{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GSGEZQC7M3WG3PAXSMFGSQFDLI","short_pith_number":"pith:GSGEZQC7","canonical_record":{"source":{"id":"1106.5736","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-06-28T17:35:09Z","cross_cats_sorted":["cs.CC","cs.CG","math.CO"],"title_canon_sha256":"39064a06c3c3d2851e6b115c39503c816112d66c821c9be68e367c89eb7d4111","abstract_canon_sha256":"71b4690d4d1dbf835d1efc443f9b27665e773098a6e6e31d1e0aa1d054a07836"},"schema_version":"1.0"},"canonical_sha256":"348c4cc05f66ec6dbc17930a6940a35a2d87590eea54d3cd72566e7273907004","source":{"kind":"arxiv","id":"1106.5736","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5736","created_at":"2026-05-18T04:19:12Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5736v1","created_at":"2026-05-18T04:19:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5736","created_at":"2026-05-18T04:19:12Z"},{"alias_kind":"pith_short_12","alias_value":"GSGEZQC7M3WG","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GSGEZQC7M3WG3PAX","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GSGEZQC7","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GSGEZQC7M3WG3PAXSMFGSQFDLI","target":"record","payload":{"canonical_record":{"source":{"id":"1106.5736","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-06-28T17:35:09Z","cross_cats_sorted":["cs.CC","cs.CG","math.CO"],"title_canon_sha256":"39064a06c3c3d2851e6b115c39503c816112d66c821c9be68e367c89eb7d4111","abstract_canon_sha256":"71b4690d4d1dbf835d1efc443f9b27665e773098a6e6e31d1e0aa1d054a07836"},"schema_version":"1.0"},"canonical_sha256":"348c4cc05f66ec6dbc17930a6940a35a2d87590eea54d3cd72566e7273907004","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:12.610663Z","signature_b64":"gI1XvySxovqFcccU5lvDwYsGAIe1jZki1gqw31K6IcCH6Q+hMwaMwi3oyP3qSfOY/8O/CS2lNHvHYvluU8I6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"348c4cc05f66ec6dbc17930a6940a35a2d87590eea54d3cd72566e7273907004","last_reissued_at":"2026-05-18T04:19:12.610231Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:12.610231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.5736","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":"2026-05-18T04:19:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WQQnaafwqAqL2yq9D9QXgbbJyEBO3agSFgVzAcNAaeNwhL9BQxsteFqyFs4ZUHFVVX/jP5Vb09ejLHEve3vJBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:28:29.762724Z"},"content_sha256":"a079491151438f5e746332cd847fa018522299322272273eacea3f2a138caaf8","schema_version":"1.0","event_id":"sha256:a079491151438f5e746332cd847fa018522299322272273eacea3f2a138caaf8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GSGEZQC7M3WG3PAXSMFGSQFDLI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algorithms for Solving Rubik's Cubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.CG","math.CO"],"primary_cat":"cs.DS","authors_text":"Andrew Winslow, Anna Lubiw, Erik D. Demaine, Martin L. Demaine, Sarah Eisenstat","submitted_at":"2011-06-28T17:35:09Z","abstract_excerpt":"The Rubik's Cube is perhaps the world's most famous and iconic puzzle, well-known to have a rich underlying mathematical structure (group theory). In this paper, we show that the Rubik's Cube also has a rich underlying algorithmic structure. Specifically, we show that the n x n x n Rubik's Cube, as well as the n x n x 1 variant, has a \"God's Number\" (diameter of the configuration space) of Theta(n^2/log n). The upper bound comes from effectively parallelizing standard Theta(n^2) solution algorithms, while the lower bound follows from a counting argument. The upper bound gives an asymptotically"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5736","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":"2026-05-18T04:19:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HCoOHXB0UsTRuyJvz8wRUTm6OwXB07ImJsdSUXVD7EbMV7jI16aNmm+XcG1aqcyvY+6MmMYNQh2ghEMzGWM9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:28:29.763224Z"},"content_sha256":"1249e2ce9040a6af2659b8342c8f765b0396681f73a483300eccc3d533a3a56a","schema_version":"1.0","event_id":"sha256:1249e2ce9040a6af2659b8342c8f765b0396681f73a483300eccc3d533a3a56a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GSGEZQC7M3WG3PAXSMFGSQFDLI/bundle.json","state_url":"https://pith.science/pith/GSGEZQC7M3WG3PAXSMFGSQFDLI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GSGEZQC7M3WG3PAXSMFGSQFDLI/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":"2026-05-31T14:28:29Z","links":{"resolver":"https://pith.science/pith/GSGEZQC7M3WG3PAXSMFGSQFDLI","bundle":"https://pith.science/pith/GSGEZQC7M3WG3PAXSMFGSQFDLI/bundle.json","state":"https://pith.science/pith/GSGEZQC7M3WG3PAXSMFGSQFDLI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GSGEZQC7M3WG3PAXSMFGSQFDLI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GSGEZQC7M3WG3PAXSMFGSQFDLI","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":"71b4690d4d1dbf835d1efc443f9b27665e773098a6e6e31d1e0aa1d054a07836","cross_cats_sorted":["cs.CC","cs.CG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-06-28T17:35:09Z","title_canon_sha256":"39064a06c3c3d2851e6b115c39503c816112d66c821c9be68e367c89eb7d4111"},"schema_version":"1.0","source":{"id":"1106.5736","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5736","created_at":"2026-05-18T04:19:12Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5736v1","created_at":"2026-05-18T04:19:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5736","created_at":"2026-05-18T04:19:12Z"},{"alias_kind":"pith_short_12","alias_value":"GSGEZQC7M3WG","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GSGEZQC7M3WG3PAX","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GSGEZQC7","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:1249e2ce9040a6af2659b8342c8f765b0396681f73a483300eccc3d533a3a56a","target":"graph","created_at":"2026-05-18T04:19:12Z","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 Rubik's Cube is perhaps the world's most famous and iconic puzzle, well-known to have a rich underlying mathematical structure (group theory). In this paper, we show that the Rubik's Cube also has a rich underlying algorithmic structure. Specifically, we show that the n x n x n Rubik's Cube, as well as the n x n x 1 variant, has a \"God's Number\" (diameter of the configuration space) of Theta(n^2/log n). The upper bound comes from effectively parallelizing standard Theta(n^2) solution algorithms, while the lower bound follows from a counting argument. The upper bound gives an asymptotically","authors_text":"Andrew Winslow, Anna Lubiw, Erik D. Demaine, Martin L. Demaine, Sarah Eisenstat","cross_cats":["cs.CC","cs.CG","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-06-28T17:35:09Z","title":"Algorithms for Solving Rubik's Cubes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5736","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:a079491151438f5e746332cd847fa018522299322272273eacea3f2a138caaf8","target":"record","created_at":"2026-05-18T04:19:12Z","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":"71b4690d4d1dbf835d1efc443f9b27665e773098a6e6e31d1e0aa1d054a07836","cross_cats_sorted":["cs.CC","cs.CG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-06-28T17:35:09Z","title_canon_sha256":"39064a06c3c3d2851e6b115c39503c816112d66c821c9be68e367c89eb7d4111"},"schema_version":"1.0","source":{"id":"1106.5736","kind":"arxiv","version":1}},"canonical_sha256":"348c4cc05f66ec6dbc17930a6940a35a2d87590eea54d3cd72566e7273907004","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"348c4cc05f66ec6dbc17930a6940a35a2d87590eea54d3cd72566e7273907004","first_computed_at":"2026-05-18T04:19:12.610231Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:12.610231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gI1XvySxovqFcccU5lvDwYsGAIe1jZki1gqw31K6IcCH6Q+hMwaMwi3oyP3qSfOY/8O/CS2lNHvHYvluU8I6BA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:12.610663Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.5736","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a079491151438f5e746332cd847fa018522299322272273eacea3f2a138caaf8","sha256:1249e2ce9040a6af2659b8342c8f765b0396681f73a483300eccc3d533a3a56a"],"state_sha256":"33a50e347f6f325b6f49e4c151b717785d4acf3ca5edb3342281922b386c3482"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DTgZoimcxoUS3F6+6fHa2CZWdMNfJVdhI68EGsYyXKnjV6qlcMH1rQp5O28vSWhdepY0kSSdfZlapdVHkKBSBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T14:28:29.765707Z","bundle_sha256":"b3884c927338ceb97e943bc8ebce22669a43620dfdeac1bbaa6962609614cec7"}}