{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VXVLO5DLU2LD7K3OJCICAZ6QCM","short_pith_number":"pith:VXVLO5DL","canonical_record":{"source":{"id":"1611.05632","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-11-17T10:52:12Z","cross_cats_sorted":[],"title_canon_sha256":"776d6ee15b6ff58ffed1768d09d17fa0c476653908d02e14e14587170526ded1","abstract_canon_sha256":"a73a1d5597a3ef43aa78fa267fcbd301b95d874c48088d2bc10d734c0d8e48c7"},"schema_version":"1.0"},"canonical_sha256":"adeab7746ba6963fab6e48902067d0132680bc6caf5fafff2effc046f3fddc04","source":{"kind":"arxiv","id":"1611.05632","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.05632","created_at":"2026-05-18T00:01:43Z"},{"alias_kind":"arxiv_version","alias_value":"1611.05632v1","created_at":"2026-05-18T00:01:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.05632","created_at":"2026-05-18T00:01:43Z"},{"alias_kind":"pith_short_12","alias_value":"VXVLO5DLU2LD","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VXVLO5DLU2LD7K3O","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VXVLO5DL","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VXVLO5DLU2LD7K3OJCICAZ6QCM","target":"record","payload":{"canonical_record":{"source":{"id":"1611.05632","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-11-17T10:52:12Z","cross_cats_sorted":[],"title_canon_sha256":"776d6ee15b6ff58ffed1768d09d17fa0c476653908d02e14e14587170526ded1","abstract_canon_sha256":"a73a1d5597a3ef43aa78fa267fcbd301b95d874c48088d2bc10d734c0d8e48c7"},"schema_version":"1.0"},"canonical_sha256":"adeab7746ba6963fab6e48902067d0132680bc6caf5fafff2effc046f3fddc04","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:43.975985Z","signature_b64":"oH+rXuUwEc+7/j2U/VAjw8nYzISQv81w/k0pg08uepE9KvNIYIJXUFlcSa4If9r00e0ZOwjDIDM9g/+lJiZsAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adeab7746ba6963fab6e48902067d0132680bc6caf5fafff2effc046f3fddc04","last_reissued_at":"2026-05-18T00:01:43.975267Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:43.975267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.05632","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":"2026-05-18T00:01:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z20i1bJJLgUA9Vf8hAewLNhXLUSmx1clwgy5//KWymoLD9JB2zmJ68sTttNDwKgvozWa/G2vpHnaPPmaiMn7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:35:49.537227Z"},"content_sha256":"c7f319d1bd5ba2665ef19b196a0dd958f914c42b35e51e3ab5627084863d4d67","schema_version":"1.0","event_id":"sha256:c7f319d1bd5ba2665ef19b196a0dd958f914c42b35e51e3ab5627084863d4d67"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VXVLO5DLU2LD7K3OJCICAZ6QCM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solving xz=yy in certain subsets of finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Tom Sanders","submitted_at":"2016-11-17T10:52:12Z","abstract_excerpt":"We show that if G is a finite group and A is a subset of G with no non-trivial solutions to xz=yy then |A| < |G|/(log log |G|)^c."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05632","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":"2026-05-18T00:01:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G6zvxJEqqCX99JeWa4+19Q+QY6yiXCU2XMphzdZ+HBCGGdmJPwUYeLUr/8kGx/M6R3SGcv+4uqNIYqLkDJmADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:35:49.537579Z"},"content_sha256":"e43da32eb65e4f769c5eda644e0e3c07c3794bb75a63d13888b49bd77fe7215e","schema_version":"1.0","event_id":"sha256:e43da32eb65e4f769c5eda644e0e3c07c3794bb75a63d13888b49bd77fe7215e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VXVLO5DLU2LD7K3OJCICAZ6QCM/bundle.json","state_url":"https://pith.science/pith/VXVLO5DLU2LD7K3OJCICAZ6QCM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VXVLO5DLU2LD7K3OJCICAZ6QCM/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":"2026-05-30T23:35:49Z","links":{"resolver":"https://pith.science/pith/VXVLO5DLU2LD7K3OJCICAZ6QCM","bundle":"https://pith.science/pith/VXVLO5DLU2LD7K3OJCICAZ6QCM/bundle.json","state":"https://pith.science/pith/VXVLO5DLU2LD7K3OJCICAZ6QCM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VXVLO5DLU2LD7K3OJCICAZ6QCM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VXVLO5DLU2LD7K3OJCICAZ6QCM","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":"a73a1d5597a3ef43aa78fa267fcbd301b95d874c48088d2bc10d734c0d8e48c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-11-17T10:52:12Z","title_canon_sha256":"776d6ee15b6ff58ffed1768d09d17fa0c476653908d02e14e14587170526ded1"},"schema_version":"1.0","source":{"id":"1611.05632","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.05632","created_at":"2026-05-18T00:01:43Z"},{"alias_kind":"arxiv_version","alias_value":"1611.05632v1","created_at":"2026-05-18T00:01:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.05632","created_at":"2026-05-18T00:01:43Z"},{"alias_kind":"pith_short_12","alias_value":"VXVLO5DLU2LD","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VXVLO5DLU2LD7K3O","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VXVLO5DL","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:e43da32eb65e4f769c5eda644e0e3c07c3794bb75a63d13888b49bd77fe7215e","target":"graph","created_at":"2026-05-18T00:01:43Z","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 show that if G is a finite group and A is a subset of G with no non-trivial solutions to xz=yy then |A| < |G|/(log log |G|)^c.","authors_text":"Tom Sanders","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-11-17T10:52:12Z","title":"Solving xz=yy in certain subsets of finite groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05632","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:c7f319d1bd5ba2665ef19b196a0dd958f914c42b35e51e3ab5627084863d4d67","target":"record","created_at":"2026-05-18T00:01:43Z","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":"a73a1d5597a3ef43aa78fa267fcbd301b95d874c48088d2bc10d734c0d8e48c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-11-17T10:52:12Z","title_canon_sha256":"776d6ee15b6ff58ffed1768d09d17fa0c476653908d02e14e14587170526ded1"},"schema_version":"1.0","source":{"id":"1611.05632","kind":"arxiv","version":1}},"canonical_sha256":"adeab7746ba6963fab6e48902067d0132680bc6caf5fafff2effc046f3fddc04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adeab7746ba6963fab6e48902067d0132680bc6caf5fafff2effc046f3fddc04","first_computed_at":"2026-05-18T00:01:43.975267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:43.975267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oH+rXuUwEc+7/j2U/VAjw8nYzISQv81w/k0pg08uepE9KvNIYIJXUFlcSa4If9r00e0ZOwjDIDM9g/+lJiZsAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:43.975985Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.05632","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7f319d1bd5ba2665ef19b196a0dd958f914c42b35e51e3ab5627084863d4d67","sha256:e43da32eb65e4f769c5eda644e0e3c07c3794bb75a63d13888b49bd77fe7215e"],"state_sha256":"08daed6729bf8477ff80d589219af43389eff6c5ca77cd7b04f8706bf46db0cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JGLgXiuogSdYJZ72TrvxnhUI3r4OiY93Ti+gajPyMya66nghuhZmW++1zRPZMqAfuPLuNnQEr39LVxwfe5rWDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:35:49.539405Z","bundle_sha256":"e665c634bbde431782f53e7ed1425cf55655aa24c6828d3d3d63afa3037814d5"}}