z","title_canon_sha256":"27427b688ab9e5fdd598f449e16550e95cb6b1afea74ab87f2caa31f38ad390c"},"schema_version":"1.0","source":{"id":"1005.2347","kind":"arxiv","version":2}},"canonical_sha256":"591edf7fe80ad365ffa44d71e3ccaeb3672cb34683344ebf5b68162af2334d5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"591edf7fe80ad365ffa44d71e3ccaeb3672cb34683344ebf5b68162af2334d5f","first_computed_at":"2026-05-18T02:45:21.793674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:21.793674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aZgJwxcXHfuCyAN3r+15YjG5GMIoyC+jSW4n4Zpn8Fhpb5li3g6YklgxUSeED31mS+bVT+c8tYAIwwiLfwN8AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:21.794159Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.2347","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa8fd40f5e2fb923d24a6011c0f6ecd66fe896de986c48e54153067bf889dcfb","sha256:0cf3ddd5bb69bf96acdac3c51d2ca3a6bbdaf82277982cf67d34099483af3c79"],"state_sha256":"771783bfebc36ecb6bda3f29b49eef1a989669215bcfab1a76221af21b652758"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N5szmH+zDj+hHAqKTigkssN/+0xGm1FsYBsei0TvXjmc6QODQdINieu2nMWMRGY0fUJimY3MA1TeM14J7bS/Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T01:54:43.366253Z","bundle_sha256":"5f52fc347abc9ae368be1af571939f8218230c925b9d99207786a163efc68816"}}