{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5CI4MAD5OEIZ4CZJOGJJXH2O5B","short_pith_number":"pith:5CI4MAD5","canonical_record":{"source":{"id":"1701.08480","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-30T04:33:42Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"db2cb149017653141236a2e3170d7ee45f03a57e720519d7410ce7d50cbae8cc","abstract_canon_sha256":"3e5f4559d611368334cfee265ab6d6fb1ac4661111a1db9765f37b5996376d6b"},"schema_version":"1.0"},"canonical_sha256":"e891c6007d71119e0b2971929b9f4ee86cecdd1b875ec77c75098c14a95392ec","source":{"kind":"arxiv","id":"1701.08480","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.08480","created_at":"2026-05-18T00:51:53Z"},{"alias_kind":"arxiv_version","alias_value":"1701.08480v1","created_at":"2026-05-18T00:51:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.08480","created_at":"2026-05-18T00:51:53Z"},{"alias_kind":"pith_short_12","alias_value":"5CI4MAD5OEIZ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5CI4MAD5OEIZ4CZJ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5CI4MAD5","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5CI4MAD5OEIZ4CZJOGJJXH2O5B","target":"record","payload":{"canonical_record":{"source":{"id":"1701.08480","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-30T04:33:42Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"db2cb149017653141236a2e3170d7ee45f03a57e720519d7410ce7d50cbae8cc","abstract_canon_sha256":"3e5f4559d611368334cfee265ab6d6fb1ac4661111a1db9765f37b5996376d6b"},"schema_version":"1.0"},"canonical_sha256":"e891c6007d71119e0b2971929b9f4ee86cecdd1b875ec77c75098c14a95392ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:53.979290Z","signature_b64":"zfTeUv9OgGDA3pmzwfRvHFLIMuH2z1E5OpjvBzrjq5l7nGvcCjOIHDnckAKZxcyHg6M9f7AuCaMstiXwbqyYAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e891c6007d71119e0b2971929b9f4ee86cecdd1b875ec77c75098c14a95392ec","last_reissued_at":"2026-05-18T00:51:53.978482Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:53.978482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.08480","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":"2026-05-18T00:51:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OhKRGfDfGJ1ba5tfwHHt+yFYsHkUubycWy/3tZoiyL9GyXzCYbypfR7sL1vlTcy1QXAHBSs0OcBd7G0OChIlBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:25:17.005971Z"},"content_sha256":"505df71b399c594fe2bd87218ffc769a9ed28042dea1086bf42af2f63c14f0a5","schema_version":"1.0","event_id":"sha256:505df71b399c594fe2bd87218ffc769a9ed28042dea1086bf42af2f63c14f0a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5CI4MAD5OEIZ4CZJOGJJXH2O5B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Combinatorial Problem from Group Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Eugene Curtin, Suho Oh","submitted_at":"2017-01-30T04:33:42Z","abstract_excerpt":"Keller proposed a combinatorial conjecture on construction of an n-by-infinite matrix, which comes from showing the existence of many orbits of different sizes in certain linear group actions. He proved it for the case n=4, and we show that conjecture is true in the general case. We also propose a combinatorial game version of the conjecture which even further generalizes the problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08480","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":"2026-05-18T00:51:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bkntt9zumQdCd6WDp4YzC/jl5b80svQB4mrA/7RGHLgKhc+AsjUsp60KSczMcwVZ2FT0R+86JVQZlZM4XstGCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:25:17.006338Z"},"content_sha256":"61373d4c9f032c9202a56549d3fa42495cdc4d32e4f63e3372768892083386c7","schema_version":"1.0","event_id":"sha256:61373d4c9f032c9202a56549d3fa42495cdc4d32e4f63e3372768892083386c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5CI4MAD5OEIZ4CZJOGJJXH2O5B/bundle.json","state_url":"https://pith.science/pith/5CI4MAD5OEIZ4CZJOGJJXH2O5B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5CI4MAD5OEIZ4CZJOGJJXH2O5B/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":"2026-05-26T13:25:17Z","links":{"resolver":"https://pith.science/pith/5CI4MAD5OEIZ4CZJOGJJXH2O5B","bundle":"https://pith.science/pith/5CI4MAD5OEIZ4CZJOGJJXH2O5B/bundle.json","state":"https://pith.science/pith/5CI4MAD5OEIZ4CZJOGJJXH2O5B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5CI4MAD5OEIZ4CZJOGJJXH2O5B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5CI4MAD5OEIZ4CZJOGJJXH2O5B","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":"3e5f4559d611368334cfee265ab6d6fb1ac4661111a1db9765f37b5996376d6b","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-30T04:33:42Z","title_canon_sha256":"db2cb149017653141236a2e3170d7ee45f03a57e720519d7410ce7d50cbae8cc"},"schema_version":"1.0","source":{"id":"1701.08480","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.08480","created_at":"2026-05-18T00:51:53Z"},{"alias_kind":"arxiv_version","alias_value":"1701.08480v1","created_at":"2026-05-18T00:51:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.08480","created_at":"2026-05-18T00:51:53Z"},{"alias_kind":"pith_short_12","alias_value":"5CI4MAD5OEIZ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5CI4MAD5OEIZ4CZJ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5CI4MAD5","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:61373d4c9f032c9202a56549d3fa42495cdc4d32e4f63e3372768892083386c7","target":"graph","created_at":"2026-05-18T00:51:53Z","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":"Keller proposed a combinatorial conjecture on construction of an n-by-infinite matrix, which comes from showing the existence of many orbits of different sizes in certain linear group actions. He proved it for the case n=4, and we show that conjecture is true in the general case. We also propose a combinatorial game version of the conjecture which even further generalizes the problem.","authors_text":"Eugene Curtin, Suho Oh","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-30T04:33:42Z","title":"A Combinatorial Problem from Group Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08480","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":"sha256:505df71b399c594fe2bd87218ffc769a9ed28042dea1086bf42af2f63c14f0a5","target":"record","created_at":"2026-05-18T00:51:53Z","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":"3e5f4559d611368334cfee265ab6d6fb1ac4661111a1db9765f37b5996376d6b","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-30T04:33:42Z","title_canon_sha256":"db2cb149017653141236a2e3170d7ee45f03a57e720519d7410ce7d50cbae8cc"},"schema_version":"1.0","source":{"id":"1701.08480","kind":"arxiv","version":1}},"canonical_sha256":"e891c6007d71119e0b2971929b9f4ee86cecdd1b875ec77c75098c14a95392ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e891c6007d71119e0b2971929b9f4ee86cecdd1b875ec77c75098c14a95392ec","first_computed_at":"2026-05-18T00:51:53.978482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:53.978482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zfTeUv9OgGDA3pmzwfRvHFLIMuH2z1E5OpjvBzrjq5l7nGvcCjOIHDnckAKZxcyHg6M9f7AuCaMstiXwbqyYAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:53.979290Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.08480","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:505df71b399c594fe2bd87218ffc769a9ed28042dea1086bf42af2f63c14f0a5","sha256:61373d4c9f032c9202a56549d3fa42495cdc4d32e4f63e3372768892083386c7"],"state_sha256":"afa08885268077dcdb9cc6acc91bb6aa0c6f996b1f3433ab64d5b1d9f432f57f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KDepcCcVkbZlpE4t5Z3z9gpdAmu0NXgUOFFkwOU5plfU68d5UtZ1lk7RvPCfhL3XSOUQiayJYo6QMkrw4HQMBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T13:25:17.008703Z","bundle_sha256":"2e67fb3fce9635a50acc21e2adf59f64072b7a81112d227ab581b3e20ed595ad"}}