{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:4VDZDM6Y4JXT37J6UO2DAKY3CW","short_pith_number":"pith:4VDZDM6Y","canonical_record":{"source":{"id":"math/0607184","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2006-07-07T09:34:15Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"044f22835994e7b3bf0a2f9624b45d04e0cf4abe3a3fcddf173d24381d4968c3","abstract_canon_sha256":"f9d4e89cf8df26f5d8c1b61f6a5f204bc10207f4eb5bd503fd38b4c1d82ab920"},"schema_version":"1.0"},"canonical_sha256":"e54791b3d8e26f3dfd3ea3b4302b1b15b1108b743e1ddb033414eeded217ef80","source":{"kind":"arxiv","id":"math/0607184","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0607184","created_at":"2026-05-18T04:21:51Z"},{"alias_kind":"arxiv_version","alias_value":"math/0607184v2","created_at":"2026-05-18T04:21:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0607184","created_at":"2026-05-18T04:21:51Z"},{"alias_kind":"pith_short_12","alias_value":"4VDZDM6Y4JXT","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"4VDZDM6Y4JXT37J6","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"4VDZDM6Y","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:4VDZDM6Y4JXT37J6UO2DAKY3CW","target":"record","payload":{"canonical_record":{"source":{"id":"math/0607184","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2006-07-07T09:34:15Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"044f22835994e7b3bf0a2f9624b45d04e0cf4abe3a3fcddf173d24381d4968c3","abstract_canon_sha256":"f9d4e89cf8df26f5d8c1b61f6a5f204bc10207f4eb5bd503fd38b4c1d82ab920"},"schema_version":"1.0"},"canonical_sha256":"e54791b3d8e26f3dfd3ea3b4302b1b15b1108b743e1ddb033414eeded217ef80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:51.897478Z","signature_b64":"ZopckbnrwtKZ1i7azIpGc+1TFyHwutkyjbwxxL2GngEqsn0xNpIH6vLpwm6kdYSa1ptBjlIWml0XyA+A6UNtAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e54791b3d8e26f3dfd3ea3b4302b1b15b1108b743e1ddb033414eeded217ef80","last_reissued_at":"2026-05-18T04:21:51.896783Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:51.896783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0607184","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":"2026-05-18T04:21:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dJRAIv4oXMHk9iiEGF52i8BiOu4l7MIQFOrp9IP1zr9fXrO1B6MLr4OrHT5yXq5f/4LcX2wdt+mmuLpstVvHCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:41:48.276785Z"},"content_sha256":"22db5d4705d68b0f454efb6be45de46b3fe237151a2fe1355bcdbd22ff06f5e5","schema_version":"1.0","event_id":"sha256:22db5d4705d68b0f454efb6be45de46b3fe237151a2fe1355bcdbd22ff06f5e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:4VDZDM6Y4JXT37J6UO2DAKY3CW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cryptanalysis of the Shpilrain-Ushakov Protocol in Thompson's Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.GR","authors_text":"Francesco Matucci","submitted_at":"2006-07-07T09:34:15Z","abstract_excerpt":"This paper shows that an eavesdropper can always recover efficiently the private key of one of the two parts of the public key cryptography protocol introduced by Shpilrain and Ushakov in [9]. Thus an eavesdropper can always recover the shared secret key, making the protocol insecure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607184","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":"2026-05-18T04:21:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5V5/jOVbaWJVnxBGfKxtcavQX7wnv8iw36iDdwBjz0bXD5Xasvm8HJepuA/eXOr0+NklgmWD2jk16TBi6ku5DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:41:48.277122Z"},"content_sha256":"40b3c7f8ed78ce086297846022a64acc68124d09d993c52b4ecab8a968dfba6b","schema_version":"1.0","event_id":"sha256:40b3c7f8ed78ce086297846022a64acc68124d09d993c52b4ecab8a968dfba6b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4VDZDM6Y4JXT37J6UO2DAKY3CW/bundle.json","state_url":"https://pith.science/pith/4VDZDM6Y4JXT37J6UO2DAKY3CW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4VDZDM6Y4JXT37J6UO2DAKY3CW/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":"2026-06-09T13:41:48Z","links":{"resolver":"https://pith.science/pith/4VDZDM6Y4JXT37J6UO2DAKY3CW","bundle":"https://pith.science/pith/4VDZDM6Y4JXT37J6UO2DAKY3CW/bundle.json","state":"https://pith.science/pith/4VDZDM6Y4JXT37J6UO2DAKY3CW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4VDZDM6Y4JXT37J6UO2DAKY3CW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:4VDZDM6Y4JXT37J6UO2DAKY3CW","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":"f9d4e89cf8df26f5d8c1b61f6a5f204bc10207f4eb5bd503fd38b4c1d82ab920","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2006-07-07T09:34:15Z","title_canon_sha256":"044f22835994e7b3bf0a2f9624b45d04e0cf4abe3a3fcddf173d24381d4968c3"},"schema_version":"1.0","source":{"id":"math/0607184","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0607184","created_at":"2026-05-18T04:21:51Z"},{"alias_kind":"arxiv_version","alias_value":"math/0607184v2","created_at":"2026-05-18T04:21:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0607184","created_at":"2026-05-18T04:21:51Z"},{"alias_kind":"pith_short_12","alias_value":"4VDZDM6Y4JXT","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"4VDZDM6Y4JXT37J6","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"4VDZDM6Y","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:40b3c7f8ed78ce086297846022a64acc68124d09d993c52b4ecab8a968dfba6b","target":"graph","created_at":"2026-05-18T04:21:51Z","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":"This paper shows that an eavesdropper can always recover efficiently the private key of one of the two parts of the public key cryptography protocol introduced by Shpilrain and Ushakov in [9]. Thus an eavesdropper can always recover the shared secret key, making the protocol insecure.","authors_text":"Francesco Matucci","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2006-07-07T09:34:15Z","title":"Cryptanalysis of the Shpilrain-Ushakov Protocol in Thompson's Group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607184","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":"sha256:22db5d4705d68b0f454efb6be45de46b3fe237151a2fe1355bcdbd22ff06f5e5","target":"record","created_at":"2026-05-18T04:21:51Z","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":"f9d4e89cf8df26f5d8c1b61f6a5f204bc10207f4eb5bd503fd38b4c1d82ab920","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2006-07-07T09:34:15Z","title_canon_sha256":"044f22835994e7b3bf0a2f9624b45d04e0cf4abe3a3fcddf173d24381d4968c3"},"schema_version":"1.0","source":{"id":"math/0607184","kind":"arxiv","version":2}},"canonical_sha256":"e54791b3d8e26f3dfd3ea3b4302b1b15b1108b743e1ddb033414eeded217ef80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e54791b3d8e26f3dfd3ea3b4302b1b15b1108b743e1ddb033414eeded217ef80","first_computed_at":"2026-05-18T04:21:51.896783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:51.896783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZopckbnrwtKZ1i7azIpGc+1TFyHwutkyjbwxxL2GngEqsn0xNpIH6vLpwm6kdYSa1ptBjlIWml0XyA+A6UNtAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:51.897478Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0607184","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22db5d4705d68b0f454efb6be45de46b3fe237151a2fe1355bcdbd22ff06f5e5","sha256:40b3c7f8ed78ce086297846022a64acc68124d09d993c52b4ecab8a968dfba6b"],"state_sha256":"0c5500d95a7909827a12da60433281b2a022aaa3969a7537aca0a3a7757ca66a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eAXy5mIRNlCqo4/jskodKp6zTVhhTH2DxdG0v96uTF4Lw08arVH6Nut7r1eckNqRMhd885DVTI1V8WImaocaDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T13:41:48.279220Z","bundle_sha256":"3d682487a6f8e4c07ef59e86ec9b2a8698f76f0a9c12951332dee2904430a8bf"}}