{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:63RZ6FLQXHDKUUF4F7ILZGP62H","short_pith_number":"pith:63RZ6FLQ","canonical_record":{"source":{"id":"0905.3290","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-05-20T12:20:48Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"081240732c9bcfd657b69a831e10c169735d6d4b0c22301ccac59fc983e4d7ad","abstract_canon_sha256":"9c7a24659ccac977cb7ba3e62ef8a3ae4ef882560277772ede8ec69531793dbd"},"schema_version":"1.0"},"canonical_sha256":"f6e39f1570b9c6aa50bc2fd0bc99fed1c1d244d456fe0b4e25ad3ec949235aaf","source":{"kind":"arxiv","id":"0905.3290","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.3290","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"0905.3290v1","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.3290","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"63RZ6FLQXHDK","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"63RZ6FLQXHDKUUF4","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"63RZ6FLQ","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:63RZ6FLQXHDKUUF4F7ILZGP62H","target":"record","payload":{"canonical_record":{"source":{"id":"0905.3290","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-05-20T12:20:48Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"081240732c9bcfd657b69a831e10c169735d6d4b0c22301ccac59fc983e4d7ad","abstract_canon_sha256":"9c7a24659ccac977cb7ba3e62ef8a3ae4ef882560277772ede8ec69531793dbd"},"schema_version":"1.0"},"canonical_sha256":"f6e39f1570b9c6aa50bc2fd0bc99fed1c1d244d456fe0b4e25ad3ec949235aaf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:51.256160Z","signature_b64":"679mnU1vSbPYsk8dnxEZhcD1A/UxHZtobSk41KnrwzetELxN+crItImXxG0zlRUdN4aLGivneIIyJGH9gyjwCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6e39f1570b9c6aa50bc2fd0bc99fed1c1d244d456fe0b4e25ad3ec949235aaf","last_reissued_at":"2026-05-18T02:41:51.255687Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:51.255687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0905.3290","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":"2026-05-18T02:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7r6IXOt6k2xR1yUg11bvrd/Z2mkuCiLA8cC2fiv622+mR5DrkdwUT45YKNN+OVQWA58ih0l9lwJX+JGB6bbvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T18:23:51.363975Z"},"content_sha256":"ae7d5cc74cd36735df87a825ca12e689b44ebdfc5c5005e3491c1c2bd4ada5e4","schema_version":"1.0","event_id":"sha256:ae7d5cc74cd36735df87a825ca12e689b44ebdfc5c5005e3491c1c2bd4ada5e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:63RZ6FLQXHDKUUF4F7ILZGP62H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"L'espace des sous-groupes ferm\\'es de RxZ","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Thomas Haettel","submitted_at":"2009-05-20T12:20:48Z","abstract_excerpt":"The space of closed subgroups of a locally compact topological group is endowed with a natural topology, called the Chabauty topology. We completely describe the space of closed sugroups of the group RxZ, which is not trivial : for example, its fundamental group is uncountable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3290","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":"2026-05-18T02:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M3x5hfVjLQsACZ834RkJjK6aCoAwfYfdFd1mTv9e74Nz1NLTmjXI53ManDvUaQlnR9HR33UWeSYYinaeNs32CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T18:23:51.364313Z"},"content_sha256":"418555d5afa3acae45f02f08becbe7ad122c00f4727660b9e376b09ff90c42e4","schema_version":"1.0","event_id":"sha256:418555d5afa3acae45f02f08becbe7ad122c00f4727660b9e376b09ff90c42e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/63RZ6FLQXHDKUUF4F7ILZGP62H/bundle.json","state_url":"https://pith.science/pith/63RZ6FLQXHDKUUF4F7ILZGP62H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/63RZ6FLQXHDKUUF4F7ILZGP62H/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":"2026-07-02T18:23:51Z","links":{"resolver":"https://pith.science/pith/63RZ6FLQXHDKUUF4F7ILZGP62H","bundle":"https://pith.science/pith/63RZ6FLQXHDKUUF4F7ILZGP62H/bundle.json","state":"https://pith.science/pith/63RZ6FLQXHDKUUF4F7ILZGP62H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/63RZ6FLQXHDKUUF4F7ILZGP62H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:63RZ6FLQXHDKUUF4F7ILZGP62H","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":"9c7a24659ccac977cb7ba3e62ef8a3ae4ef882560277772ede8ec69531793dbd","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-05-20T12:20:48Z","title_canon_sha256":"081240732c9bcfd657b69a831e10c169735d6d4b0c22301ccac59fc983e4d7ad"},"schema_version":"1.0","source":{"id":"0905.3290","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.3290","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"0905.3290v1","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.3290","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"63RZ6FLQXHDK","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"63RZ6FLQXHDKUUF4","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"63RZ6FLQ","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:418555d5afa3acae45f02f08becbe7ad122c00f4727660b9e376b09ff90c42e4","target":"graph","created_at":"2026-05-18T02:41:51Z","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":"The space of closed subgroups of a locally compact topological group is endowed with a natural topology, called the Chabauty topology. We completely describe the space of closed sugroups of the group RxZ, which is not trivial : for example, its fundamental group is uncountable.","authors_text":"Thomas Haettel","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-05-20T12:20:48Z","title":"L'espace des sous-groupes ferm\\'es de RxZ"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3290","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:ae7d5cc74cd36735df87a825ca12e689b44ebdfc5c5005e3491c1c2bd4ada5e4","target":"record","created_at":"2026-05-18T02:41:51Z","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":"9c7a24659ccac977cb7ba3e62ef8a3ae4ef882560277772ede8ec69531793dbd","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-05-20T12:20:48Z","title_canon_sha256":"081240732c9bcfd657b69a831e10c169735d6d4b0c22301ccac59fc983e4d7ad"},"schema_version":"1.0","source":{"id":"0905.3290","kind":"arxiv","version":1}},"canonical_sha256":"f6e39f1570b9c6aa50bc2fd0bc99fed1c1d244d456fe0b4e25ad3ec949235aaf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6e39f1570b9c6aa50bc2fd0bc99fed1c1d244d456fe0b4e25ad3ec949235aaf","first_computed_at":"2026-05-18T02:41:51.255687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:51.255687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"679mnU1vSbPYsk8dnxEZhcD1A/UxHZtobSk41KnrwzetELxN+crItImXxG0zlRUdN4aLGivneIIyJGH9gyjwCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:51.256160Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.3290","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae7d5cc74cd36735df87a825ca12e689b44ebdfc5c5005e3491c1c2bd4ada5e4","sha256:418555d5afa3acae45f02f08becbe7ad122c00f4727660b9e376b09ff90c42e4"],"state_sha256":"e9e284ddeb9d3466a01de4efd8b92edc9fd1a9208b2f84cc45609be6d79bcfdd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZQKPD7D8dz3LQozb281sZXYTuOj7PMuDDpfi0Lw9RTvTodtJF0rH90/9/SlFuKXmFh6eo0FNKb6BWWzebjYCDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T18:23:51.366295Z","bundle_sha256":"8408b52b7462e49771e52a3c5efd31ab7c87492ec12ffe6df5bc65b7c21d88f0"}}