{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1995:MXMCZ2QPWPB63ZVEGQIKJW26ZE","short_pith_number":"pith:MXMCZ2QP","canonical_record":{"source":{"id":"math/9504209","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"1995-04-07T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"a08eb6f25ff0e37e232be954ebf59914da09129ffdcfd1be4c4050360be5d13d","abstract_canon_sha256":"71449131a495341cf56f35ec44be375efcc56d4cefb8083c4f217d91bc05a63b"},"schema_version":"1.0"},"canonical_sha256":"65d82cea0fb3c3ede6a43410a4db5ec914925c37e61042b2f00d57a47ce87ddb","source":{"kind":"arxiv","id":"math/9504209","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9504209","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"arxiv_version","alias_value":"math/9504209v1","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9504209","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"pith_short_12","alias_value":"MXMCZ2QPWPB6","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"MXMCZ2QPWPB63ZVE","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"MXMCZ2QP","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1995:MXMCZ2QPWPB63ZVEGQIKJW26ZE","target":"record","payload":{"canonical_record":{"source":{"id":"math/9504209","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"1995-04-07T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"a08eb6f25ff0e37e232be954ebf59914da09129ffdcfd1be4c4050360be5d13d","abstract_canon_sha256":"71449131a495341cf56f35ec44be375efcc56d4cefb8083c4f217d91bc05a63b"},"schema_version":"1.0"},"canonical_sha256":"65d82cea0fb3c3ede6a43410a4db5ec914925c37e61042b2f00d57a47ce87ddb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:50.279552Z","signature_b64":"RW7Cg5uOvC9nlG2WSP17HfgvllLObwp/1fYPnUBN83JzxedFuEQ2XXX9nS5uaE0oOhAZPBpAZJJsvGe63CDsBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65d82cea0fb3c3ede6a43410a4db5ec914925c37e61042b2f00d57a47ce87ddb","last_reissued_at":"2026-05-18T01:05:50.278890Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:50.278890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9504209","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":"2026-05-18T01:05:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eYETl1QKeELSscIyrUtz5qYe9sjt6GXIZDLWh4tTAc8GvLfWUwpSTMkVHLn0jlPLgmaJmKXKtcCFzEW+bCcBDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:37:43.792613Z"},"content_sha256":"c57a3a793f15f315222042c5fadbd0fa8841656947927fa91333e35c955161e1","schema_version":"1.0","event_id":"sha256:c57a3a793f15f315222042c5fadbd0fa8841656947927fa91333e35c955161e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1995:MXMCZ2QPWPB63ZVEGQIKJW26ZE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Margulis constant for Kleinian groups, I curvature","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"F. W. Gehring, G. J. Martin","submitted_at":"1995-04-07T00:00:00Z","abstract_excerpt":"The Margulis constant for Kleinian groups is the smallest constant $c$ such that for each discrete group $G$ and each point $x$ in the upper half space ${\\bold H}^3$, the group generated by the elements in $G$ which move $x$ less than distance c is elementary. We take a first step towards determining this constant by proving that if $\\langle f,g \\rangle$ is nonelementary and discrete with $f$ parabolic or elliptic of order $n \\geq 3$, then every point $x$ in ${\\bold H}^3$ is moved at least distance $c$ by $f$ or $g$ where $c=.1829\\ldots$. This bound is sharp."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9504209","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":"2026-05-18T01:05:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qhRErOFrMLylXrtdZyu3+ar7vHkByluUgKH0IKmG0sWbY9IoOz9tL8IGY8xnY6/1rsUm1PkCG+oAKpYeIlYVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:37:43.792958Z"},"content_sha256":"4192cb4ab5ed576e0484d19ff1328593f6fb0c7ca1308f25a835e534a7ebc149","schema_version":"1.0","event_id":"sha256:4192cb4ab5ed576e0484d19ff1328593f6fb0c7ca1308f25a835e534a7ebc149"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MXMCZ2QPWPB63ZVEGQIKJW26ZE/bundle.json","state_url":"https://pith.science/pith/MXMCZ2QPWPB63ZVEGQIKJW26ZE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MXMCZ2QPWPB63ZVEGQIKJW26ZE/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":"2026-06-21T20:37:43Z","links":{"resolver":"https://pith.science/pith/MXMCZ2QPWPB63ZVEGQIKJW26ZE","bundle":"https://pith.science/pith/MXMCZ2QPWPB63ZVEGQIKJW26ZE/bundle.json","state":"https://pith.science/pith/MXMCZ2QPWPB63ZVEGQIKJW26ZE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MXMCZ2QPWPB63ZVEGQIKJW26ZE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:MXMCZ2QPWPB63ZVEGQIKJW26ZE","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":"71449131a495341cf56f35ec44be375efcc56d4cefb8083c4f217d91bc05a63b","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"1995-04-07T00:00:00Z","title_canon_sha256":"a08eb6f25ff0e37e232be954ebf59914da09129ffdcfd1be4c4050360be5d13d"},"schema_version":"1.0","source":{"id":"math/9504209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9504209","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"arxiv_version","alias_value":"math/9504209v1","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9504209","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"pith_short_12","alias_value":"MXMCZ2QPWPB6","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"MXMCZ2QPWPB63ZVE","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"MXMCZ2QP","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:4192cb4ab5ed576e0484d19ff1328593f6fb0c7ca1308f25a835e534a7ebc149","target":"graph","created_at":"2026-05-18T01:05:50Z","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 Margulis constant for Kleinian groups is the smallest constant $c$ such that for each discrete group $G$ and each point $x$ in the upper half space ${\\bold H}^3$, the group generated by the elements in $G$ which move $x$ less than distance c is elementary. We take a first step towards determining this constant by proving that if $\\langle f,g \\rangle$ is nonelementary and discrete with $f$ parabolic or elliptic of order $n \\geq 3$, then every point $x$ in ${\\bold H}^3$ is moved at least distance $c$ by $f$ or $g$ where $c=.1829\\ldots$. This bound is sharp.","authors_text":"F. W. Gehring, G. J. Martin","cross_cats":[],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"1995-04-07T00:00:00Z","title":"On the Margulis constant for Kleinian groups, I curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9504209","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:c57a3a793f15f315222042c5fadbd0fa8841656947927fa91333e35c955161e1","target":"record","created_at":"2026-05-18T01:05:50Z","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":"71449131a495341cf56f35ec44be375efcc56d4cefb8083c4f217d91bc05a63b","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"1995-04-07T00:00:00Z","title_canon_sha256":"a08eb6f25ff0e37e232be954ebf59914da09129ffdcfd1be4c4050360be5d13d"},"schema_version":"1.0","source":{"id":"math/9504209","kind":"arxiv","version":1}},"canonical_sha256":"65d82cea0fb3c3ede6a43410a4db5ec914925c37e61042b2f00d57a47ce87ddb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65d82cea0fb3c3ede6a43410a4db5ec914925c37e61042b2f00d57a47ce87ddb","first_computed_at":"2026-05-18T01:05:50.278890Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:50.278890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RW7Cg5uOvC9nlG2WSP17HfgvllLObwp/1fYPnUBN83JzxedFuEQ2XXX9nS5uaE0oOhAZPBpAZJJsvGe63CDsBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:50.279552Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9504209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c57a3a793f15f315222042c5fadbd0fa8841656947927fa91333e35c955161e1","sha256:4192cb4ab5ed576e0484d19ff1328593f6fb0c7ca1308f25a835e534a7ebc149"],"state_sha256":"426e34a1deeff922560a0fea0d077126594071937d74e9d2e966893645a97772"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xl9NgrWqwn8LFcfjlJK6eqB9OJvHDRg8kTEa2qQQXEp12wGlg/zz9Y3Y3FgZEcTsJYf3kGiUyRYs2Olz7alQDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T20:37:43.794910Z","bundle_sha256":"58269886b490709f8873239d4e610f6b78ab7b4ea2d3aae7b032df00fe563c21"}}