{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7LSARATTIO54XDR7OQ72CCTWE2","short_pith_number":"pith:7LSARATT","canonical_record":{"source":{"id":"1105.1535","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-08T17:12:38Z","cross_cats_sorted":[],"title_canon_sha256":"d0491e8ab0cae64b3cc4e7688b6ae72a60f9ec24efb7fa777dd8be147b1eff34","abstract_canon_sha256":"dac12726e124235ba5c2aac530c297f83d5db74f23f3fe5d81f549f01e4d4435"},"schema_version":"1.0"},"canonical_sha256":"fae408827343bbcb8e3f743fa10a7626a4c81643b47c214c0c382454e97a5912","source":{"kind":"arxiv","id":"1105.1535","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1535","created_at":"2026-05-18T04:22:39Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1535v1","created_at":"2026-05-18T04:22:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1535","created_at":"2026-05-18T04:22:39Z"},{"alias_kind":"pith_short_12","alias_value":"7LSARATTIO54","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7LSARATTIO54XDR7","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7LSARATT","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7LSARATTIO54XDR7OQ72CCTWE2","target":"record","payload":{"canonical_record":{"source":{"id":"1105.1535","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-08T17:12:38Z","cross_cats_sorted":[],"title_canon_sha256":"d0491e8ab0cae64b3cc4e7688b6ae72a60f9ec24efb7fa777dd8be147b1eff34","abstract_canon_sha256":"dac12726e124235ba5c2aac530c297f83d5db74f23f3fe5d81f549f01e4d4435"},"schema_version":"1.0"},"canonical_sha256":"fae408827343bbcb8e3f743fa10a7626a4c81643b47c214c0c382454e97a5912","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:39.233391Z","signature_b64":"t/7fcMWxFtjJigwwtuJMtXbiVS72JzxEeeOi1CSn10a20OyH6MIzC6owTPlZFAANTb0moFnm6PMjCFr3sfXWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fae408827343bbcb8e3f743fa10a7626a4c81643b47c214c0c382454e97a5912","last_reissued_at":"2026-05-18T04:22:39.232956Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:39.232956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.1535","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":"2026-05-18T04:22:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mekPIqZCMx/jN8yZZkOXda8mg+C77aLSFYuGgKOSxUTTghm6PoOGQ9lGCletJLBE9s3uCYiomZQbOmrujFTVCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:49:45.276918Z"},"content_sha256":"e82b99249dcc3480c978fb425822b2f746f29a73709321abf26cbca58fbdb426","schema_version":"1.0","event_id":"sha256:e82b99249dcc3480c978fb425822b2f746f29a73709321abf26cbca58fbdb426"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7LSARATTIO54XDR7OQ72CCTWE2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hyperbolic hydra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Noel Brady, Tim Riley, Will Dison","submitted_at":"2011-05-08T17:12:38Z","abstract_excerpt":"We give examples of hyperbolic groups with finite-rank free subgroups of huge (Ackermannian) distortion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1535","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":"2026-05-18T04:22:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CfZsYYqTvCRaLBbFCit/nM8zMonvlF5nXnGfYMyR3/h6r+gyghk2CUa77we9oAoA+k8D5a3h+IbS4PrAlM0DAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:49:45.277281Z"},"content_sha256":"7cd083dfe83f8a8d42d78d4a011e67f5feea75b6fec8b67d7694c9798ee87b57","schema_version":"1.0","event_id":"sha256:7cd083dfe83f8a8d42d78d4a011e67f5feea75b6fec8b67d7694c9798ee87b57"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7LSARATTIO54XDR7OQ72CCTWE2/bundle.json","state_url":"https://pith.science/pith/7LSARATTIO54XDR7OQ72CCTWE2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7LSARATTIO54XDR7OQ72CCTWE2/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":"2026-06-22T13:49:45Z","links":{"resolver":"https://pith.science/pith/7LSARATTIO54XDR7OQ72CCTWE2","bundle":"https://pith.science/pith/7LSARATTIO54XDR7OQ72CCTWE2/bundle.json","state":"https://pith.science/pith/7LSARATTIO54XDR7OQ72CCTWE2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7LSARATTIO54XDR7OQ72CCTWE2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7LSARATTIO54XDR7OQ72CCTWE2","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":"dac12726e124235ba5c2aac530c297f83d5db74f23f3fe5d81f549f01e4d4435","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-08T17:12:38Z","title_canon_sha256":"d0491e8ab0cae64b3cc4e7688b6ae72a60f9ec24efb7fa777dd8be147b1eff34"},"schema_version":"1.0","source":{"id":"1105.1535","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1535","created_at":"2026-05-18T04:22:39Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1535v1","created_at":"2026-05-18T04:22:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1535","created_at":"2026-05-18T04:22:39Z"},{"alias_kind":"pith_short_12","alias_value":"7LSARATTIO54","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7LSARATTIO54XDR7","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7LSARATT","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:7cd083dfe83f8a8d42d78d4a011e67f5feea75b6fec8b67d7694c9798ee87b57","target":"graph","created_at":"2026-05-18T04:22:39Z","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 give examples of hyperbolic groups with finite-rank free subgroups of huge (Ackermannian) distortion.","authors_text":"Noel Brady, Tim Riley, Will Dison","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-08T17:12:38Z","title":"Hyperbolic hydra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1535","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:e82b99249dcc3480c978fb425822b2f746f29a73709321abf26cbca58fbdb426","target":"record","created_at":"2026-05-18T04:22:39Z","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":"dac12726e124235ba5c2aac530c297f83d5db74f23f3fe5d81f549f01e4d4435","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-08T17:12:38Z","title_canon_sha256":"d0491e8ab0cae64b3cc4e7688b6ae72a60f9ec24efb7fa777dd8be147b1eff34"},"schema_version":"1.0","source":{"id":"1105.1535","kind":"arxiv","version":1}},"canonical_sha256":"fae408827343bbcb8e3f743fa10a7626a4c81643b47c214c0c382454e97a5912","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fae408827343bbcb8e3f743fa10a7626a4c81643b47c214c0c382454e97a5912","first_computed_at":"2026-05-18T04:22:39.232956Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:39.232956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t/7fcMWxFtjJigwwtuJMtXbiVS72JzxEeeOi1CSn10a20OyH6MIzC6owTPlZFAANTb0moFnm6PMjCFr3sfXWBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:39.233391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.1535","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e82b99249dcc3480c978fb425822b2f746f29a73709321abf26cbca58fbdb426","sha256:7cd083dfe83f8a8d42d78d4a011e67f5feea75b6fec8b67d7694c9798ee87b57"],"state_sha256":"955639e32586b208037a1bbdccccfbd9d43d9995e06ad47149837d8871a9c1e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uYaMwnialZv0+gksYGMwEbtVMsJ88FqI7u2sYZVhpEedV5Y/T/QhHKwUYN9llHAMYJizOs5Zxd/SLcR/FTlQDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T13:49:45.279374Z","bundle_sha256":"9b0e0fc1fc08671ede4e11708d9bfedcd295b2d9e4114a22da252238cb286826"}}